A nonlinear data classification method and system based on deep transfer learning visual recognition capability

Abstract

This invention belongs to the field of nonlinear data classification technology and discloses a nonlinear data classification method based on deep transfer learning and visual recognition capabilities. This invention transforms high-dimensional numerical features into structured images, enabling convolutional neural networks to leverage their powerful visual recognition capabilities to handle tabular data classification tasks. This image-based representation naturally reveals the implicit nonlinear relationships within the data. By further integrating deep transfer learning, this method effectively alleviates the data sparsity problem in small-sample scenarios and improves generalization performance through a series of training optimization strategies. The framework proposed in this invention achieves an effective connection between the numerical feature space and the image-based deep learning architecture, providing theoretical innovation and practical value for complex nonlinear data classification tasks.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear data classification technology, and in particular relates to a nonlinear data classification method and system based on deep transfer learning visual recognition capabilities. Background Technology

[0002] In an era of deep integration of big data and artificial intelligence, non-linear tabular data, characterized by complex feature associations, mixed data types, and non-stationary distributions, is widely found in key fields such as financial risk control, medical diagnosis, cybersecurity testing, and industrial quality inspection. Traditional machine learning methods, such as logistic regression and support vector machines, often struggle to capture the inherent patterns of this complex data, ultimately leading to poor classification performance. The core reasons for this limitation are twofold: first, these methods cannot effectively model high-dimensional, non-linear feature interactions; second, their performance is highly dependent on manual feature engineering, making them ill-suited to the dynamic characteristics of modern tabular data.

[0003] To address the numerous challenges of tabular data modeling, researchers have developed a series of advanced machine learning and deep learning algorithms, each possessing unique advantages in capturing complex data patterns. Gradient Boosting Decision Tree (GBDT) algorithms, represented by XGBoost, LightGBM, and CatBoost, have become the de facto standard in tabular data analysis due to their superior performance in sequentially constructing weak learners to correct prediction errors. Specifically, XGBoost achieves high accuracy and strong robustness by performing a second-order Taylor expansion of the loss function and introducing L2 regularization; LightGBM achieves ultra-fast training speed by employing a histogram-based sampling strategy and gradient-based one-sided sampling technology; and CatBoost effectively alleviates overfitting by performing specific optimizations for categorical features through ordered boosting and adaptive feature combination strategies. These GBDT variants have demonstrated outstanding performance in numerous practical applications, including insurance claims modeling, mine water source classification, and harmful algal bloom prediction.

[0004] In the field of deep learning-based tabular data analysis, TabNet, by combining the interpretability of decision trees with the powerful representation learning capabilities of neural networks, has become a highly representative network architecture in this field. The core innovation of this architecture lies in its sequential attention mechanism and sparse feature selection module, which enables the model to focus on a task-relevant subset of features at each decision step, achieving native feature importance interpretability while maintaining high prediction efficiency. Furthermore, the contrastive learning paradigm, represented by SimCLR, has also been extended to tabular data analysis. This paradigm learns semantically rich feature representations from unlabeled data by distinguishing between similar and dissimilar sample pairs, thus significantly reducing the model's dependence on large-scale labeled data. Combining SimCLR pre-training with simple linear classifiers such as logistic regression has become an effective solution for learning small-sample tabular data. Multilayer perceptrons (MLPs), as fundamental feedforward neural networks, also play a crucial role in tabular data modeling due to their general function approximation capabilities, and are also a core foundational module for building more complex deep learning architectures.

[0005] Convolutional Neural Networks (CNNs) are the cornerstone of modern visual pattern recognition technology. They revolutionize feature extraction paradigms by learning hierarchical spatial features through convolutional layers, pooling operations, and weight-sharing mechanisms. The successful applications of CNNs cover numerous network architectures, including fundamental models like LeNet-5 and its improved variants, as well as advanced models like DeepLab that use dilated convolutions to expand the receptive field. These technological advancements fully demonstrate that CNNs possess unparalleled capabilities to capture complex spatial and structural patterns from visual data without requiring manual feature engineering. Despite the milestone achievements of CNNs in computer vision, their potential in tabular data analysis remains far from being fully explored. The core reason is that tabular data lacks the native spatial structure that CNNs are naturally suited for.

[0006] Beyond traditional image and tabular data domains, neural network architectures have been successfully adapted to various pattern recognition tasks across multiple disciplines. In facial recognition, deep neural networks can achieve high-precision identity authentication through CNN-based methods and emerging Vision Transformers, and can also model complex input-output relationships using models such as probabilistic decision-based neural networks (PDBNN). In the medical field, deep learning technology is widely used for lesion segmentation, disease diagnosis, and prognosis prediction, with applications including diagnosis of hyperinsulinemia, prognostic assessment of Parkinson's disease, and screening for COVID-19 cases. Furthermore, neural networks have also demonstrated excellent performance in specialized applications such as handwritten digit recognition, sensor-based human behavior recognition, natural scene text detection, and traffic accident severity prediction.

[0007] Despite significant progress in related research, the practical deployment of neural networks still faces numerous challenges: the tree-based GBDT algorithm has limitations in modeling ultra-high-dimensional, abstract feature interactions; TabNet requires meticulous hyperparameter tuning to balance model complexity and interpretability, and its performance significantly degrades in small-sample scenarios; contrastive learning for tabular data lacks data augmentation strategies naturally adapted to the visual data domain, and its performance highly depends on the design of specific feature perturbation methods; furthermore, when tabular labeled data is scarce and labeling costs are high, all of the above methods suffer from insufficient generalization performance. Moreover, most current cutting-edge tabular data models cannot provide intuitive interpretability for feature interaction patterns, severely restricting their application in high-risk fields such as medical diagnosis and cybersecurity, where decision-making transparency is paramount. Meanwhile, neural networks are vulnerable to adversarial attacks and typically consume substantial computational resources; early models also suffer from hardware constraints and slow convergence speeds. To address these limitations, researchers have developed several optimization strategies, including transfer learning for small-data scenarios, automated neural network architecture search, and robust training techniques.

[0008] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0009] (1) The tree-based GBDT algorithm has limitations in its ability to model interactions of ultra-high-dimensional and abstract features; TabNet requires fine hyperparameter tuning to balance model complexity and interpretability, and its performance will significantly degrade in small sample scenarios; comparative learning for tabular data lacks data augmentation strategies that are naturally adapted to the visual data domain, and its performance is highly dependent on the design of specific feature perturbation methods.

[0010] (2) When tabular labeled data is scarce and labeling costs are high, all of the above methods suffer from insufficient generalization performance. Moreover, most current cutting-edge tabular data models cannot provide intuitive interpretability for feature interaction patterns, which severely restricts their application in high-risk fields such as medical diagnosis and cybersecurity, where decision-making transparency is highly demanding.

[0011] (3) Neural networks are vulnerable to adversarial attacks and usually require a lot of computing resources. Early models also had problems such as hardware constraints and slow convergence speed. Summary of the Invention

[0012] To address the problems existing in the prior art, this invention provides a nonlinear data classification method based on deep transfer learning visual recognition capabilities.

[0013] This invention is implemented as follows: a nonlinear data classification method based on deep transfer learning visual recognition capabilities includes:

[0014] Step 1: A nonlinear data visualization mechanism that transforms numerical features into spatial structure images;

[0015] Step 2: Adapt the capabilities of the pre-trained convolutional neural network to the progressive transfer learning architecture for the target task.

[0016] Furthermore, the nonlinear data visualization mechanism:

[0017] (1) Core Mechanism

[0018] The process of image transformation is formally defined as a transformation from numerical data space to image space, which comprises three basic components:

[0019] Feature permutation: For an n-dimensional feature vector Rearrangement function σ: →𝓚(wherein) Generate rearranged feature vectors for the feature index set: ; Select a set of p representative rearrangements using a fixed random seed s { , ,…, This is to ensure the reproducibility of the rearrangement process and experimental results;

[0020] Color encoding: Color mapping function Assign a unique RGB color C(k) to each feature = ( , , ),in , , ∈ [0,1]; and the difference between any two distinct feature colors Distance satisfies:

[0021]

[0022] This ensures that the convolutional neural network (CNN) can effectively distinguish different feature regions in the image;

[0023] Spatial mapping: rearranging the feature vectors The image is mapped to a standard H × W × 3 bar chart (H = 224, W = 224), where the horizontal axis represents the rearranged feature index and the vertical axis represents the normalized feature value. The calculation formula is as follows:

[0024]

[0025] This normalization method can match the input requirements of pre-trained CNN models;

[0026] (2) Image generation algorithm;

[0027] (3) Test data processing.

[0028] Furthermore, the image generation algorithm:

[0029] The preprocessing workflow aims to preserve the core information of nonlinear data features while constructing a spatial topology. It includes four consecutive and interconnected steps, fully aligned with the core logic of Algorithm 1. Label separation: As a fundamental step, the classification labels are... From the original feature vector The system separates the training samples into independent label files (L) to avoid label interference during subsequent image processing and ensures complete traceability of each training sample and its corresponding image. Feature sorting employs a fixed-seed permutation mechanism to generate p rearranged feature sequences for each sample, expanding the diversity of the original data without losing intrinsic feature correlations and laying the foundation for multi-view image representation. Visual encoding converts each sorted feature vector into a bar chart image with feature color encoding. The horizontal axis represents the permuted feature index, and the vertical axis represents the normalized feature value, enabling convolutional neural networks (CNNs) to capture individual feature values ​​and patterns of association between features through the spatial structure of the image. A standardized three-level folder structure (root directory → sample index → ​​permutation method) stores all generated images, facilitating batch loading and efficient management of image data within the deep learning framework while ensuring perfect compatibility with subsequent model training processes.

