High-order polynomial layer driven multi-view clustering representation learning method and system

Abstract

The invention discloses a multi-view clustering representation learning method and system driven by a high-order polynomial layer, relates to the field of multi-view clustering, and endows a model with the ability of learning nonlinear information by introducing a high-order term on the basis of a full connection layer. Meanwhile, a dynamic weight matrix is adopted to balance the relation between a nonlinear high-order term and a linear transformation term. Besides, a normalization process is embedded in a full-connection layer, so that the layer (a polynomial linear layer) is associated with the feature number of input data, and the calculation stability of the model is further improved. Finally, an HOCN representation learning framework based on quadratic polynomial and polynomial linearity is constructed and used for mining potential feature information in view data; experimental results developed on six public data sets show that the method provided by the invention shows excellent clustering performance.

Description

Technical Field

[0001] This invention belongs to the field of multi-view clustering, and more specifically, it relates to a multi-view clustering representation learning method and system driven by high-order polynomial layers. Background Technology

[0002] With the rapid development and widespread application of multimedia technology, a large amount of data from multiple sources is collected and described with different attributes. These data types include images, videos, text, and sensor data, forming rich multi-view information. Multi-View Clustering (MVC) aims to utilize the diverse perspectives of data and improve the accuracy and robustness of clustering by fusing information from different views. This method can not only effectively capture the characteristics of each view but also mine consensus information between views, thereby revealing the inherent structure and patterns of the data more deeply. Based on the type of technology used, current research broadly divides mainstream multi-view clustering methods into two categories: traditional methods and deep learning methods.

[0003] Traditional multi-view clustering (MVC) methods can be broadly categorized into three types from a technical perspective: subspace-based multi-view clustering methods, matrix factorization-based multi-view clustering methods, and graph learning-based multi-view clustering methods. However, traditional MVC methods typically face the following challenges: high computational complexity, sensitivity to noise and outliers, and poor scalability. These limitations significantly impact their performance in handling complex data scenarios, making them unsuitable for the demands of big data environments.

[0004] To address the shortcomings of traditional multi-view clustering, researchers have proposed deep multi-view clustering (DMVC). DMVC leverages deep learning techniques to enhance data representation capabilities, effectively capturing the underlying structures in complex data and improving robustness against noise and outliers. Furthermore, DMVC significantly improves computational efficiency through parallel processing and optimized algorithm design, making it more feasible for large-scale datasets.

[0005] While significant progress has been made in existing deep multi-view clustering methods, several unresolved issues remain. In mainstream representation learning frameworks, fully connected layers based on linear transformations are directly connected to the view data. Since the features in the view data are actually composed of both linear and nonlinear information, and fully connected layers can only capture linear features but not effectively nonlinear features, subsequent dimensionality reduction and the nonlinear activation functions applied in the representation learning framework are based on the linear features obtained from the fully connected layers. Therefore, this issue leads to a lack of nonlinear relationships in the original view data within the feature information obtained from the original data. This ultimately affects downstream clustering tasks.

[0006] Multi-view clustering is attracting increasing attention due to its ability to extract consensus semantic information from multiple views. In existing frameworks, the fully connected layers directly connected to the view data are limited by their linear transformation characteristics, only able to capture linear features in the data. In representation learning frameworks, subsequent dimensionality reduction operations and activation functions are actually based on these linear features. This makes it difficult for the representation learning framework to capture the crucial non-linear information in the original data. This problem directly leads to limited model performance in complex data scenarios. Summary of the Invention

[0007] To address the problems in related technologies, this invention proposes a high-order polynomial layer-driven multi-view clustering representation learning method and system to overcome the aforementioned technical problems in existing related technologies.

[0008] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0009] This invention is a high-order polynomial layer-driven multi-view clustering representation learning method, comprising the following steps:

[0010] S1. Normalize the current view data sample to obtain the current processed view data sample;

[0011] S2. Construct a nonlinear transformation and a linear layer based on the current processed post-view data samples, and construct a high-order representation network based on the nonlinear transformation and the linear layer; the nonlinear transformation includes a weight matrix of high-order terms and linear terms;

[0012] S3. Perform a pre-training operation on the high-order feature network using a nonlinear transformation and set an overall feature contrast loss function between the view training samples for formal training of the pre-trained high-order feature network.

[0013] S4. Calculate the classification labels of the view training samples based on the overall feature contrast loss function and perform contrastive learning to dynamically adjust and optimize them to obtain the optimized classification labels; use the view training samples and the optimized classification labels to formally train the pre-trained high-order feature network to obtain the final high-order feature network.

[0014] S5. Input the current processed view data sample into the final high-order feature network to perform view clustering operation, and obtain the current high-order view features and the current data label.

[0015] Preferably, step S1 includes the following steps:

[0016] S11. Set the current view data sample; perform normalization processing on the current view data sample to obtain the current processed view data sample; the normalization processing formula is as follows.

[0017]

[0018] In the formula, x represents the mean of the current view data samples, N represents the total number of current view data samples, and x represents the mean of the current view data samples. i MAX(x) represents the i-th data sample in the current view data sample, and MAX(x) represents the maximum value sample in the current view sample; X represents the normalized view data, and x represents the current view data sample.

[0019] This invention, through standardization, or normalization, enables the model to better capture the inherent structure of the data without being affected by specific feature scales, thus helping to improve the model's generalization ability.

