Industrial imbalanced data augmentation method based on topology analysis and manifold sampling

Abstract

The application belongs to the technical field of artificial intelligence, industrial data processing, unbalanced learning and data enhancement, and relates to an industrial unbalanced data enhancement method based on topological analysis and manifold sampling, comprising the following steps: obtaining an industrial data set and preprocessing the same to obtain a preprocessed industrial data set; the preprocessed industrial data set comprises sample sets of multiple categories; topological boundary analysis is performed on each minority-class sample set to obtain a topological summary of each minority class; topological boundary reconstruction and gradual enhancement are performed on each minority-class sample set according to the topological summary of each minority class to obtain candidate enhanced samples of each minority class; and the preprocessed industrial data set and the candidate enhanced samples of all minority classes are combined to obtain an enhanced industrial data set; and the topological boundary sensitive index is jointly constructed by the persistent feature quantity, the neighborhood category heterogeneity degree and the normalized local sparse discrete degree, so that the recognition accuracy of the boundary region needing enhancement is improved.

Description

Technical Field

[0001] This invention belongs to the fields of artificial intelligence, industrial data processing, imbalanced learning and data augmentation technology, and relates to an industrial imbalanced data augmentation method based on topology analysis and manifold sampling. Background Technology

[0002] With the rapid development of artificial intelligence and the industrial internet, machine learning-based data analysis technologies are playing an increasingly important role in fields such as industrial fault detection, financial risk control, medical diagnosis, and quality prediction. However, in practical applications, the class imbalance problem in training data has become a key bottleneck restricting model performance. Especially in industrial scenarios, minority class data, such as fault samples and defective products, are often far fewer than normal samples, with ratios often reaching 1:100 or even lower, resulting in a severe lack of accuracy for traditional machine learning models in identifying minority classes.

[0003] However, the resulting problems include the following: First, the data imbalance problem is severe. In industrial scenarios, the ratio of faulty samples to normal samples often reaches 1:100 or even lower. Traditional classification algorithms are severely inadequate in recognizing minority class samples, and the model's decision boundary is biased towards the majority class, leading to a large number of misclassified minority class samples. Second, boundary region identification is difficult. Minority class samples are often distributed near class boundaries, and these boundary region samples are crucial to model performance. However, existing methods struggle to effectively identify and augment boundary samples, resulting in insufficient discriminative ability of the model in boundary regions. Third, the quality of generated data is low. Existing data augmentation methods may generate synthetic samples that deviate from the true data distribution, introducing noisy samples and even causing class overlap, which actually reduces model performance. Fourth, there is a lack of topological preservation. Most existing methods perform sample interpolation in Euclidean space, without considering the inherent manifold structure and topological features of the data. The generated samples may violate the geometric constraints of the data and do not conform to the distribution patterns of the true data.

[0004] To address the aforementioned issues, various imbalanced data processing schemes have been proposed in existing technologies. SMOTE oversampling is a classic method for handling imbalanced data. Its basic principle is to randomly select a sample from its k nearest neighbors for each minority class sample, and then randomly select a point on the line connecting the two samples as a new synthetic sample. SMOTE and its variants, such as Borderline-SMOTE and ADASYN, generate new samples through linear interpolation between minority class samples, mitigating the data imbalance problem to some extent. Generative Adversarial Networks (GANs) are deep generative models composed of two neural networks: a generator and a discriminator. The generator generates samples from random noise, while the discriminator determines whether a sample is real or generated. The two networks continuously optimize through adversarial training. For tabular data, methods such as CTGAN have specifically designed mechanisms to handle mixed-type data, addressing class imbalance through conditional generation and training sampling strategies. Variational Autoencoders (VAEs) are another important class of deep generative models. VAEs map data to a latent space through an encoder, assuming the latent variables follow a Gaussian distribution. A decoder then reconstructs the data from the latent space. Methods like TVAE apply VAEs to tabular data generation, generating new synthetic samples by sampling from the latent space. Diffusion models are generative models that have emerged in recent years. They generate new samples by progressively adding noise to the data (forward process) and learning to denoise (backward process). Methods like TabSyn combine diffusion models with VAEs, applying the diffusion model to the latent space of the VAE to achieve high-quality tabular data generation. Topological Data Analysis (TDA) is a method that uses algebraic topology tools to analyze the shape and structure of data. Its core tool is persistent homology. By constructing simple complexes such as Rips complexes and calculating topological features (such as connected components, loops, holes, etc.) at different scales, a persistence diagram is obtained to describe the topological structure of the data. Manifold learning assumes that high-dimensional data is distributed on a low-dimensional manifold. It performs dimensionality reduction or data analysis by learning the intrinsic geometric structure of the data. Common methods include Isomap and LLE (Locally Linear Embedding). These methods learn the manifold structure by preserving the geodesic distance or local geometric relationship between data points.