[0030] Furthermore, the test data processing:

[0031] The color encoding function C(·) used in the training phase is completely reused in the feature encoding of the test data, ensuring that the RGB color mapped to the same feature in the image in the test set is completely consistent with that in the training set; the training phase uses p feature permutation methods determined by a fixed random seed s. , ,…, All features are reused to generate multi-view feature sequences for test samples, ensuring the consistency of feature sorting rules; the standardized three-level hierarchical folder structure used for training data is also applied to test image storage, ensuring that the input data format of the trained model remains consistent during the testing phase; the test dataset... The feature dimensions are strictly consistent with the training dataset to ensure that the generated training image dataset and the test image dataset have no structural differences.

[0032] Furthermore, the progressive transfer learning architecture:

[0033] (1) Deep transfer learning architecture

[0034] The architecture uses a pre-trained ResNet18 model as the backbone feature extractor and integrates two core strategies: progressive unfreezing and hierarchical learning rate. It balances the preservation of general features of the pre-trained model with the adaptive learning of features specific to the target task. The core of the architecture is the progressive unfreezing training algorithm.

[0035] Data separation strategy based on personnel ID: As a fundamental innovation, this strategy strictly separates the training set and the validation set based on personnel ID to ensure no data leakage during the training and evaluation phases; this method avoids the model memorizing individual-specific patterns and forces the model to learn fraud detection features with generalizability;

[0036] Adaptive parameter control strategy: As a core optimization innovation, this strategy includes two interrelated sub-strategies; Hierarchical learning rate strategy: Assigning a lower learning rate to the pre-trained backbone network. To retain its learned general image feature extraction capabilities; a higher learning rate is assigned to the newly designed balanced classification head. To accelerate its adaptive learning for fraud detection tasks; the mathematical expression of this strategy is:

[0037]

[0038] A gradual defrosting strategy with parameter control:

[0039] Initially, all parameters of the backbone network are frozen. First, the classification head is unfrozen, and then deeper layers (Layer 4 → Layer 3) are gradually unfrozen based on the total number of target parameters (approximately 2.5 million trainable parameters). Specifically, this is first achieved by using numeric... ) Calculate the balanced classification head ( The number of parameters (the number of elements in the classification head parameter tensor) is defined as follows: the remaining trainable parameters of the backbone network to be unfrozen are defined as... (in = 2.5× (For the target, there are always trainable parameters); first iterate through the Layer4 parameters (each time from...) (Subtract the number of elements that have been unfrozen) If If the value is still positive, continue unfreezing the Layer3 parameters until... ≤0; This strategy controls model complexity and prevents overfitting, and its mathematical expression is:

[0040] ,

[0041]

[0042] in This represents the thawing ratio of the parameters in the i-th layer;

[0043] (2) Parameter-controllable progressive thawing training algorithm

[0044] The core training algorithm of this architecture implements an adaptive transfer learning strategy with precise parameter control, systematically balancing pre-training feature preservation, adaptive learning of target task features, and model complexity control.

[0045] (3) Training optimization strategy.

[0046] Furthermore, the training optimization strategy is as follows:

[0047] 1) Data Augmentation

[0048] During model training, online data augmentation is applied to the training image data in real time, effectively expanding the distribution range of the training data, reducing the model's sensitivity to minor changes in image spatial structure and color features, and significantly improving the model's robustness. The core augmentation transformations during the training phase include: geometric transformation: random cropping to... Pixels, random horizontal flip with a probability of 0.3 Random rotations within the range enhance the model's spatial invariance to image features; color jitter: brightness and contrast adjustment factors are both set to 0.2; only size adjustment (224×224) and normalization are performed on the validation and test sets; all images are normalized using the mean [0.485, 0.456, 0.406] and standard deviation [0.229, 0.224, 0.225] of the ImageNet dataset.

[0049] 2) Category balancing

[0050] Introducing a class-weighted cross-entropy loss function effectively addresses the potential class imbalance problem in the training dataset (where some classes have significantly fewer labeled samples than others, potentially leading to model bias towards the majority class). For each class c (0 ≤ c ≤ 1, with a sample size of...),... ), category weights are calculated as

[0051] (Where N is the total number of training samples); the weighted cross-entropy loss is defined as... Where B is the batch size. For real labels, This is the predicted probability corresponding to the true class; this method allows minority class samples to contribute more to the loss, effectively avoiding the model from having a classification bias towards the majority class.

[0052] 3) Learning rate scheduling

[0053] A cosine annealing learning rate scheduling strategy is adopted to dynamically optimize the learning rate during training, avoiding the model from getting trapped in local optima and ensuring efficient convergence. The cosine annealing strategy dynamically reduces the learning rate with each training iteration, allowing the model to fully explore the parameter space in the early stages of training and then fine-tune the parameters to approach the global optimum in the later stages. Its update formula is as follows: ,in Let be the initial learning rate, t be the current training epoch, and T be the total number of training epochs. Minimum learning rate;

[0054] 4) Training stability assurance

[0055] Early Stopping Strategy: During training, monitor the performance of the validation set. If the accuracy of the validation set does not improve for 5 consecutive rounds, immediately stop training and save the current optimal model parameters to effectively avoid overfitting the model on the training set.

[0056] Gradient Clipping: Sets a fixed gradient norm threshold. During backpropagation, if the gradient is lost... If the norm exceeds this threshold, then it is determined by the formula. Gradient pruning effectively suppresses the gradient explosion problem during deep network training.

[0057] Another objective of this invention is to provide a nonlinear data classification system based on deep transfer learning visual recognition capabilities, comprising:

[0058] The transformation module is a nonlinear data visualization mechanism used to transform numerical features into spatial structure images.

[0059] An adaptation module is used to adapt the capabilities of pre-trained convolutional neural networks (CNNs) to a progressive transfer learning architecture for a target task.

[0060] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the nonlinear data classification method based on deep transfer learning visual recognition capabilities.

[0061] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the nonlinear data classification method based on deep transfer learning visual recognition capabilities.

[0062] Another objective of this invention is to provide an information data processing terminal for implementing the nonlinear data classification system based on deep transfer learning visual recognition capabilities.

[0063] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0064] This invention makes three core academic contributions to the field of tabular data analysis: (1) It proposes a novel value-graph recognition and classification method for nonlinear tabular data, which innovatively transforms the tabular data classification task into an image recognition task, realizing the effective application of CNN in tabular data modeling; (2) Through the synergistic effect of structured image transformation and deep transfer learning, it constructs a practical solution suitable for learning small sample tabular data, effectively alleviating the problem of data scarcity in high-risk real-world scenarios; (3) It constructs a reproducible end-to-end processing flow, which not only achieves high classification accuracy on nonlinear tabular data, but also provides visualization and interpretability for the feature interaction process and model decision logic, providing support for the application of the model in scenarios with strict requirements for the transparency and interpretability of artificial intelligence.

[0065] To overcome the core challenge of classifying nonlinear tabular data and fully leverage the powerful feature learning capabilities of CNNs, this invention proposes a novel Value-to-Image Recognition and Classification Method. This method organically integrates structured image transformation with deep transfer learning. The core innovation lies in transforming the numerical and categorical features in high-dimensional tabular data into spatially structured visual representations through a customized numerical-image mapping process. This process successfully breaks down the modal barriers between tabular and visual data by injecting artificially constructed spatial structures into the originally unstructured tabular features. This transformation allows CNNs to transfer their hierarchical feature learning capabilities, originally designed for visual recognition tasks, to capturing potential nonlinear feature interactions and complex patterns in tabular data. Furthermore, the visual representation of tabular data provides intuitive interpretability for previously abstract feature relationships, further enhancing the transparency of the model's decision-making process.

[0066] The framework proposed in this invention addresses the data scarcity problem through transfer learning, leveraging a pre-trained CNN model to extract general visual features. This strategy transfers knowledge learned from large-scale visual datasets to tabular data classification tasks, significantly accelerating model convergence and improving generalization performance in small-sample scenarios. To ensure the model's robustness and performance stability on non-linear tabular data, this invention further introduces a comprehensive optimization strategy, including progressive unfreezing of pre-trained layers, hierarchical differentiated learning rates, image enhancement methods adapted to tabular data, and an integrated prediction strategy based on image mapping with multiple feature permutations.

[0067] The research work of this invention has made three core academic contributions to the field of tabular data analysis: (1) It proposes a new value-graph recognition and classification method for nonlinear tabular data, which innovatively transforms the tabular data classification task into an image recognition task, realizing the effective application of CNN in tabular data modeling; (2) Through the synergistic effect of structured image transformation and deep transfer learning, a practical solution suitable for learning small sample tabular data is constructed, which effectively alleviates the problem of data scarcity in high-risk real-world scenarios; (3) A reproducible end-to-end processing flow is constructed. This flow not only achieves high classification accuracy on nonlinear tabular data, but also provides visualization and interpretability for the feature interaction process and model decision logic, providing support for the application of the model in scenarios with strict requirements for the transparency and interpretability of artificial intelligence.

[0068] This invention proposes a nonlinear tabular data classification method based on numerical-image conversion and deep transfer learning, filling the following technological gaps in the industry both domestically and internationally:

[0069] ① For the first time, the task of classifying nonlinear tabular data was systematically transformed into a visual recognition task.

[0070] Traditionally, Convolutional Neural Networks (CNNs) have been primarily applied to data with natural spatial structure, such as images and videos. However, tabular data (such as structured data in financial risk control, medical diagnosis, and cybersecurity testing) lacks spatial topological relationships, making it difficult to directly utilize the powerful feature extraction capabilities of CNNs. This invention designs a complete numerical-image coding framework to transform high-dimensional nonlinear tabular data into bar chart images with spatial structure. This is the first time that visual modeling of tabular data classification tasks has been achieved, filling the gap in the technical path from tabular data to image to CNN classification.