[0020] Preferably, step S2 includes the following steps:

[0021] S21. Construct a nonlinear transformation and a linear layer (PolynomialLinear) for the currently processed post-view data sample. The expression for the nonlinear transformation is as follows:

[0022] y = ax 2 +bx+c (11)

[0023] In the formula, a and b are coefficient weight matrices, and c is a bias term;

[0024] S22. Construct high-order characteristic networks (HOCN) based on the nonlinear transformation and linear layers;

[0025] The high-order feature network introduces higher-order terms, enabling the model to learn nonlinear features in the original view data and dynamically adjust the balance between nonlinear and linear information through a learnable weight matrix. Finally, the network improves the model's adaptability to complex data and achieves better feature modeling for downstream clustering tasks.

[0026] Preferably, step S22 includes the following steps:

[0027] S221. Construct a high-order feature network; introduce the nonlinear transformation into the encoding layer of the high-order feature network, and use the linear layer as the linear layer of the high-order feature network.

[0028] Preferably, step S3 includes the following steps:

[0029] S31. The high-order feature network is pre-trained using a nonlinear transformation to obtain a pre-trained high-order feature network.

[0030] S32. Set training view data samples; set the overall feature contrast loss function among the samples in the training view data samples.

[0031] Preferably, the formal training operation of the pre-trained high-order feature network in step S32 includes the following steps:

[0032] S321. Employ reconstruction loss to constrain the pre-trained high-order feature network model and capture view features. The reconstruction loss formula is as follows.

[0033]

[0034] In the formula, X v Indicates input data, Z represents reconstructed data. v This represents the feature information of the captured v-th view, where V represents the total number of captured views; Loss Rec Represents the reconstruction loss; HDecoder and HEncoder represent two modules of the high-order feature network model, respectively. It is an F-norm constraint; This represents the reconstruction loss of the v-th view;

[0035] S322. Construct a feedforward neural network G(·) shared by multiple views, and use the feedforward neural network to analyze view features. Compression processing is performed to obtain the processed feature information. The specific process is as follows:

[0036] H v =G(Z) v ;ρ v (13)

[0037] Where, ρ v H is a hyperparameter of the feedforward neural network. v To process the feature information of the v-th view;

[0038] S323. Set the processed feature information. The overall feature contrast loss function among all samples.

[0039] Preferably, step S323 includes the following steps:

[0040] S3231. Feature information processed using cosine similarity calculation The similarity between different samples in the mid-view; the calculation formula is as follows.

[0041]

[0042] In the formula, and These are feature samples from two different views; express and The dissimilarity function between them; τ F The temperature coefficient of the function; express and Cosine similarity between them;

[0043] S3232. Based on the similarity between different samples in the views calculated in S3231, set the overall feature contrast loss function; as follows.

[0044]

[0045] In the formula, Loss Feature This represents the overall feature contrast loss function.

[0046] Preferably, step S4 includes the following steps:

[0047] S41. Calculate the processed feature information based on the overall feature contrast loss function. The classification label Q of each sample v ;

[0048] S42, regarding the classification label Q v Comparative learning is used to dynamically adjust and optimize the classification labels, resulting in optimized classification labels.

[0049] S43. Set the maximum number of training iterations; perform formal training on the pre-trained high-order feature network based on the maximum number of training iterations, the overall feature contrast loss function, and the optimized classification labels; when the number of training iterations is greater than or equal to the maximum number of training iterations, end the training and obtain the final high-order feature network.

[0050] Preferably, step S42 includes the following steps:

[0051] S421. Set classification labels for feature samples from two different views.

[0052] S422, Setting Calculation The loss function for the difference in values ​​between the two categories is denoted as the classification label loss function; as follows:

[0053]

[0054] In the formula, τ LThis represents the temperature coefficient within the classification label loss function; express Cosine similarity between them;

[0055] S423. Apply additional constraints to the classification label loss function to obtain the constrained classification label loss function, as follows:

[0056]

[0057] in, This represents the probability that the i-th sample in the v-th view data belongs to the j-th cluster category. This indicates the importance of category j in this view;

[0058] S424. Construct a contrastive loss function for clustering based on the classification label loss function and the constrained classification label loss function; as follows.

[0059]

[0060] Loss S It is used as a regularization term to deal with special cases and improve the robustness of the model.

[0061] A high-order polynomial layer-driven multi-view clustering representation learning system includes a current view data sample preprocessing module, a high-order representation network construction module, a high-order representation network pre-training loss function setting module, a view training sample classification label optimization module, a high-order representation network training module, and a current view data clustering module.

[0062] The present invention has the following beneficial effects:

[0063] 1. This invention introduces higher-order terms on top of fully connected layers, endowing the model with the ability to learn nonlinear information. Simultaneously, a dynamic weight matrix is ​​used to balance the relationship between the nonlinear higher-order terms and the linear transformation terms. Furthermore, a normalization process is embedded in the fully connected layers to establish a correlation between this layer (the polynomial-linear layer) and the number of features in the input data, thereby improving the computational stability of the model. Finally, a HOCN representation learning framework based on quadratic polynomials and polynomial linearity is constructed to mine latent feature information in view data. Experimental results on six public datasets demonstrate that the proposed method exhibits superior clustering performance.

[0064] 2. In this invention, HOCN adds higher-order operations to the traditional linear transformation. By dynamically adjusting the weights of linear and higher-order terms through a learnable weight matrix, a balance is achieved between complex nonlinear features and linear features. Secondly, local normalization is embedded into the fully connected layer to adapt the behavior to the number of input features, thereby improving the stability of the model. By endowing the model with the ability to learn nonlinear information and balancing nonlinear higher-order terms and linear transformation terms through a dynamic weight matrix, more comprehensive feature modeling is achieved during the feature learning process.