[0005] The following solutions exist for the problem of imbalanced data in existing technologies.

[0006] Patent CN202310034445.0 discloses an industrial imbalance data classification method based on an improved SMOTE. The technical solution of this patent first obtains sample monitoring record data of industrial equipment to form an imbalanced dataset containing numerical features and class labels. Then, the k-nearest neighbor algorithm is used to calculate the k nearest neighbors of each minority class sample and divide the minority class samples into three classes: safe samples, boundary samples, and noise samples according to the proportion of majority class samples in the neighbors. Next, SMOTE oversampling is performed only on the boundary samples. Then, the Local Outlier Factor (LOF) algorithm is used to evaluate the quality of the generated synthetic samples and filter out noise samples with high outlier values. Finally, the filtered synthetic samples are merged with the original dataset to form a relatively balanced training dataset for training the classifier. The shortcomings of this solution are that linear interpolation in Euclidean space may cause the generated samples to deviate from the real data manifold when the data is distributed on a nonlinear manifold. Boundary recognition is based only on the proportion of neighbors and does not consider topological stability. The linear interpolation assumption is too simplified and it is difficult to capture complex class boundary topological features.

[0007] Patent No. CN202311154225.8 discloses a generalized zero-shot fault diagnosis method for industrial processes based on DSECMR-VAE. The technical solution of this patent first collects fault sample data of industrial processes and their corresponding fault semantic attribute vectors. Then, it uses two VAEs to encode the fault sample data and semantic attribute vectors into the latent space respectively. Next, it aligns the latent spaces of the two modes through a cross-modal reconstruction mechanism. For unseen fault classes, it generates synthetic samples through semantic attribute vectors. Finally, it trains a classifier. The shortcomings of this solution are that the random sampling in the latent space based on VAE does not enhance the boundary region, the Gaussian assumption of VAE is too simplified, and the additional semantic attribute vectors are difficult to apply in scenarios lacking prior knowledge.

[0008] CTGAN (Conditional Tabular GAN) is a generative adversarial network specifically designed for tabular data, published at NeurIPS 2019. Its technical approach first uses a Gaussian mixture model for pattern normalization of numerical features and one-hot encoding for categorical features. Then, it designs conditional vectors to specify the class attributes of generated samples and uses a training sampling strategy to handle class imbalance. Next, it inputs random noise vectors and conditional vectors to generate tabular data through a multi-layer fully connected network. PacGAN technology is used to improve training stability. Finally, Wasserstein distance and gradient penalty are used to optimize the adversarial training process. The shortcomings of this approach include the risk of pattern collapse during GAN training, the uniform distribution of generated samples in the feature space without enhancement for boundary regions, instability in the adversarial training process, and the failure to consider the topological structure and manifold geometry of the data.

[0009] TabSyn, published at ICLR 2024, is a tabular data generation method combining VAE and diffusion models. Its technical approach first designs a VAE architecture specifically for handling mixed-type data, training the VAE to map tabular data to a continuous latent space. Then, the training data is mapped to the latent space via a VAE encoder. Next, a score-based diffusion model is trained in the latent space, sampling noise from a standard Gaussian distribution and generating latent representations through the reverse process of the diffusion model. These representations are then decoded into tabular data by a VAE decoder. Finally, numerical features are de-normalized, and categorical features are discretized. The drawbacks of this approach include potentially insufficient sample density in uniformly sampling boundary regions of the latent space, failure to explicitly consider the data's topological structure, and difficulty in effectively enhancing the boundary regions of minority classes in imbalanced data.

[0010] However, the aforementioned solutions all have the following drawbacks:

[0011] 1. Insufficient accuracy in boundary region identification. Patent CN202310034445.0 uses the k-nearest neighbor majority class ratio to determine boundary samples. This method only considers the class distribution of local neighborhoods and does not analyze the stability of boundary regions from the perspective of the global topological structure of the data. When the data distribution is complex or there is noise, it is easy to misclassify samples within a class as boundary samples or miss true boundary samples, resulting in inaccurate selection of target regions for subsequent oversampling. The generated synthetic samples cannot effectively cover the boundary regions that truly need enhancement.