[0071] ② For the first time, a system integrates multi-view image generation and progressive transfer learning in a scenario with small sample nonlinear tabular data.

[0072] Current mainstream methods (such as XGBoost, LightGBM, TabNet, and SimCLR) generally suffer from overfitting, poor generalization ability, and training instability in scenarios with small sample sizes, high dimensions, and non-linear tabular data. This invention generates multiple sets of feature permutations using a fixed seed to form multi-view image samples. It then combines strategies such as progressive unfreezing, hierarchical learning rates, weighted loss functions, and cosine annealing scheduling to construct a deep transfer learning framework adapted to small sample sizes. In experiments, this approach achieved a test accuracy of 99.16% with only 1600 training samples, significantly outperforming traditional methods and filling the technological gap in the field of deep learning visual transfer learning for small-sample non-linear tabular data.

[0073] ③ Achieving a highly stable multi-view integrated prediction mechanism for the first time in tabular data classification.

[0074] This invention proposes generating 50 sets of images with different feature orders for each sample and performing ensemble prediction through a majority voting mechanism. Experimental results show that over 88% of the samples are correctly classified across all 50 views, with an average prediction variability of only 0.012, demonstrating extremely high prediction consistency. This multi-view ensemble mechanism is the first of its kind in tabular data classification tasks, filling the technical gap in stability and robustness between tabular data visualization and multi-view ensemble learning.

[0075] ④ For the first time, visualization of model decisions and interpretability of feature importance were achieved in tabular data classification.

[0076] This invention utilizes graphical feature mapping to visually represent the originally abstract nonlinear feature relationships in terms of color, position, bar height, etc., making them easier for humans to understand and for models to interpret. Simultaneously, it designs an importance assessment method based on feature permutation, successfully identifying the features (such as dstport and Duration) that have the greatest impact on classification results, filling the technological gap in nonlinear tabular data + CNN visual models + interpretability analysis.

[0077] This invention successfully solves the following technical problems that have long been unsolved in the field of tabular data classification:

[0078] ① Traditional models cannot effectively model the problem of high-dimensional nonlinear feature interactions.

[0079] For a long time, models such as Logistic Regression, SVM, and even XGBoost have struggled to capture complex feature interactions when dealing with high-dimensional, nonlinear, and strongly correlated tabular data. This invention transforms numerical features into image structures, enabling CNNs to automatically learn local, global, and nonlinear feature combination patterns. Experiments show that this method improves the F1 score by 16.9% and the accuracy by 15.3% compared to LightGBM on the same dataset. It achieves near-perfect classification performance (F1=0.994) for the first time in nonlinear tabular data classification, overcoming the performance bottleneck that traditional methods have long been unable to overcome.

[0080] ② The problem of deep learning models struggling to generalize in scenarios with few samples

[0081] Deep learning models typically rely on large amounts of labeled data, but high-quality labeled data is often scarce in real-world applications (such as healthcare, finance, and security). This invention, through strategies such as transfer learning, data augmentation, progressive unfreezing, and tiered learning rates, achieves a test accuracy of 99.16% with only 1600 training samples, exhibiting stable training curves and good overfit control. This solves the long-standing technical challenge of combining small-sample nonlinear tabular data with deep learning.

[0082] ③ The problem of tabular data models lacking interpretability and understandability

[0083] While traditional deep learning models (such as MLP and TabNet) have improved performance, their decision-making processes lack intuitive interpretability, making it difficult to meet the transparency requirements of highly sensitive fields such as healthcare, finance, and security. This invention transforms tabular data into color bar charts, giving each feature a fixed color and position within the image, making the model's learning process visible and traceable. Users can directly observe which feature regions have a greater impact on classification results, significantly improving the model's interpretability and solving the long-standing challenge of balancing high performance and interpretability.

[0084] ④ The problem of unstable predictions when the model faces changes in feature order.

[0085] In traditional tabular modeling, the model is highly sensitive to the order of input features, and changes in feature arrangement can lead to significant differences in prediction results. This invention, through multi-view feature arrangement and ensemble prediction mechanism, enables the model to maintain highly consistent prediction results (average prediction variability of only 0.012) when faced with different feature orders. For the first time, robustness to feature order has been achieved in tabular data classification, solving the long-neglected but critical technical problem of feature order sensitivity in practical applications. Attached Figure Description

[0086] Figure 1 This is a flowchart of a nonlinear data classification method based on deep transfer learning visual recognition capabilities provided in an embodiment of the present invention.

[0087] Figure 2 This is a block diagram of a nonlinear data classification system based on deep transfer learning visual recognition capabilities, provided in an embodiment of the present invention.

[0088] Figure 3 This is a schematic diagram of the value-to-image encoding framework provided in an embodiment of the present invention.

[0089] Figure 4 This is a schematic diagram of a deep learning-based classification model framework provided in an embodiment of the present invention.

[0090] Figure 5 This is a graph showing the training duration of 10 epochs provided in this embodiment of the invention.

[0091] Figure 6 This is a confusion matrix diagram on the test set provided in the embodiments of the present invention.

[0092] Figure 7 This is a visualization of the prediction consistency of a representative test sample under 50 image permutations provided in an embodiment of the present invention.

[0093] Figure 8This is a category definition diagram of the predicted category distribution of each sample provided in the embodiments of the present invention.

[0094] Figure 9 This is a graph showing the validation set evaluation metrics for each training round under the baseline configuration provided in this embodiment of the invention. Detailed Implementation

[0095] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0096] like Figure 1 As shown, the nonlinear data classification method based on deep transfer learning visual recognition capability provided in this embodiment of the invention includes the following steps:

[0097] S101 is a nonlinear data visualization mechanism that transforms numerical features into spatial structure images.

[0098] S102 is a progressive transfer learning architecture that adapts the capabilities of pre-trained convolutional neural networks to the target task.

[0099] like Figure 2 As shown, the nonlinear data classification system based on deep transfer learning visual recognition capability provided in this embodiment of the invention includes:

[0100] The transformation module is a nonlinear data visualization mechanism used to transform numerical features into spatial structure images.

[0101] An adaptation module is used to adapt the capabilities of pre-trained convolutional neural networks (CNNs) to a progressive transfer learning architecture for a target task.

[0102] Another objective of this invention is to provide a computer device, the computer device including a memory and a processor, the memory storing a computer program, the computer program being executed by the processor causing the processor to perform the steps of the nonlinear data classification method based on deep transfer learning visual recognition capabilities.

[0103] Another objective of this invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the nonlinear data classification method based on deep transfer learning visual recognition capabilities.

[0104] Another objective of this invention is to provide an information data processing terminal for implementing the nonlinear data classification system based on deep transfer learning visual recognition capabilities.

[0105] Figure 3 This is a schematic diagram of the value-to-image encoding framework provided in an embodiment of the present invention. By separating labels, arranging features, color encoding, and hierarchical storage, the original tabular data is converted into a multi-view bar chart image, thereby enabling visual recognition based on a convolutional neural network (CNN) to achieve classification.

[0106] Figure 4 This is a schematic diagram of a deep learning-based classification model framework provided in an embodiment of the present invention.

[0107] This invention transforms traditional tabular nonlinear numerical data into structured images that can be directly processed by convolutional neural networks using a value-to-image encoding framework. First, the label columns are separated from the original m×n data, generating independent files containing sample indices and classification labels, thus decoupling the data from the labels. Second, the feature columns of each sample are randomly rearranged, generating multiple representative permutations using a fixed seed to construct a multi-view feature perspective. Subsequently, the numerical values ​​are mapped to the height of a bar chart, and different features are assigned highly discriminative fixed colors, completing the visual encoding. Finally, the generated m×p images are stored in hierarchical folders, forming a dataset adapted to the CNN input format. This gives nonlinear data, which was originally unprocessable by visual models, a spatial structure foundation from which features can be extracted using convolutional operations.

[0108] To efficiently transfer the visual recognition capabilities of pre-trained CNNs to target classification tasks, this invention constructs a progressive transfer learning architecture. First, a pre-trained ResNet18 model is loaded, and the backbone network parameters are frozen to retain its general feature extraction capabilities. Simultaneously, the classification head is replaced with a fully connected layer adapted to the target task, and class weight calculations alleviate the data imbalance problem. During the training phase, a hierarchical learning rate strategy is adopted: a low learning rate is used for the backbone network to retain pre-trained knowledge, while a high learning rate is used for the classification head to quickly adapt to the new task. A cosine annealing scheduler is used to dynamically adjust the learning rate, and gradient clipping is introduced to avoid gradient explosion. Through multiple training-validation loops, only the model with the best performance on the validation set is saved. If performance does not improve, the learning rate is dynamically updated to ensure that the model accurately adapts to non-linear data classification tasks without forgetting general features.

[0109] This invention ensures the stability of model training and classification performance through a multi-dimensional optimization strategy. At the data level, data augmentation is achieved through multi-view feature arrangement, expanding the diversity of training samples. At the training level, a weighted random sampler is used to balance the class distribution, preventing the model from biased towards the majority class. At the optimization level, an early stopping mechanism prevents overfitting; training is automatically terminated when the validation set performance shows no improvement for several consecutive rounds, and gradient pruning techniques are combined to suppress abnormal gradient fluctuations. Finally, the optimal model is loaded for batch testing, generating visualization results and statistical reports such as confusion matrices and heatmaps, completing a closed loop from nonlinear data to classification results, achieving high-precision nonlinear data classification results that are difficult to achieve with traditional machine learning methods.