[0065] 3. In this invention, a novel polynomial linear transformation layer is constructed based on a fully connected layer. By embedding a normalization process, the behavior of this layer (polynomial) is adapted to the number of input features, thereby improving the stability of the model.

[0066] 4. In this invention, by assigning independent weights to higher-order terms and linear terms, the nonlinear and linear features in the captured information are balanced, thereby fully capturing the view feature information.

[0067] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0068] To more clearly illustrate the technical solutions of the embodiments of the invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0069] Figure 1 This invention relates to QuadraticLinear and traditional linear tomography.

[0070] Figure 2 This is a schematic diagram of the working structure of the QuadraticLinear of this invention;

[0071] Figure 3 This is a structural diagram of the PolynomialLinear of the present invention;

[0072] Figure 4 This is a structural diagram of the HOCN of the present invention;

[0073] Figure 5The following are visualization results of the datasets of this invention: (a) represents the visualization result of the MNIST-USPS dataset, (b) represents the visualization result of the NoisyMNIST-70000 dataset, (c) represents the visualization result of the Fashion dataset, (d) represents the visualization result of the Hdigit dataset, and (e) represents the visualization result of the Caltech-5V dataset.

[0074] Figure 6 Loss of this invention Rec A graph showing the change in training iterations as the number of training sessions increases;

[0075] Figure 7 This is a graph showing the increase of the loss of this invention with the number of training iterations;

[0076] Figure 8 This is a graph showing how the evaluation metrics of this invention change with the number of training iterations;

[0077] Figure 9 The graph shows the variation of ACC of the MLFVC and HOCN models on Caltech-5V as a function of training iterations.

[0078] Figure 10 The view feature Z obtained by this invention on the 200th training iteration. v Clustering visualization;

[0079] Figure 11 The view feature Z obtained by this invention on the 211th training iteration. v Clustering visualization;

[0080] Figure 12 The view feature Z obtained by this invention on the 221st training iteration. v Clustering visualization;

[0081] Figure 13 The view feature Z obtained by this invention on the 241st training iteration. v Clustering visualization;

[0082] Figure 14 The view feature Z obtained at the 200th training iteration of MFLVC v Clustering visualization;

[0083] Figure 15 The view feature Z obtained at the 211th training iteration of MFLVC v Clustering visualization;

[0084] Figure 16 The view features Z obtained at the 221st training iteration of MFLVC v Clustering visualization;

[0085] Figure 17 The view feature Z obtained after the 241st training iteration of MFLVC v Clustering visualization;

[0086] Figure 18 The view feature H obtained by this invention on the 200th training iteration v Clustering visualization;

[0087] Figure 19 The view feature H obtained by this invention on the 211th training iteration v Clustering visualization;

[0088] Figure 20 The view feature H obtained by this invention on the 221st training iteration. v Clustering visualization;

[0089] Figure 21 The view feature H obtained by this invention on the 241st training iteration. v Clustering visualization;

[0090] Figure 22 The view features H obtained in the 200th training iteration of MFLVC v Clustering visualization;

[0091] Figure 23 The view features H obtained at the 211th training iteration of MFLVC v Clustering visualization;

[0092] Figure 24 The view features H obtained in the 221st training iteration of MFLVC v Clustering visualization;

[0093] Figure 25 The view features H obtained during the 241st training iteration of MFLVC v Clustering visualization; Detailed Implementation

[0094] The technical solutions of the embodiments of the invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the invention, and not all embodiments. Based on the embodiments of the invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the invention.

[0095] Example 1

[0096] This embodiment presents a high-order polynomial layer-driven multi-view clustering representation learning method, proposing a novel feature network—high-order characteristic networks (HOCN). This network introduces higher-order terms, enabling the model to learn nonlinear features from the original view data, and dynamically adjusts the balance between nonlinear and linear information through a learnable weight matrix. Finally, this network improves the model's adaptability to complex data, achieving superior feature modeling for downstream clustering tasks.

[0097] In view data, feature information typically consists of complex nonlinear and linear features. A common linear layer extracts feature information from the original data through a basic linear transformation (y = wx + b), and assigns features using an activation function to achieve nonlinearity. However, this feature derivation method, primarily based on linear transformations, may not effectively capture the nonlinear relationships in the original data, limiting the feature's ability to represent the original view data. Therefore, before introducing activation functions, we need to simultaneously acquire both nonlinear and linear features to enhance the model's representational power.

[0098] Specifically, we explicitly introduce a non-linear transformation within the encoding layer to achieve better feature modeling, as expressed below:

[0099] y = ax 2 +bx+c (19)

[0100] Where x is the input data, a and b are coefficient weight matrices, and c is the bias term. Compared to linear layers, it achieves nonlinear transformation of information by introducing higher-order terms and balances nonlinear and linear features through the coefficient matrix, thereby capturing view feature information as comprehensively as possible. The difference between it and basic linear transformations is as follows: Figure 1 As shown. Therefore, we define it as:

[0101] y=QuadraticLinear(x;{a,b,c}) (20)

[0102] To visualize the QuadraticLinear workflow, we drew its structure diagram, as follows: Figure 2 shown.

[0103] Specifically, before inputting the data into a higher-order polynomial expression, we need to normalize the input data as follows:

[0104]

[0105] in MAX(x) represents the mean of the current view data samples, and MAX(x) represents the maximum value sample in the current view. X represents the standardized view data. Since different features may have different scales and distributions, the input data is standardized. Without standardization, some features may excessively influence the model's learning, causing the model to be highly dependent on these features. This could make the model's training unstable. Standardization allows the model to better capture the inherent structure of the data without being affected by specific feature scales, thus improving the model's generalization ability. Subsequently, the standardized input data is fed into a higher-order polynomial expression. Since the features in the original view data are not entirely composed of nonlinear or linear features, but rather both, independent weights need to be assigned to the higher-order and linear terms to balance the nonlinear and linear features in the captured information, thereby fully capturing the view feature information.

[0106] Similarly, the linear layer in our model also needs to normalize the data, so we designed a new linear layer, PolynomialLinear, with the following structure: Figure 3 shown.

[0107] Finally, a high-order representation network (HOCN) is constructed based on PolynomialLinear and QuadraticLinear, and the structure of HOCN is as follows: Figure 4 shown.

[0108] Our HOCN consists of two modules: HOCNEncoder (HEncoder) and HOCNDecoder (HDecoder). In the experimental section, besides the construction method shown in the figure, we also tried several other HOCN construction methods and conducted comprehensive experiments and comparative analyses. During the training of HOCN, we also used reconstruction loss to constrain the model and capture view features.

[0109]

[0110] Where X v Indicates input data, X v Z represents reconstructed data. v This represents the feature information of the captured v-th view, where V represents the total number of captured views; Loss Rec Represents the reconstruction loss; HDecoder and HEncoder represent two modules of the high-order feature network model, respectively. It is an F-norm constraint; This represents the reconstruction loss of the v-th view.

[0111] Compared with mainstream autoencoders, the viewpoint features obtained by the designed HOCN are more reasonable and effective. We analyze the possible reasons as follows: (1) The introduction of higher-order nonlinear transformation enables this layer to capture the nonlinear features of the input data, rather than assigning nonlinear relationships to linear features through activation functions; (2) By using a learnable weight matrix, the relationship between higher-order terms and linear terms is dynamically adjusted to achieve a balance between complex nonlinear features and linear features; (3) The normalization process is embedded on the basis of the linear layer, so that the behavior of the model has a multinomial linear relationship with the number of input features, which improves the stability of the model. We also conducted relevant experiments and analyses in Section 4.

[0112] 3.3. Multi-view comparison learning

[0113] To enable the model to focus on learning the common semantic information of all views in multi-view data and to improve the robustness of the model and the performance of downstream clustering tasks, we will adopt non-fusion contrastive learning to achieve this goal.

[0114] First, the view feature Z obtained through HOCN v There may be some information redundancy in the data, which could affect the model's performance to some extent, leading to a decrease in the model's generalization ability when processing new data. Therefore, a feedforward neural network G(·) shared by multiple views was designed. By compressing the features, information redundancy is effectively reduced, thereby extracting more refined and useful feature representations. The specific process is as follows:

[0115] H v =G(Z) v ;ρ v ), (twenty three)

[0116] Where ρ v H is a hyperparameter of the feedforward neural network. v To process the feature information of the v-th view, H is learned through contrastive learning. v This invention learns consistent semantic information across different view data. Furthermore, it uses cosine similarity as a metric to measure the similarity between different features, defined as follows:

[0117]

[0118] Where (·) represents the dot product operator, and ||·|| represents the modulus length operator. Using cosine similarity, we can calculate the similarity between different samples of different views; therefore, feature samples from different views... and The dissimilarity function between them can be expressed as:

[0119]

[0120] Where τ F Let be the temperature coefficient of the function, therefore the overall feature contrast loss function can be expressed as:

[0121]

[0122] Meanwhile, considering that the same sample may be misclassified in different views in multi-view data, it is necessary to ensure that the same sample belongs to the same category in different views to enhance the robustness of the model. Specifically, we start from Z... v Calculate the category label Q v And it is dynamically adjusted and optimized through comparative learning. Therefore, referring to expression (25), we can represent the loss function as follows:

[0123]

[0124] Similar to τ L This also represents the temperature coefficient within the function. In the context of clustering, especially when all samples are assigned to a single cluster, it is necessary to impose additional constraints on the loss function:

[0125]

[0126] in This represents the probability that the i-th sample in the v-th view data belongs to the j-th cluster category. The loss function represents the importance of category j in this view. S It is used as a regularization term to deal with special cases and improve the robustness of the model.

[0127] Therefore, the contrastive loss function for clustering is defined as follows:

[0128]

[0129] In current multi-view clustering, feature processing methods are mainly divided into two categories: feature fusion and non-fusion. In this chapter, we construct a framework based on a non-fusion deep multi-view contrastive clustering framework. However, from a purely theoretical perspective, we cannot determine the effectiveness of the proposed Higher-Order Contrast Network (HOCN) in feature-fusion multi-view clustering. Therefore, in the experimental section, we added extended experiments, porting HOCN to a feature-fusion multi-view clustering algorithm and validating it experimentally. Experimental results demonstrate the effectiveness and portability of the proposed HOCN in feature-fusion scenarios. In summary, our overall loss function is as follows:

[0130] Loss = Loss Rec +Loss Feature +LosLabel (30)

[0131] 3.4. Optimization

[0132] Algorithm 1 summarizes the entire optimization process of MFLVC-HOCN, and the specific process is shown in Algorithm 1.

[0133]

[0134] 4. Experiment

[0135] Experiments were conducted on five datasets and compared with other clustering methods. Furthermore, we analyzed the experimental results and evaluated the convergence of the proposed method.

[0136] 4.1. Experimental Setup

[0137] 4.1.1. Dataset

[0138] To verify the performance of the algorithm, we conducted extensive experiments on five different public datasets, the specific parameters of which are shown in Table 1.

[0139] Table 1. Relevant information about the dataset in the experiment.