[0110] This invention will elucidate the fundamental concepts and technical background necessary for understanding the numerical-image recognition and classification method proposed in this invention. First, this invention formally defines the nonlinear data classification problem and its inherent challenges. Next, it describes the core idea of ​​mapping structured data to image representations, which serves as a bridge connecting the numerical feature space and the visual processing paradigm. Subsequently, it introduces the basic architecture and learning mechanism of the convolutional neural network that constitutes the computational core of the system in this invention. Finally, it outlines the principle of transfer learning, a key strategy for overcoming data scarcity in the target task and accelerating model convergence by utilizing pre-trained knowledge.

[0111] The core characteristic of nonlinear data lies in the complex non-additive interactions between features, making the input vector... Its target label The relationship between them cannot be adequately described by a linear function. Formally, for the dataset... If there are no parameters W, b such that If it holds true across the entire data distribution, then the potential mapping... This is nonlinearity. Such nonlinearity typically stems from high-dimensional feature coupling, non-stationary distributions, and complex correlation structures. Traditional linear models, such as logistic regression and linear support vector machines, rely on assumptions of linear separability and feature independence, making them ineffective at handling such data and resulting in poor performance. This fundamental limitation prompted the embodiments of this invention to develop advanced methods capable of modeling complex hierarchical feature interactions.

[0112] Visual representation of structured data refers to converting numerical feature vectors into an image-like format while preserving the inherent spatial and structural information of the original data. Let... Given a feature vector in the original numerical space, the image mapping function... 𝓘 is used to convert x into an image. Where H, W, and C represent the height, width, and number of channels of the generated image, respectively. Bar chart encoding is a widely used mapping strategy. In this method, each feature value in the feature vector... Represented as bars in the generated image, the height of the bars is proportional to the normalized value of the corresponding feature. Simultaneously, different features are distinguished through specific color coding rules, thus preserving the uniqueness of each feature in the visual representation. Heatmap encoding first rearranges the one-dimensional numerical feature vector into a fixed-shape two-dimensional matrix, such as an r × c matrix (satisfying r · c = n). Then, the value at each position in the matrix is ​​mapped to the corresponding color intensity in the heatmap, thus achieving an efficient conversion from discrete numerical features to continuous visual image information. Time series plots are a specialized mapping method suitable for sequential structured data. This method plots feature values ​​as a continuous line graph with the feature index or time step as the horizontal axis. This representation can completely preserve the sequential correlation and temporal characteristics of the original data in the image. This numerical-to-image conversion allows powerful image-based deep learning models (such as convolutional neural networks) to be directly applied to process traditional structured numerical data, thus providing the possibility of capturing hidden nonlinear patterns in data that are difficult to extract using traditional machine learning methods.

[0113] Deep learning is a subset of machine learning that uses multi-layered neural networks containing stacked nonlinear transformation layers to learn hierarchical and abstract feature representations from raw input data. Convolutional Neural Networks (CNNs) are deep learning architectures specifically designed to process grid-like data with inherent spatial structure, such as images and videos. Convolutional layers are the core component of a CNN architecture. They perform convolution operations on input data by applying a set of learnable convolutional kernels to extract local spatial features. Shallow convolutional layers capture basic visual features such as edges and textures, while deep convolutional layers learn higher-level semantic information. The output of each convolutional layer is a feature map that effectively captures the spatial hierarchy of the input information. Pooling layers are typically connected after convolutional layers in a CNN architecture. They reduce the spatial dimensionality of the feature map through downsampling operations such as max pooling and average pooling. This downsampling process achieves translation invariance of the extracted features and effectively reduces the computational complexity of subsequent network layers while preserving key feature information. Fully connected layers are typically placed in the latter half of the CNN architecture. It flattens the high-dimensional two-dimensional feature maps output by the preceding convolutional and pooling layers into one-dimensional feature vectors, and then aggregates these high-level semantic features through a series of linear transformations and non-linear activation operations to complete the final classification or regression task. From a mathematical perspective, the convolutional layer in a convolutional neural network can be represented as:

[0114] ,

[0115] Where * represents a two-dimensional convolution operation, and These are the learnable weight matrix and bias vector of the l-th convolutional layer, respectively, and σ is a non-linear activation function (such as ReLU or Sigmoid), which introduces the necessary non-linearity into the network to model complex data relationships. Convolutional neural networks have demonstrated outstanding and leading performance in various image recognition and computer vision tasks, mainly due to their unique structural design, which enables them to automatically learn discriminative and task-relevant features from raw pixel data without relying on manual feature engineering.

[0116] Transfer learning is a key machine learning technique that transfers knowledge gained from training a model in a source domain to a target domain. The source domain refers to a task with sufficient labeled data and mature, learnable patterns, while the target domain is a related task with limited labeled data or scarce training samples. In deep learning for vision tasks, transfer learning typically involves using a pre-trained deep model (such as one trained on the ImageNet dataset) as a general feature extractor and fine-tuning its parameters on target task data to adapt to the specific needs of the target task. A pre-trained model refers to a deep neural network trained on a large, diverse dataset (such as ImageNet, containing millions of images and covering thousands of object categories), such as ResNet, VGG, or AlexNet. Such well-trained models can learn general and transferable feature representations of visual data, which are often applicable to other related visual recognition tasks as well. Feature extraction is a fundamental and widely used transfer learning strategy. This method fixes the convolutional layers of the pre-trained model, using them to extract high-level visual features from images in the target domain, while replacing the original fully connected layers in the pre-trained model that are relevant to the source domain task with new fully connected layers designed for the target task. During training, only newly added layers are updated, thus reducing training costs. Fine-tuning is an advanced transfer learning strategy. It involves further training some or all layers of a pre-trained model on the target dataset with a small learning rate. This process allows general features learned from the source domain to adapt to the specific characteristics of the target domain data, thereby further improving the model's generalization performance on the target task. Formally, let... For large-scale source datasets The core objective of transfer learning is to train a source model on a small target dataset. Learn a high-performance target model .in and These are the input spaces for the source task and the target task, respectively. and This corresponds to the output space. Transfer learning utilizes the source model. Train sufficient parameters to initialize the target model. The parameters not only significantly reduce the need for a large amount of labeled target domain data, but also effectively accelerate the training convergence speed and improve the final classification performance and generalization ability of the target model.

[0117] This invention proposes a unified framework for nonlinear data classification that integrates structured data visualization and deep transfer learning. The framework centers on two core modules: first, a nonlinear data visualization mechanism that transforms numerical features into spatially structured images; and second, a progressive transfer learning architecture that adapts the capabilities of pre-trained convolutional neural networks (CNNs) to the target task. The specific implementation of each module, including core algorithms, operational mechanisms, and optimization strategies, will be detailed below.

[0118] The core objective of this framework is to map high-dimensional nonlinear numerical data to image space while preserving the inherent correlations of data features, enabling convolutional neural networks to leverage their powerful spatial feature extraction capabilities. The framework consists of four key modules: core mechanism definition, image generation algorithm, data preprocessing workflow, and test data alignment, as detailed in Algorithm 1.

[0119] This invention formally defines the image transformation process as a transformation from numerical data space to image space, which comprises three basic components:

[0120] Feature permutation: For an n-dimensional feature vector Rearrangement function σ: →𝓚(wherein) Generate rearranged feature vectors for the feature index set: A set of p representative rearrangements is selected using a fixed random seed s. , ,…, This is to ensure the reproducibility of the rearrangement process and experimental results.

[0121] Color encoding: Color mapping function Assign a unique RGB color C(k) to each feature = ( , , ),in , , ∈ [0,1]; and the difference between any two distinct feature colors Distance satisfies:

[0122]

[0123] This ensures that the convolutional neural network (CNN) can effectively distinguish different feature regions in the image.

[0124] Spatial mapping: rearranging the feature vectors The image is mapped to a standard H × W × 3 bar chart (H = 224, W = 224), where the horizontal axis represents the rearranged feature index and the vertical axis represents the normalized feature value. The calculation formula is as follows:

[0125]

[0126] This normalization method can match the input requirements of pre-trained CNN models.

[0127] The core algorithm of the image framework provided in this embodiment of the invention can systematically convert the original nonlinear dataset into a multi-view image dataset with spatial topological structure and completely corresponding labels.

[0128] Algorithm 1: Nonlinear Data Visualization Framework enter: Input: n, p, C, H×W, seed s, p, C, H×W, seed s Output: Image dataset Tag set L1:L ← % Tag Mapping 2: Generate a permutation set based on seed s { ,…, }3: for i=1 to m:4: for j=1 to p:5: 6: Initialize the image matrix 7:for k = 1 to n: 8: color = C(k)9: , 10: At coordinates ( , 11: Draw a bar chart of the corresponding color at the specified location; 12: End the loop; 13: Save the image. 13: End the loop 14: End the loop 15: Return , L

[0129] The preprocessing workflow aims to preserve the core information of nonlinear data features while constructing a spatial topology. It comprises four consecutive and interconnected steps, fully aligned with the core logic of Algorithm 1. Label separation: As a fundamental step, the classification labels are separated... From the original feature vector The system separates the training samples into independent label files (L) to avoid label interference during subsequent image processing and ensure complete traceability of each training sample to its corresponding image. Feature sorting: A fixed-seed permutation mechanism generates p groups of rearranged feature sequences for each sample, expanding the diversity of the original data without losing the intrinsic correlation of features and laying the foundation for multi-view image representation. Visual encoding: Each group of sorted feature vectors is converted into a bar chart image with feature color encoding. The horizontal axis represents the permuted feature index, and the vertical axis represents the normalized feature value, enabling convolutional neural networks (CNNs) to capture individual feature values ​​and patterns of association between features through the spatial structure of the image. Hierarchical file organization: A standardized three-level folder structure (root directory → sample index → ​​permutation method) is constructed to store all generated images, facilitating batch loading and efficient management of image data in deep learning frameworks while ensuring perfect compatibility with subsequent model training processes.