[0140] Dataset Name Sample size Number of views Number of categories MNIST-USPS 5,000 2 10 Fashion 10,000 3 10 Caltech-4V 1,400 4 7 Caltech-5V 1,400 5 7 Hdigit 10,000 2 10 NoisyMNIST 70,000 2 10

[0141] MNIST-USPS: The MNIST-USPS dataset is an image dataset for handwritten digit recognition that combines two very well-known handwritten digit datasets: a modified version of the National Institute of Standards and Technology (MNIST) and the United States Postal Service (USPS). These two datasets have different features and sources and are commonly used to train and evaluate the performance of machine learning and deep learning models. This dataset contains 5000 samples and two different types of digit images.

[0142] The Fashion:Fashion dataset is a standard dataset for clothing image classification, designed to provide challenging tasks for machine learning and deep learning models. This dataset is primarily used to evaluate the performance of models in image classification tasks. Typically, three different styles in the dataset are treated as three views of the same sample, thereby improving the model's ability to learn and recognize different clothing styles.

[0143] Hdigit: The Hdigit dataset is an image dataset for handwritten digit recognition, primarily used to test and evaluate the performance of machine learning and deep learning models on handwritten digit classification tasks. This dataset aims to provide diverse handwritten character samples to facilitate researchers' experimentation with different models and algorithms.

[0144] NoisyMNIST: The NoisyMNIST dataset is an extension of the classic MNIST handwritten digit dataset, designed to test the robustness and adaptability of machine learning and deep learning models for digit recognition tasks by introducing various types of noise. This dataset contains 70,000 28x28 pixel grayscale images, each labeled with a corresponding handwritten digit (0-9).

[0145] The Caltech:Caltech-5V dataset is part of a computer vision research project at Caltech, typically used for image classification and object recognition research. It is primarily used to test and evaluate the performance of computer vision algorithms. Caltech-4V includes WM, CENTRIST, LBP, and GIST; Caltech-5V includes WM, CENTRIST, LBP, GIST, and HOG.

[0146] To help readers understand the composition of the dataset more intuitively, we have visualized the dataset above, as shown below. Figure 5 shown.

[0147] 4.1.2. Experimental Setup

[0148] In the experiment, the parameter sequence used by our high-order feature representation network (HOCN) is consistent with the parameters used by the autoencoders in MLFVC and SCMVC to ensure consistency under objective conditions.

[0149] 4.1.3. Comparison Algorithm

[0150] We compared the proposed HOCN algorithm with seven other deep clustering algorithms. To demonstrate the superiority of each algorithm, we fine-tuned the parameters to achieve optimal performance. A brief description of the experimental algorithms follows:

[0151] DEMVC: The Deep Embedded Multi-View Clustering and Co-Training (DEMVC) algorithm proposed in this invention independently learns the embedded representations of multiple views through a deep autoencoder. Combined with a novel co-training mechanism, it fully considers the consistency and complementarity among multiple views, thereby improving clustering performance. Furthermore, an improved consistency strategy is used to initialize cluster centers, further optimizing the clustering effect.

[0152] SiMVC and CoMVC: Current deep multi-view clustering models suffer from several shortcomings in view representation distribution alignment, leading to reduced cluster separability in the representation space and inhibiting view prioritization within the model. This invention proposes a simple baseline model that completely avoids representation alignment while achieving performance comparable to or better than existing state-of-the-art methods. A contrastive learning component is added to the baseline model, introducing a selective alignment process that preserves the model's ability to prioritize views.

[0153] APADC: This invention proposes a deep IMVC (Incomplete Multi-View Clustering) method that addresses two major problems in existing methods. The proposed APADC algorithm chooses to use an autoencoder to learn the features of each view and utilizes adaptive feature projection to bypass the imputation of missing data.

[0154] MFLVC: This invention proposes a novel framework aimed at resolving the conflict between consistent public semantic learning and reconstructing private information from inconsistent views in multi-view clustering. Existing methods often penalize multiple objectives within the same feature space, ignoring this contradiction. This method employs multi-level feature learning to learn low-level features, high-level features, and semantic labels / features separately from the original features, effectively achieving reconstruction and consistency objectives across different feature spaces in a non-fusion manner.

[0155] FMCSC: In this invention, a novel Federated Multi-View Clustering (FedMVC) framework is proposed to address two major challenges in real-world FedMVC scenarios involving heterogeneous hybrid views: client gap and view gap.

[0156] HFMVC: Addressing the privacy concerns of multi-view data in multi-entity environments and the poor performance of existing algorithms in feature representation alignment, information integration, and heterogeneous scenarios, HFMVC proposes a heterogeneity-aware federated deep multi-view clustering method. HFMVC adaptively perceives the heterogeneity of the environment, utilizing contrastive learning to explore the consistency and complementarity information among client-side multi-view data. Furthermore, during local training, HFMVC promotes consensus among local data from the same view by introducing contrast loss between the local and global models.

[0157] SCMVC: This invention proposes a novel self-weighted contrastive fusion framework (SCMVC) for deep multi-view clustering, which aims to resolve the conflict between learning consistent information from views and reconstructing private information from inconsistent views, as well as to mitigate representation degradation caused by achieving consistency goals.

[0158] 4.1.4. Evaluation Indicators

[0159] To evaluate the performance of MFLVC-HOCN, we selected three evaluation metrics: accuracy (ACC), normalized mutual information (NMI), and purity (PUR).

[0160] 4.2. Experimental Content and Analysis

[0161] 4.2.1. Results Analysis

[0162] In comparative experiments, we evaluated the performance of multiple models on different datasets, including MNIST-USPS, Hdigit, Fashion, Caltech-4V, Caltech-5V, and NoisyMNIST-70000. Performance metrics included accuracy (ACC), normalized mutual information (NMI), and purity (PUR). Specific results are shown in Tables 1 and 2. In this experiment, we used an alternating QuadraticLinear and PolynomialLinear structure for the HOCN framework. The performance and analysis of other structures will be detailed below. The experimental results show that introducing the proposed HOCN framework into the MFLVC algorithm achieves best performance on almost all metrics. Especially on the Caltech-5V dataset, in both the four-view scenario (Caltech-4V), MFLVC-HOCN improves performance by approximately 6% compared to the original MFLVC method across the three evaluation metrics (ACC and PUR approximately 73%, NMI approximately 65%). Similarly, in the full 5-view scenario (Caltech-5V), HO CN improves upon the suboptimal MFLVC method by approximately 10% on ACC and PUR, and by approximately 11% on NMI. This improvement is attributed to the addition of higher-order operations to the traditional linear transformation, which effectively captures the complex nonlinearities of the input features and adjusts the dimensionality of the feature space and the weights of higher-order terms through a learnable weight matrix, thereby better learning feature information consistent with the view data.

[0163] Table 2. Clustering results of each method on the MNIST-USPS, Hdigit, and Fashion datasets.

[0164]

[0165]

[0166] Table 3. Clustering results of each method on the Caltech-4V, NoisyMNIST, and Caltech-5V datasets.

[0167]

[0168]

[0169] To further investigate the performance of our designed two-layer QuadraticLinear (Q) and PolynomialLinear (P) encoding frameworks on different public datasets, the results are shown in Tables 4 and 5. It can be seen that the QQQQ model performs best on multiple datasets, especially on the Caltech-5V dataset, exhibiting high accuracy and NMI values, demonstrating an advantage in handling complex data. The QPQP model also performs well on the MNIST-USPS dataset, with an accuracy close to 100%. Although the QPPP and PPQP models perform well in handwritten digit recognition tasks, their performance on the Caltech-5V dataset is relatively weak, showing the limitations of these models when handling complex data. Overall, the QQQQ and QPQP models demonstrate strong robustness and adaptability across different tasks. In summary, we can find that on most datasets, the encoding framework built by higher-order feature representation networks generally achieves better model performance than mainstream autoencoders. This also verifies our conjecture in the previous section that adding higher-order operations to traditional linear transformations can effectively capture the complex nonlinearities of input features. By adjusting the feature space dimension and higher-order term weights using a learnable weight matrix, feature information consistent with the view data can be learned more effectively.

[0170] Table 4. Clustering results of different high-order feature network methods on the MNIST-USPS, Hdigit, and Fashion datasets.

[0171]

[0172]

[0173] Table 5. Clustering results of different high-order feature network methods on the Caltech-4V, NoisyMNIST, and Caltech-5V datasets.

[0174]

[0175] 4.2.2. Convergence Analysis

[0176] like Figure 6 and Figure 7 As shown, these are the Loss Rec The graphs show the changes in loss function with increasing training iterations and the curves showing the loss function with increasing training iterations. It's easy to see that our loss function gradually stabilizes with increasing training iterations, and... Figure 8 As shown, the clustering effect generally increases with the number of training iterations until it gradually stabilizes. In summary, this indicates that the model has good convergence.

[0177] In addition, we also plotted a comparison of the convergence speeds of the original ACC and HOCN models, such as... Figure 9 As shown, replacing the autoencoder with HOCN significantly reduces the number of training iterations required for the model to achieve stable performance. This is likely because in HOCN, local normalization is embedded into the forward propagation process of each network layer, improving computational stability and reducing fluctuations during training. This, in turn, improves the model's convergence speed and overall performance.

[0178] 4.2.3. Visual Analysis of the Training Process

[0179] To visually demonstrate the difference between the view features captured from the raw data by the coding framework composed of high-order representation networks and the feature information learned from view data by mainstream autoencoder frameworks, the Caltech-5V dataset is used as an example to intuitively illustrate the model training process. Since there are two types of features in MFLVC, view features and high-order features, their clustering structures need to be visualized. We will apply the tS NE method to visualize these two types of features separately. Figures 18-21 Visualization results of high-order features of MFLVC-HOCN. Figures 10-13 Visualization results of MFLVC-HOCN view features. Figures 14-17 as well as Figures 22-25 The high-order features and view features in MFLVC are displayed.

[0180] contrast Figures 10-13 and Figures 14-17 We can observe that, compared to MFLVC, which uses an autoencoder framework to obtain view features, MFLVC, which uses an encoding framework composed of high-order feature representation networks, produces a clearer clustering structure. After applying the same contrastive learning method, the discriminative power of each cluster in MFLVC-HOCN is superior to that of MFLVC (e.g., ...). Figure 13 and Figure 17 (As shown). Similarly, compare the visualization of higher-order features. Figures 18-21 and Figures 22-25 We can see that the sample distribution density of higher-order features obtained by the higher-order feature representation network in MFLVC-HOCN is significantly higher than that of MFLVC, which uses an autoencoder framework to obtain view features. Therefore, the higher-order features of MFLVC-HOCN exhibit a superior low-dimensional manifold, with more distinct boundaries between clusters and a relatively lower probability of misclassification (e.g., ...). Figure 21 and Figure 25 (As shown). By adding higher-order operations to the traditional linear transformation, the complex nonlinearity of the input features can be effectively captured. By adjusting the dimension of the feature space and the weights of higher-order terms through a learnable weight matrix, feature information consistent with the view data can be learned more effectively.