[0130] To ensure strict consistency between the model training and testing phases and avoid distribution shifts between training and testing data, the testing data must undergo the exact same processing as the training data without adjusting any parameters: the color encoding function C(·) used in the training phase is completely reused for feature encoding in the testing data, ensuring that the RGB color mapped to the same feature in the image in the testing set is completely consistent with that in the training set; the training phase uses p feature permutation methods determined by a fixed random seed s. , ,…, All features are reused to generate multi-view feature sequences for test samples, ensuring the consistency of feature sorting rules; the standardized three-level hierarchical folder structure used for training data is also applied to test image storage, ensuring that the input data format of the trained model remains consistent during the testing phase; the test dataset... The feature dimensions are strictly consistent with the training dataset to ensure that the generated training image dataset and the test image dataset have no structural differences.

[0131] Deep transfer learning architecture: This architecture uses a pre-trained ResNet18 model as the backbone feature extractor, integrating two core strategies: progressive unfreezing and hierarchical learning rates. It balances the preservation of general features from the pre-trained model with the adaptive learning of task-specific features. The core of the architecture is the progressive unfreezing training algorithm (Algorithm 2), supplemented by a multi-dimensional training optimization strategy system to further improve the model's classification performance, generalization ability, and training stability.

[0132] The technological innovation of this architecture lies in the organic integration of deep transfer learning mechanisms with nonlinear data features, enabling efficient adaptation of pre-trained CNN models to nonlinear data classification tasks through two core components.

[0133] Data separation strategy based on personnel ID: As a fundamental innovation, this strategy strictly separates the training set and validation set based on personnel ID, ensuring no data leakage during the training and evaluation phases. This approach avoids the model memorizing individual-specific patterns, forcing the model to learn fraud detection features with generalizability.

[0134] Adaptive parameter control strategy: As a core optimization innovation, this strategy comprises two interconnected sub-strategies. Hierarchical learning rate strategy: Assigning a lower learning rate to the pre-trained backbone network. To retain its learned general image feature extraction capabilities; a higher learning rate is assigned to the newly designed balanced classification head. This accelerates its adaptive learning for fraud detection tasks. The mathematical expression of this strategy is:

[0135]

[0136] A parameter-controlled progressive unfreezing strategy: Initially, all parameters of the backbone network are frozen, first unfreezing the classification head, and then progressively unfreezing deeper layers (Layer 4 → Layer 3) based on the target total number of parameters (approximately 2.5 million trainable parameters). Specifically, first, through numeric( ) Calculate the balanced classification head ( The number of parameters (the number of elements in the classification head parameter tensor) is defined as follows: the remaining trainable parameters of the backbone network to be unfrozen are defined as... (in = 2.5× (For the target, there are always trainable parameters); first iterate through the Layer4 parameters (each time from...) (Subtract the number of elements that have been unfrozen) If If the value is still positive, continue unfreezing the Layer3 parameter until... ≤0. This strategy controls model complexity and prevents overfitting; its mathematical expression is:

[0137] ,

[0138]

[0139] in This represents the thawing ratio of the parameters in the i-th layer.

[0140] A parameter-controlled progressive unfreezing training algorithm: The core training algorithm of this architecture implements an adaptive transfer learning strategy with precise parameter control, systematically balancing pre-training feature preservation, adaptive learning of target task features, and model complexity control. The specific implementation steps are as follows:

[0141] Algorithm 2: Parameter-Controllable Gradual Thawing Input: Image dataset Tag set Total number of target parameters Number of training rounds Base learning rate Output: Optimized fraud detection model 1: Initialization: Replace the fully connected (FC) header with a balanced classification header. 2: Frozen Model : Thawing and sorting head 3: 4: Unfreeze Layer4 → Layer3 parameters (until...) 5: Set the optimizer W: The backbone network learning rate is The learning rate of the classification head is 6: Calculate category weights loss function Using weighted cross-entropy (CE) loss: A cosine annealing learning rate scheduler is set, with a minimum learning rate of... 8: for t = 1 to T 9: Perform training transformation (·) → Calculate loss → Backpropagation → Gradient clipping (threshold) → Update parameter 10: Update learning rate: 11: Construct the validation set (No overlap in personnel IDs) → Evaluation model metrics 12: If the model metrics meet the conditions, save the optimal model. 13: End the loop 14: Return

[0142] To address common issues in deep learning model training such as overfitting, class imbalance, learning rate stagnation, and training instability, this invention integrates four complementary and mutually reinforcing training optimization strategies to form a comprehensive optimization system, ensuring the model's classification performance and training stability.

[0143] Data augmentation: During model training, online data augmentation is applied to the training image data in real time, effectively expanding the distribution range of the training data, reducing the model's sensitivity to minor changes in image spatial structure and color features, and significantly improving the model's robustness. Core augmentation transformations during the training phase include: Geometric transformation: random cropping to... Pixels, random horizontal flip with a probability of 0.3 Random rotations within the specified range enhance the model's spatial invariance to image features; color jitter: brightness and contrast adjustment factors are both set to 0.2. Only resizing (224×224) and normalization are performed on the validation and test sets. All images are normalized using the mean [0.485, 0.456, 0.406] and standard deviation [0.229, 0.224, 0.225] of the ImageNet dataset.

[0144] Class imbalance handling: A class-weighted cross-entropy loss function is introduced to effectively address the potential class imbalance problem in the training dataset (where some classes have far fewer labeled samples than others, potentially leading to model bias towards the majority class). For each class c (0 ≤ c ≤ 1, the number of samples is...) ), category weights are calculated as

[0145] (Where N is the total number of training samples). The weighted cross-entropy loss is defined as... Where B is the batch size. For real labels, This represents the predicted probability corresponding to the true class. This approach allows minority class samples to contribute more to the loss, effectively avoiding classification bias towards the majority class.

[0146] Learning Rate Scheduling: A cosine annealing learning rate scheduling strategy is employed to dynamically optimize the learning rate during training, preventing the model from getting trapped in local optima and ensuring efficient convergence. The cosine annealing strategy dynamically reduces the learning rate with each training iteration, allowing the model to fully explore the parameter space in the early stages of training and then fine-tune the parameters in the later stages to approach the global optimum; its update formula is as follows: ,in Let t be the initial learning rate, t be the current training epoch, and T be the total number of training epochs. This is the minimum learning rate.

[0147] Training Stability Guarantee: Two core strategies are designed to ensure the stability of the model training process and prevent overfitting and training crashes. Early Stopping: During training, the validation set performance is monitored. If the validation set accuracy does not improve for five consecutive rounds, training is immediately stopped and the current optimal model parameters are saved, effectively avoiding overfitting on the training set. Gradient Clipping: A fixed gradient norm threshold is set. During backpropagation, if the gradient is lost... If the norm exceeds this threshold, then it is determined by the formula. Gradient pruning effectively suppresses the gradient explosion problem in deep network training. Furthermore, this architecture achieves strict data leakage prevention by ensuring no overlap between the training and validation set user IDs, and employs memory cleanup techniques after each validation phase to guarantee system stability during long-term training.

[0148] This invention first introduces the dataset used for evaluation, referred to as the Fraudulent Websites dataset. This dataset contains 3,193 samples, each with 23 numerical / categorical features and a binary label indicating a fraudulent website. To effectively apply convolutional neural networks to this type of tabular data, the specific process of converting each sample into an image is as follows:

[0149] IP address decomposition: The two IP address columns ('srcip', 'dscip') are split into four independent octets, resulting in eight integer features with values ​​in the range [0, 255].

[0150] Numerical Feature Scaling: The remaining 13 numerical features (e.g., 'final byte number', 'Duration') have significantly different dimensions and include negative values. They are shifted by subtracting the minimum value and adding 1, followed by a linear transformation. (Choose appropriate parameters k and b to maintain relative size) map it to the interval [0, 255].

[0151] Binary feature mapping: Maps seven binary behavioral indicators (e.g., 'Dangerous Words') to: 255 for true values ​​and 0 for false values.

[0152] Column permutation: To create multiple views of the same sample, the order of 13 scaled features and seven binary features is randomly permuted using a fixed random seed. A total of 50 different permutations are generated, each producing a different image. The first eight feature columns derived from the IP address are always kept at the beginning. The image filename encodes the permutation order (e.g., 1 2 3 4 5 6 7 8 24 18 23 16 21 19 15 28 12 9 25 14 20 27 11 13 26 10 2217).

[0153] After conversion, this embodiment of the invention yields 3193 samples × 50 images = 159650 images. These images are divided into a training set (1600 samples, 80000 images), a validation set (the remaining 400 samples, 20000 images), and a test set (the remaining 1193 samples, 59650 images). All images of the same given sample retain the same person-level label.

[0154] This invention employs a ResNet-18 model pre-trained on ImageNet, replacing its last fully connected layer with a custom classification head (containing two hidden layers and introducing Dropout and batch normalization). The training process uses the AdamW optimizer, combined with a cosine annealing learning rate scheduler, early stopping mechanism, and class weights to address potential data imbalance issues. Cross-entropy is used as the loss function.

[0155] Figure 5 The graphs show the changes in training loss, validation loss, training accuracy, and validation accuracy over 10 training epochs. Observations show that both types of losses rapidly decreased and stabilized, while the validation accuracy reached 99.0%, very close to the training accuracy, indicating that the model experienced almost no overfitting (the accuracy difference between the training and validation sets was very small). The final model was selected based on a multi-criteria strategy: prioritizing the highest validation F1 score, while also considering improvements in validation accuracy (F1 score > 0.5), high recall (> 0.5) with a small accuracy difference (< 10%), and high F1 score (> 0.6) with an accuracy difference of less than 15%.

[0156] The best model was evaluated on a test set containing 1,193 test samples (50 images per sample). For each sample, its 50 predictions were aggregated using majority voting to produce the final class label. The overall evaluation metrics are as follows: Figure 5 As shown, the model achieved an accuracy of 99.16%, a precision of 99.76%, a recall of 99.06%, and an F1 score of 99.41%, demonstrating excellent discriminative ability.

[0157] Table 1. Core evaluation metrics on the test set

[0158] Measurement Standards value accuracy 99.16% Accuracy 99.76% Recall rate 99.06% F1 score 99.41%

[0159] Confusion matrix ( Figure 6 The results show that out of 343 normal samples, 341 were correctly classified as normal, and 2 were misclassified as fraudulent websites; out of 850 fraudulent samples, 842 were correctly detected, and 8 were missed. This balanced performance confirms that the model was not significantly affected by class imbalance.

[0160] For each test sample, this embodiment of the invention analyzed the variability of 50 independent single-image prediction results. Figure 7The above prediction results for a representative subset of samples are presented intuitively, with each row corresponding to one subject and each column corresponding to a different image permutation method. The nearly uniform color of each row indicates that the model's prediction results have extremely high consistency regardless of the feature order, which fully demonstrates the robustness improvement brought to the model by the multi-permutation ensemble strategy.

[0161] Figure 7 The visualization shows the predictive consistency of representative test samples under 50 image permutations. Each row corresponds to one subject, and each column corresponds to a different column permutation method. Blue represents non-fraudulent samples (label 0), and yellow represents fraudulent samples (label 1). The extremely high uniformity shown in each row fully demonstrates the model's strong stability.

[0162] Figure 8 This shows the distribution of samples based on the percentage of correct predictions. Over 88% of the samples (1058 out of 1193 samples) had all 50 predictions correctly (All Correct), while only 10 samples (0.84%) had predominantly incorrect predictions. The model's average prediction variability... The value of 0.012 indicates that the ensemble model has extremely high stability.

[0163] Figure 8 The predicted category distribution for each sample is defined as follows: All Correct (all 50 predictions were correct); Mostly Correct (at least 45 predictions were correct (≥90%)); Largely Correct (35-44 predictions were correct (70%-89%)); Half Correct (25-34 predictions were correct (50%-69%)); Mostly Incorrect (less than 25 correct predictions (<50%).

[0164] This invention compares the proposed image-based deep learning method with several classic machine learning models trained directly on raw tabular features (without image conversion). The models compared include LightGBM, XGBoost, CatBoost, Multilayer Perceptron (MLP), SimCLR (using a contrastive learning followed by logistic regression paradigm), and TabNet. All models are evaluated under identical training / validation / test set partitions and employ the same feature selection process to completely eliminate data leakage. For the XGBoost model, this invention uses the SMOTE oversampling method to alleviate class imbalance; while CatBoost and LightGBM models natively support categorical feature processing. Except for adjustments noted in the text (such as early stopping mechanism and class weight adjustment), all models are trained using default hyperparameters to replicate typical usage in real-world applications.

[0165] Table 2 summarizes the performance of each baseline model and the method proposed in this embodiment on the test set. The results show that the method proposed in this embodiment achieves the best values ​​across all evaluation metrics, with an accuracy of 99.16%, precision of 99.76%, recall of 99.06%, and F1 score of 99.41%. Compared to the best-performing traditional method, LightGBM, the method in this embodiment improves accuracy by 15.3% (from 86.01% to 99.16%), precision by 18.0% (from 84.58% to 99.76%), recall by 15.9% (from 85.53% to 99.06%), and F1 score by 16.9% (from 85.00% to 99.41%). These significant performance improvements fully demonstrate that the image-based representation method and multi-permutation ensemble strategy proposed in this embodiment can effectively capture complex data patterns that traditional tabular models cannot uncover.

[0166] Table 2 Performance comparison of each baseline model (test set)

[0167] method accuracy Accuracy Recall rate F1 value The method proposed in this invention 0.9916 0.9976 0.9906 0.9941 LightGBM 0.8601 0.8458 0.8553 0.8500 XGBoost 0.7931 0.7920 0.8177 0.7886 CatBoost 0.7755 0.7668 0.7890 0.7682 MLP 0.6893 0.7017 0.7182 0.6859 SimCLR 0.6834 0.6894 0.7058 0.6786 TabNet 0.6667 0.6276 0.5838 0.5785

[0168] The method proposed in this embodiment of the invention significantly outperforms all baseline models, improving the F1 score from 0.85 (LightGBM model) to 0.994. This performance improvement is attributed to the ability of convolutional neural networks (CNNs) to capture complex nonlinear relationships encoded in image structures, as well as the ensemble effect brought about by multi-column permutations.

[0169] To systematically evaluate the contribution of each core component in the framework of this invention, ablation experiments were conducted on the validation set. To improve experimental efficiency, all experiments reduced the training epochs to 5, while maintaining complete consistency between the dataset partitioning and the model architecture throughout. The baseline configuration included: pre-training based on the ImageNet dataset, group learning rate, cosine annealing scheduler, and a partial unfreezing strategy (fine-tuning only a portion of the layup). Then, each component was individually removed or modified, and the impact on validation accuracy and F1 score was measured. Table 3 summarizes the results.

[0170] Table 3 Ablation Experiment Results (Validation Set Accuracy and F1 Score)

[0171] Configuration Validation set accuracy (%) F1 score of the validation set Baseline (including all components) 98.995 0.9917 Remove group learning rate 98.615 0.9884 Remove cosine learning rate scheduler 98.570 0.9880 Remove pre-training 97.640 0.9802 Only retain the fully connected header (pure fully connected layer). 79.575 0.7978 Limited image input (25 images per subject) 98.390 0.9866

[0172] The following conclusions can be drawn from the above experimental results:

[0173] The grouped learning rate strategy (i.e., setting a higher learning rate for newly added classifiers) improved the model accuracy by approximately 0.38% and the F1 score by 0.0033. This result confirms that differentiated learning rates can help randomly initialized classifiers adapt more quickly without perturbing the pre-trained features.

[0174] Compared to a fixed learning rate, the cosine annealing learning rate scheduler delivers similar performance gains (0.425% improvement in accuracy and 0.0037 improvement in F1 score), indicating that a gradually decaying learning rate helps the model achieve better convergence.

[0175] Pre-training on the ImageNet dataset significantly improves model performance: removing the pre-training data reduces the model accuracy by 1.35% and the F1 score by 0.0115. This result fully demonstrates the crucial importance of transferring general visual features to the fraud detection image task specific to this embodiment of the invention.

[0176] Fine-tuning only the classification head (a purely fully connected layer) leads to a sharp drop in model performance (accuracy 79.6%, F1 score 0.798). This result clearly demonstrates that adapting and fine-tuning the deep layers of a convolutional neural network (CNN) is a core prerequisite for capturing the complex patterns inherent in tabular data image representations.

[0177] Reducing the number of images per subject from 50 to 25 only resulted in a slight decrease in model performance (accuracy decreased by 0.6%, F1 score decreased by 0.0051). This indicates that setting multi-view inputs (i.e., column permutation) for a single sample can improve the robustness of the model, and the model can still maintain excellent performance even with a reduction in the number of input images.

[0178] Figure 9 The results demonstrate the trends in validation set accuracy, precision, recall, and F1 score over five training epochs with the baseline configuration. The curves show that the model converges quickly, completing convergence in the third training epoch, and its performance remains stable after convergence, with negligible overfitting – fully demonstrating the effectiveness of the regularization strategies (Dropout, batch normalization, and early stopping mechanism) employed in this embodiment of the invention.

[0179] Overall, the ablation experiments fully validated the rationality of the design choices in the embodiments of this invention: each core component brought positive gains to the model performance, and the combination of pre-training, group learning rate, cosine annealing scheduling strategy, and partial fine-tuning enabled the model to achieve near-optimal performance. When the number of single-sample input images decreased, the model performance only showed limited degradation, which further confirmed the robustness of the model.

[0180] Figure 9 Evaluation metrics for the validation set at each training epoch under the baseline configuration. Accuracy, precision, recall, and F1 score all tend to stabilize after the third training epoch, indicating that the model converges quickly and has excellent generalization performance.

[0181] 4.7 Feature Importance Analysis

[0182] To reduce computational overhead and storage requirements, this embodiment of the invention randomly selected 50 samples from the test set (a fixed random seed was used to ensure experimental reproducibility). For each of the 20 non-IP features, this embodiment independently permuted its value within these 50 samples, while keeping all other features unchanged. Subsequently, for each sample, this embodiment generated 50 images corresponding to the 50 column permutation methods (see Section 3.1 for details) and input them into the trained model. For each sample, this embodiment recorded the number of times the result was flipped in 50 predictions compared to the undisturbed baseline result; the average flip rate of the 50 samples was used as the importance score of that feature. A higher flip rate indicates a stronger influence of that feature on the model's decision.

[0183] Table 4 lists the features ranked in descending order of importance score. The feature with the greatest impact on model decision-making is the destination port (dstport), with a flip rate of 6.44%; followed by session duration (flip rate 5.72%), and a set of features related to packet size (including Received Packet Length, Total SentTCP Length, Received Payload Size, etc.), with flip rates concentrated between 3% and 4%. In contrast, binary behavioral indicators (including Dangerous Words, Bank Card Operation, Transfer & Payment Behavior, etc.) have extremely low flip rates (mostly below 0.1%), indicating that the model's decision-making mainly relies on numerical traffic statistics features rather than explicitly labeled behavioral features.

[0184] This result may initially seem counterintuitive, as people typically believe that behavioral characteristics are the most direct indicators of fraudulent behavior. This phenomenon can be explained by several factors. First, numerical features themselves encode rich information about traffic patterns; the model may have learned to associate specific packet sizes or session duration patterns with...