[0181] In summary, by comparing the clustering structures of MFLVC and MFLVC-HOCN with different features, we can see the significant advantages of higher-order representation networks in feature extraction and clustering tasks. Introducing higher-order operations not only better captures the complex nonlinear structure of data but also increases the density of sample distribution. This results in clearer cluster boundaries and lower misclassification risk, effectively improving model performance.

[0182] 4.2.4. Ablation Test

[0183] We conducted parameter ablation experiments on the hyperparameter configuration of QuadraticLinear to verify the effectiveness of all components in QuadraticLinear. Table 6 shows the corresponding experimental results in the ablation experiments. (1) Experimental results with complete higher-order terms, linear terms, and bias terms. (2) Final clustering results after removing linear terms. (3) Final experimental results after assigning the same weights to higher-order terms and linear terms. (4) Clustering performance of the original linear layer after removing higher-order terms. From the results, the result of (1) is optimal, far superior to the result of (4), which proves the superiority of our proposed QuadraticLinear over the original fully connected layer in the clustering task. The performance of experimental result (1) is better than that of (2) and (3), proving the effectiveness of balancing complex nonlinear and linear features in the downstream clustering task feature acquisition task. The performance of (2) is better than that of (3), which may be because when nonlinear terms and linear terms are assigned the same weights, it will eventually lead to mutual interference between the two features. This proves the effectiveness of balancing the two functional decisions in QuadraticLinear.

[0184] Table 6. Hyperparameter ablation experiments of QuadraticLinear

[0185]

[0186] 4.2.5 Extended Experiment

[0187] To verify the effectiveness and portability of the proposed High-Order Representation Network (HOCN) in view feature extraction tasks, we conducted experiments on several influential models, and the specific results are shown in Table 7. Experimental results show that the SCMVC-HOCN model using HOCN improves performance on the Caltech-4V, Hdigit, and Caltech-5V datasets. The performance improvement is most significant on the Caltech-4V dataset. The experimental results demonstrate that SCMVC, as a contrast-fusion deep multi-view clustering algorithm, achieves overall performance improvement by replacing the original autoencoder framework with HOCN. Comparative experiments on MFLVC further validate the effectiveness of the HOCN framework in non-fusion deep multi-view clustering algorithms. These experimental results fully demonstrate the wide applicability and superior performance of HOCN in multi-view clustering tasks.

[0188] Table 7. Clustering results expansion experiments performed on the Hdigit, Caltech-4V, and Caltech-5V datasets respectively.

[0189]

[0190]

[0191] 4.2.6. Confirmatory Experiment

[0192] Table 8. Validation experiments on clustering results of each method on the Hdigit, Fashion, and Caltech-5V datasets.

[0193]

[0194] To verify the impact of increasing the order of higher-order terms on feature acquisition quality, cubic and quartic terms were introduced into the mainstream linear layers TubicLinear and FubicLinear, respectively, to construct a single-layer representation learning framework without activation functions for feature acquisition tasks. The clustering performance of models with different orders is shown in Table 8. We can see that QuadraticLinear, based on quadratic terms, achieved the best results on the three datasets used, outperforming traditional linear structures. This may be because Linear, as a fully connected layer built on linear transformations, can only describe linear relationships in complex data. Due to the limited representation capability of nonlinear relationships, and because QuadraticLinear retains linear terms while having nonlinear quadratic terms, it can effectively acquire both linear and nonlinear features when facing complex data environments. By comparing QuadraticLinear, TubicLinear, and FubicLinear, we can find that blindly increasing the order of higher-order terms does not improve the model's representation learning ability. When the order of higher-order terms increases to 4, the model performance significantly decreases. This is likely because as the number of higher-order terms increases, model complexity increases significantly, leading to problems such as overfitting during training (in particular, FubicLinear with quartic terms only achieves 10% success rate on the Hdigit dataset). Appropriately introducing higher-order terms (such as quadratic terms) can significantly improve the model's representation learning ability. Quadratic terms not only capture linear relationships but also effectively model nonlinear relationships, thus performing well in complex data environments. However, blindly increasing the order of higher-order terms does not improve model performance and may even lead to overfitting and performance degradation due to an excessive number of higher-order terms.

[0195] Example 2

[0196] This embodiment discloses a high-order polynomial layer-driven multi-view clustering representation learning system. The system can implement the methods of the above embodiments, including a current view data sample preprocessing module, a high-order representation network construction module, a high-order representation network pre-training loss function setting module, a view training sample classification label optimization module, a high-order representation network training module, and a current view data clustering module.

[0197] The current view data sample preprocessing module performs normalization processing on the current view data sample to obtain the current processed view data sample;

[0198] The higher-order representation network construction module constructs a nonlinear transformation and a linear layer based on the current processed post-view data samples, and constructs a higher-order representation network based on the nonlinear transformation and the linear layer; the nonlinear transformation includes a weight matrix of higher-order terms and linear terms;

[0199] The high-order representation network pre-training loss function setting module uses nonlinear transformation to perform pre-training operation on the high-order feature network and sets the overall feature contrast loss function between the view training samples for formal training of the pre-trained high-order feature network.

[0200] The view training sample classification label optimization module calculates the classification label of the view training sample based on the overall feature contrast loss function and performs contrast learning to dynamically adjust and optimize it, thereby obtaining the optimized classification label.

[0201] The higher-order representation network training module uses view training samples and optimized classification labels to formally train the pre-trained higher-order feature network to obtain the final higher-order feature network.

[0202] The current view data clustering module inputs the current processed view data sample into the final high-order feature network to perform view clustering operations, thereby obtaining the current high-order view features and the current data label.