[0185] Table 4 shows that feature importance is measured by the average proportion of prediction results that are reversed after feature replacement. The larger the value, the stronger the influence of the feature.

[0186] Table 4 Characteristic Change Rate

[0187] feature rate of change dstport 0.0644 Duration 0.0572 Received Packet Length 0.0368 Total Sent TCP Length 0.0356 Received Payload Size 0.0356 Total Received TCP Length 0.0292 Average Payload Size 0.0204 fine number 0.0140 Sent Payload Size 0.0076 Sent Packet Count 0.0068 Received Packet Count 0.0052 Transfer & Payment Behavior 0.0008 Dangerous Words 0.0004 Fraud & Game-related Behavior 0.0000 Data Loading Behavior 0.0000 Personal Information Disclosure Behavior 0.0000 fine byte number 0.0000 Bank Card Operation 0.0000 Sent Packet Length 0.0000 Other Unknown Behavior 0.0000

[0188] The image-based deep learning method proposed in this invention successfully converts tabular web traffic data into images and achieves near-perfect classification of fraudulent websites. Extensive experiments demonstrate that this method outperforms traditional machine learning models, is robust to column permutations, and can identify key predictive features. Therefore, this method is a powerful tool for fraud detection in imbalanced, high-dimensional tabular data.

[0189] This invention proposes a classification system based on image representation and deep transfer learning, providing a novel and effective solution for nonlinear data classification. Key innovations are as follows: First, a customized image mapping strategy transforms abstract numerical data into images with spatial structure, enabling the system to fully utilize the feature extraction capabilities of convolutional neural networks. Second, various optimization techniques—including dynamic layer unfreezing, hierarchical adaptive learning rate, and multi-view data augmentation—are seamlessly integrated into the transfer learning framework, significantly improving nonlinear modeling capabilities and few-shot learning performance. Experimental results show that on multiple nonlinear datasets, the proposed system outperforms traditional machine learning methods and conventional deep learning models in terms of classification accuracy and generalization ability, while also exhibiting good training stability and interpretability.

[0190] Example 1: This example applies the proposed nonlinear data classification method based on deep transfer learning visual recognition capabilities to the clinical diagnostic scenario of non-invasive prenatal testing (NIPT) for fetal chromosomal abnormality screening. The NIPT dataset used in the experiment contains 1687 clinical test samples, each with 26 numerical key features and a binary label indicating whether the fetal chromosome is abnormal. To adapt to the image input requirements of convolutional neural networks, a systematic image transformation was performed on the original tabular NIPT data: min-max normalization was used to linearly scale the 26-dimensional continuous features to the [0,100] interval to eliminate dimensional differences; unique RGB color values ​​in the range of 0 to 255 were assigned to each of the 26 feature dimensions to achieve accurate mapping from features to visual labels; the normalized feature values ​​were mapped to the height of a histogram, completing the image transformation from numerical features to RGB color histograms. To enhance data diversity, a fixed random seed was used to randomly perturb the order of the 26 features, generating 100 different feature arrangements. Each original sample was used to generate 100 different color bar chart images, resulting in a total of 168,700 images. These images were divided into a training set (1,181 samples, 118,100 images), a validation set (169 samples, 16,900 images), and a test set (337 samples, 33,700 images) in a 7:1:2 ratio. All images from the same sample retained the same fetal chromosomal abnormality label.

[0191] In model training and evaluation, a ResNet-50 pre-trained on ImageNet was used as the backbone network, replacing the classification head with a customized binary classification structure. A transfer learning strategy of progressively unfreezing convolutional layer parameters was employed, combined with an early stopping mechanism, cosine annealing learning rate scheduling, and gradient pruning to optimize the training process, effectively mitigating the risk of overfitting. Experimental results on the test set show that the proposed method achieved a classification accuracy of 99.10% and a validation set accuracy of 97.68%. The model can accurately identify chromosomal abnormalities such as trisomy 13, trisomy 18, and trisomy 21 in fetuses. Feature ablation experiments further validated that the Z-value of chromosome 21 is the core feature predicted by the model, highly consistent with clinical screening logic. Statistical analysis of the health coefficient of 100 single-image predictions for each test sample showed excellent model prediction consistency, validating the high robustness brought by the multi-permutation perturbation ensemble strategy.

[0192] Comparative experiments with traditional NIPT screening and interpretation methods and machine learning methods further highlight the superiority of our proposed method. Under identical dataset partitioning, the decision tree model achieved an accuracy of only 90.35%, and traditional ensemble learning methods such as random forests also performed significantly poorly, failing to capture the complex nonlinear interaction patterns between NIPT features. In contrast, our method significantly outperformed traditional methods in all core metrics, including accuracy, precision, recall, and F1 score, increasing screening accuracy from approximately 90% to 99.10%, a relative improvement of over 9.7%. This demonstrates that the framework based on image representation and deep transfer learning can effectively uncover hidden clinical feature associations in NIPT data, significantly reducing false positive and false negative rates, and providing an efficient and reliable technical solution for intelligent prenatal screening of fetal chromosomal abnormalities.

[0193] Example 2:

[0194] This embodiment applies the proposed nonlinear data classification method based on deep transfer learning visual recognition capabilities to the scenario of identifying authors of classical literature, specifically using the Gengchen edition of *Dream of the Red Chamber* as the research object, aiming to distinguish the authorship of the first eighty chapters from the last forty chapters. The original data used in the experiment is the textual character statistics of the entire 120 chapters of the Gengchen edition of *Dream of the Red Chamber*. After merging chapters (the content of chapters seventeen and eighteen is continuous and has no clear chapter boundary, so they are merged into one record), a total of 119 chapter character records were obtained. During the statistical process, proper identifiers such as personal names and nicknames in the text were removed, and only commonly used Chinese characters were retained for quantitative statistics. The entire book involves 732,345 commonly used Chinese characters and 4,348 different types of Chinese characters. Each record contains the usage frequency of 4,348 types of Chinese characters as the core feature. At the same time, based on the mainstream classification consensus that Cao Xueqin wrote the first eighty chapters and Gao E continued the last forty chapters, the first eighty chapters (including the merged chapters seventeen and eighteen) were labeled as 1, and the last forty chapters were labeled as 0, forming binary labeled data. The ratio of positive to negative samples is 79:40, indicating a clear class imbalance.

[0195] To adapt to the training requirements of convolutional neural networks, a systematic image transformation and data augmentation were performed on the original character frequency data. First, 4348 Chinese characters were uniquely numbered and assigned corresponding RGB color values, ensuring that any two characters had completely different colors. The frequency of each character was mapped to the height of a line segment in a histogram through a non-linear transformation (formula: h_i = average frequency × arctan(frequency of the i-th character / average frequency)). The horizontal axis represents the character number, the width of each line segment is 1 pixel, and the color is the corresponding RGB value of the character, thus transforming the character usage features of each episode into an RGB histogram image. To address the small sample size problem of the original 119 records, which is insufficient for deep learning training, a random sampling method was used to augment the content of each episode: for any episode, assuming the total number of characters is n_i, n_i characters were randomly sampled and their frequencies were recounted, generating a new histogram image according to the above rules. Each episode's original content, plus 499 random samples, generated a total of 500 images. All 119 records generated a total of 119 × 500 = 59,500 image samples, effectively expanding the training dataset. The training set consisted of the first 39 records with a label of 1 (episodes 1 to 40) and the last 20 records with a label of 0 (episodes 101 to 120), totaling 59 records, generating 29,500 images (19,667 for training and 9,833 for validation). The test set consisted of the remaining 60 records, generating 30,000 images for final performance evaluation.

[0196] The model is built upon a ResNet50 convolutional neural network, employing transfer learning to load pre-trained ImageNet weights, freezing convolutional layer parameters, and replacing the classifier head with binary classification output. To address class imbalance, a weighted FocalLoss loss function is used, with positive and negative sample weights set to approximately 0.75 and 1.49, respectively. During training, optimization strategies include hierarchical learning rates (higher learning rate for the classifier head than the backbone network), cosine annealing learning rate scheduling, and gradient pruning. After training, the recognition accuracy on the independent test set reaches 0.8865. Experimental results are presented as a recognition result matrix and a dichromatic image, clearly demonstrating the model's distinct division between chapters 80 and 81, indicating a significant difference in character usage features between the first eighty chapters and the last forty chapters, reflecting the differences in the authors' knowledge space. Further analysis of the dichromatic identification results revealed that Chapter 67 tends to be attributed to the author of the last forty chapters (Gao E), consistent with the conclusions of several scholars of *Dream of the Red Chamber*, including Zhang Ailing, Yu Pingbo, Zhou Ruchang, Liu Mengxi, and Ma Ruifang, indicating that Chapter 67 is not Cao Xueqin's original work. Furthermore, the knowledge space reflected in the identification results of Chapter 87 is similar to that of the first eighty chapters, suggesting that the last forty chapters may contain imitations of the style of the first eighty chapters or retain fragments from Cao Xueqin's original work. This embodiment fully verifies the effectiveness of the proposed method in the task of identifying authors of classical literature. It can intelligently distinguish the creative styles of different authors based on the quantitative analysis of Chinese character usage characteristics, providing a new interdisciplinary technical path for digital humanities research.

[0197] Example 3: This example applies the proposed nonlinear data classification method based on deep transfer learning visual recognition ability to the scenario of identifying students' innovation and entrepreneurship abilities, specifically focusing on the international police affairs major in public security colleges. The experiment collected course grades and innovation and entrepreneurship competition results data from 432 students in this major from 2019 to 2022. Course grades covered 212 courses; after expert screening, 123 core courses were selected for analysis, including examination courses (out of 100) and assessment courses (five-level system, mapped to out of 100). Courses not taken were scored as 0. Innovation and entrepreneurship competition results data included national and provincial-level undergraduate innovation training programs, the New Seedling Talent Program, the Public Security College Student Science and Technology Application Innovation Competition, and awards in various subject competitions, serving as label data for students' innovation abilities: students with innovation project funding or competition awards were marked as 1 (positive innovation ability), totaling 156 students; students without any achievements were marked as 0 (negative innovation ability), totaling 276 students. The positive-to-negative sample ratio was approximately 1:1.77, indicating a significant class imbalance.

[0198] To adapt to the training requirements of convolutional neural networks, a systematic image transformation and data augmentation were performed on the original grade data. First, a one-to-one mapping relationship was established between 123 courses and RGB colors, with each course assigned a unique RGB color value (R, G, B all between 0 and 255). The grades for each student record were converted into RGB histogram images: the horizontal axis represents the course number (0 to 122), and the vertical axis represents the course grade (0 to 100). Each small rectangle corresponds to a course, with the color being the pre-assigned RGB color for that course, and the height proportional to the grade. To address the small sample size problem of the original 432 records, which is insufficient for deep learning training, a data augmentation method based on feature rearrangement was adopted: 200 unique course sequences (random permutations of 0 to 122) were randomly generated for each student record, and a histogram image was generated for each sequence, resulting in a total of 432 × 200 = 86,400 image samples. The training set consists of 100 records, including 50 students with a label of 1 and 50 students with a label of 0, generating 20,000 images (16,000 for training and 4,000 for validation). The test set consists of the remaining 332 records, generating 66,400 images for final performance evaluation.

[0199] The model is built upon a ResNet18 convolutional neural network, employing transfer learning to load pre-trained ImageNet weights, freezing convolutional layer parameters, and replacing the classifier head with a binary classification output. To address the class imbalance problem, a weighted FocalLoss loss function is used, with positive and negative sample weights set to approximately 1.38 and 0.78, respectively. During training, optimization strategies include hierarchical learning rates (higher learning rate for the classifier head than the backbone network), cosine annealing learning rate scheduling, and gradient pruning. Experimental results on the test set after training demonstrate that the proposed method achieves 82.76% accuracy, 82.88% precision, 82.76% recall, and an F1 score of 82.92%.

[0200] Comparative experiments with traditional tabular data modeling methods further validated the effectiveness of our proposed method. Under identical training / validation / test set partitioning, XGBoost achieved an accuracy of 80.23%, precision of 79.34%, recall of 80.09%, and an F1 score of 79.61%; CatBoost achieved the same metrics as XGBoost; Multilayer Perceptron (MLP) achieved an accuracy of 80.23%, precision of 80.23%, recall of 81.62%, and an F1 score of 80.01%; SimCLR achieved an accuracy of 75.58%, precision of 74.82%, recall of 75.74%, and an F1 score of 75.01%; and TabNet achieved an accuracy of 72.09%, precision of 72.30%, recall of 67.76%, and an F1 score of 68.23%. In comparison, our proposed method outperforms traditional methods across all metrics. Compared to the high-performing XGBoost and CatBoost, it improves accuracy by 2.53%, precision by 3.54%, recall by 2.67%, and F1 score by 3.31%. Regarding training time, our method requires only 0.23 seconds per prediction, which is superior to XGBoost (0.37 seconds), CatBoost (0.41 seconds), SimCLR (1.59 seconds), and TabNet (4.41 seconds). This embodiment fully validates the effectiveness of the proposed method in identifying students' innovation and entrepreneurship abilities. It can intelligently distinguish the strength of students' innovation abilities based on course performance data, providing quantifiable technical support for universities to accurately assess students' innovation abilities and optimize talent training programs.

[0201] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0202] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A nonlinear data visualization method based on deep transfer learning visual recognition capability, characterized in that, Includes the following steps: Step 1: Perform feature rearrangement operation on the n-dimensional feature vector. Based on a fixed random seed, select p representative rearrangement methods to generate the corresponding rearranged feature vector. The fixed random seed ensures that the rearrangement process and experimental results are reproducible. Step 2: Perform color encoding operation. Assign a unique RGB color to each feature through a color mapping function. The L2 distance between the corresponding RGB colors of any two different features is not less than 0.3, ensuring that the convolutional neural network can effectively distinguish different feature regions. Step 3: Perform a spatial mapping operation to map the rearranged feature vectors into a standard 224×224×3 bar chart image. The horizontal axis corresponds to the rearranged feature index, and the vertical axis corresponds to the normalized feature value. Feature value normalization is achieved by subtracting the minimum value of the rearranged feature vector from the current feature value, dividing by the difference between the maximum and minimum values ​​of the rearranged feature vector, and then multiplying by 224. This method matches the input requirements of the pre-trained convolutional neural network.

2. The method of non-linear data visualization of claim 1, wherein, After completing feature rearrangement, color encoding, and spatial mapping, the image generation preprocessing process is executed, which includes: separating the classification labels from the original feature vectors to generate independent label files; generating p rearranged feature sequences for a single sample based on a fixed seed permutation mechanism; converting each rearranged feature vector into a bar chart image with corresponding color encoding; and constructing a three-level folder structure to store all generated images, enabling batch loading and efficient management of image data.

3. The method of non-linear data visualization of claim 2, wherein, The color encoding function from the training phase is fully reused in the test data processing phase to ensure that the RGB colors of the same feature mapping in the test set and the training set are completely consistent. The p feature permutation methods determined by the fixed random seed during the training phase are reused to generate multi-view feature sequences for test samples. Test images are stored using a three-level folder structure consistent with the training data to ensure that the test images and training images have the same data format; the feature dimensions of the test dataset are completely consistent with the feature dimensions of the training dataset.

4. A nonlinear data classification method based on deep transfer learning visual recognition capabilities, characterized in that, After generating image data based on the nonlinear data visualization method according to any one of claims 1 to 3, a progressive transfer learning architecture is built to complete the classification. This architecture uses a pre-trained ResNet18 model as the backbone feature extractor and implements the following core strategies: The training and validation sets are strictly separated based on personnel IDs to prevent data leakage during the training and evaluation phases. A layered learning rate strategy is adopted, allocating a learning rate of 10 to the power of -3 to the pre-trained backbone network and a learning rate of twice that of the backbone network to the newly added balanced classifier head. A progressive unfreezing strategy with parameter control is implemented, initially freezing all parameters of the backbone network, first unfreezing the classifier head, and then gradually unfreezing parameters layer by layer from Layer 4 to Layer 3 of the backbone network according to the target total number of trainable parameters of 2.5 million, controlling the model complexity and preventing overfitting.

5. The nonlinear data classification method according to claim 4, characterized in that, The parameter calculation method of the progressive unfreezing strategy is as follows: First, count the total number of parameters of the balanced classifier head. Subtract the number of classifier head parameters from the total number of trainable parameters of 2.5 million to obtain the number of parameters to be unfrozen in the backbone network. First, iteratively unfreeze the parameters of Layer 4. When the unfrozen parameters are still positive after deducting the number of unfrozen parameters, continue to unfreeze the parameters of Layer 3 until the number of parameters to be unfrozen is less than or equal to 0.

6. The nonlinear data classification method according to claim 4, characterized in that, During the model training phase, data augmentation strategies were implemented, with online augmentation performed on the training images in real time. Geometric transformations included random cropping to 224×224 pixels, random horizontal flipping with a probability of 0.3, and random rotation within the range of -5 degrees to 5 degrees. Color jitter included adjusting the brightness and contrast factors to 0.

2. The validation and test sets only underwent 224×224 resizing and normalization operations. All images were normalized using the ImageNet dataset mean of 0.485, 0.456, 0.406 and standard deviation of 0.229, 0.224, 0.

225.

7. The nonlinear data classification method according to claim 6, characterized in that, During the training phase, a class-weighted cross-entropy loss function is introduced to address the class imbalance problem. The class weight is the total number of training samples divided by twice the number of samples in the corresponding class. The weighted cross-entropy loss is calculated based on the batch size, true label, predicted probability, and corresponding class weight. A cosine annealing learning rate scheduling strategy is used to optimize the learning rate. The minimum learning rate is set to 10 to the power of -5, and the learning rate is dynamically adjusted with the number of training rounds. Implement early stopping and gradient clipping strategies. The early stopping strategy monitors the performance on the validation set and stops training if there is no performance improvement for 5 consecutive rounds. The gradient clipping strategy sets the gradient norm threshold to 0.5 to suppress gradient explosion.

8. A nonlinear data classification system based on deep transfer learning visual recognition capabilities, characterized in that, include: A data visualization module is used to execute the nonlinear data visualization method according to any one of claims 1 to 3, converting the original numerical nonlinear features into a spatial structure image that conforms to the input standard of a pre-trained convolutional neural network. The transfer learning classification module is used to build the progressive transfer learning architecture as described in any one of claims 4 to 7, load the image data output by the visualization module, and complete the model training and nonlinear data classification tasks.

9. The nonlinear data classification system according to claim 8, characterized in that, The data visualization module has a built-in rearrangement unit, encoding unit, and mapping unit. The rearrangement unit is used to perform feature rearrangement operations with a fixed seed, the encoding unit is used to perform feature RGB color encoding operations, and the mapping unit is used to convert the rearranged and encoded features into a standard-sized bar chart image.

10. The nonlinear data classification system according to claim 8, characterized in that, The transfer learning classification module includes a parameter control unit and a training optimization unit. The parameter control unit is used to perform hierarchical learning rate allocation and progressive parameter unfreezing operations, while the training optimization unit is used to implement data augmentation, class balancing, learning rate scheduling, and training stability assurance operations.

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