[0203] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0204] The preferred embodiments of the invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A high-order polynomial layer-driven multi-view clustering representation learning method, characterized in that, The following steps are involved: S1. Normalize the current view data sample to obtain the current processed view data sample; S2. Construct a nonlinear transformation and a linear layer based on the current processed post-view data samples, and construct a high-order representation network based on the nonlinear transformation and the linear layer; the nonlinear transformation includes a weight matrix of high-order terms and linear terms; S3. Perform a pre-training operation on the high-order feature network using a nonlinear transformation, and set an overall feature contrast loss function between the view training samples for formal training of the pre-trained high-order feature network. S4. Calculate the classification labels of the view training samples based on the overall feature contrast loss function and perform contrastive learning to dynamically adjust and optimize them to obtain the optimized classification labels; use the view training samples and the optimized classification labels to formally train the pre-trained high-order feature network to obtain the final high-order feature network. S5. Input the current processed view data sample into the final high-order feature network to perform view clustering operation, and obtain the current high-order view features and the current data label.

2. The high-order polynomial layer-driven multi-view clustering representation learning method according to claim 1, characterized in that, S1 includes the following steps: S11. Set the current view data sample; perform normalization processing on the current view data sample to obtain the current processed view data sample; the normalization processing formula is as follows. In the formula, x represents the mean of the current view data samples, N represents the total number of current view data samples, and x represents the mean of the current view data samples. i MAX(x) represents the i-th data sample in the current view data sample, and MAX(x) represents the maximum value sample in the current view sample; X represents the normalized view data, and x represents the current view data sample.

3. The high-order polynomial layer-driven multi-view clustering representation learning method according to claim 2, characterized in that, S2 includes the following steps: S21. Construct a nonlinear transformation and a linear layer for the currently processed post-view data sample. The expression for the nonlinear transformation is as follows: y=ax 2 +bx+c (2) In the formula, a and b are coefficient weight matrices, and c is a bias term; S22. Construct a high-order representation network based on the nonlinear transformation and the linear layer.

4. The high-order polynomial layer-driven multi-view clustering representation learning method according to claim 3, characterized in that, S22 includes the following steps: S221. Construct a high-order feature network; introduce the nonlinear transformation into the encoding layer of the high-order feature network, and use the linear layer as the linear layer of the high-order feature network.

5. The high-order polynomial layer-driven multi-view clustering representation learning method according to claim 4, characterized in that, S3 includes the following steps: S31. The high-order feature network is pre-trained using a nonlinear transformation to obtain a pre-trained high-order feature network. S32. Set training view data samples; set the overall feature contrast loss function among the samples in the training view data samples.

6. The high-order polynomial layer-driven multi-view clustering representation learning method according to claim 5, characterized in that, The formal training operation of the pre-trained high-order feature network in S32 includes the following steps: S321. Employ reconstruction loss to constrain the pre-trained high-order feature network model and capture view features. The reconstruction loss formula is as follows. In the formula, X v Indicates input data, Z represents reconstructed data. v This represents the feature information of the captured v-th view, where V represents the total number of captured views; Loss Rec Represents the reconstruction loss; HDecoder and HEncoder represent two modules of the high-order feature network model, respectively. It is an F-norm constraint; This represents the reconstruction loss of the v-th view; S322. Construct a feedforward neural network G(·) shared by multiple views, and use the feedforward neural network to analyze view features. Compression processing is performed to obtain the processed feature information. The specific process is as follows: H v =G(Z v ;p v ) (4) Where, p v H is a hyperparameter of the feedforward neural network. v To process the feature information of the v-th view; S323. Set the processed feature information. The overall feature contrast loss function among all samples.

7. The high-order polynomial layer-driven multi-view clustering representation learning method according to claim 6, characterized in that, S323 includes the following steps: S3231. Feature information processed using cosine similarity calculation The similarity between different samples in the mid-view; the calculation formula is as follows. In the formula, and These are feature samples from two different views; express and The dissimilarity function between them; τ F The temperature coefficient of the function; express and Cosine similarity between them; S3232. Based on the similarity between different samples in the views calculated in S3231, set the overall feature contrast loss function; as follows. In the formula, Loss Feature This represents the overall feature contrast loss function.

8. The high-order polynomial layer-driven multi-view clustering representation learning method according to claim 7, characterized in that, S4 includes the following steps: S41. Calculate the processed feature information based on the overall feature contrast loss function. The classification label Q of each sample v ; S42, regarding the classification label Q v Comparative learning is used to dynamically adjust and optimize the classification labels, resulting in optimized classification labels. S43. Set the maximum number of training iterations; perform formal training on the pre-trained high-order feature network based on the maximum number of training iterations, the overall feature contrast loss function, and the optimized classification labels; when the number of training iterations is greater than or equal to the maximum number of training iterations, end the training and obtain the final high-order feature network.

9. The high-order polynomial layer-driven multi-view clustering representation learning method according to claim 8, characterized in that, S42 includes the following steps: S421. Set classification labels for feature samples from two different views. S422, Setting Calculation The loss function for the difference in values ​​between the two categories is denoted as the classification label loss function; as follows: In the formula, τ L This represents the temperature coefficient within the classification label loss function; express Cosine similarity between them; S423. Apply additional constraints to the classification label loss function to obtain the constrained classification label loss function, as follows: in, This represents the probability that the i-th sample in the v-th view data belongs to the j-th cluster category. This indicates the importance of category j in this view; S424. Construct a contrastive loss function for clustering based on the classification label loss function and the constrained classification label loss function; as follows.

10. A system for implementing the high-order polynomial layer-driven multi-view clustering representation learning method as described in any one of claims 1-9.

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