[0012] 2. Sample generation path deviates from the data manifold. Both patent CN202310034445.0 and CTGAN generate samples in Euclidean space. The former uses linear interpolation, while the latter directly maps random noise to the feature space. Both methods assume that the data is uniformly distributed in Euclidean space, without considering that the actual data is often distributed on a low-dimensional nonlinear manifold. When the data manifold is curved or has a complex geometric structure, the straight path in Euclidean space may cross the external region of the manifold. The generated synthetic samples deviate from the true data distribution, introducing out-of-distribution noise samples, which in turn reduces the performance of the classifier.

[0013] 3. Lack of boundary-oriented sampling in the latent space. Both patents CN202311154225.8 and TabSyn use VAE to encode data into the latent space before sampling. However, both of their sampling strategies involve random or uniform sampling in the latent space without targeted enhancement for class boundary regions. This results in the generated samples being uniformly distributed in the latent space, with the sample density in the boundary regions being the same as or even lower than that in the internal regions of the class. This fails to effectively improve the classifier's discriminative ability in the boundary regions and provides limited improvement for the problem of scarce minority class boundary samples in imbalanced data.

[0014] 4. The topological consistency of the generated samples cannot be guaranteed. None of the four existing schemes consider the topological characteristics of the data during the sample generation process. Patent CN202310034445.0 only uses LOF for post-processing noise filtering, patent CN202311154225.8 relies on the reconstruction loss of VAE, CTGAN relies on the adversarial loss of the discriminator, and TabSyn relies on the denoising loss of the diffusion model. These quality control mechanisms cannot guarantee the topological consistency between the generated samples and the original data, which may destroy the original connectivity, loop structure, and other topological features of the data, resulting in a topological difference between the overall distribution of the generated sample set and the original data.

[0015] 5. Lack of a theoretically guided boundary reconstruction framework. Most existing boundary identification and sample generation strategies are based on heuristic design or empirical parameter tuning, lacking rigorous mathematical analysis and theoretical modeling of data boundaries from the perspective of topology and differential geometry. The effectiveness of the methods depends on the specific dataset and parameter settings, resulting in insufficient generalization ability and interpretability.

[0016] Therefore, the technical problem to be solved by this invention is: how to establish a collaborative control mechanism that takes into account topological sensitivity, path reliability, sample credibility and adaptive allocation of augmentation tasks for minority class boundary regions in unbalanced industrial tabular data, so as to improve the augmentation quality and classification recognition ability of minority class boundary samples while maintaining the consistency of local data structure. Summary of the Invention

[0017] To address the aforementioned problems in the prior art, this invention employs an industrial imbalance data augmentation method based on topology analysis and manifold sampling, comprising:

[0018] S1. Obtain the industrial dataset, preprocess the industrial dataset to obtain the preprocessed industrial dataset; the preprocessed industrial dataset includes sample sets of multiple categories;

[0019] S2. Perform topological boundary analysis on the sample sets of each minority class c to obtain the topological summary of each minority class c.

[0020] S3. Based on the topological summary of each minority class c, perform topological boundary reconstruction and progressive enhancement on the sample set of each minority class c to obtain candidate enhanced samples for each minority class c.

[0021] S4. Combining the preprocessed industrial dataset with all candidate augmentation samples of the minority class c, we obtain the augmented industrial dataset.

[0022] Beneficial effects:

[0023] 1. This invention no longer identifies boundary samples solely based on the category ratio in the local neighborhood. Instead, it constructs a topological boundary sensitivity index by combining persistent feature quantity, neighborhood category heterogeneity, and normalized local sparse dispersion, which is used to identify vulnerable regions of the real boundary, thereby improving the identification accuracy of regions that need to be enhanced.

[0024] 2. This invention no longer generates samples solely based on Euclidean linear relationships in the original feature space. Instead, it first establishes a manifold representation that reflects the continuity of the local structure and the reachability of the neighborhood. Then, it constructs candidate paths based on this representation and filters the paths that can be used for generation using the manifold interpolation reliability function. This makes the generated samples more consistent with the local structure orientation and reduces the risk of distribution deviation.

[0025] 3. This invention constructs a unified sample credibility evaluation function, which jointly evaluates candidate samples from four aspects: geometric location rationality, boundary attribute consistency, local structural continuity and numerical stability. In the unified quality control and filtering steps, a consistent retention standard is adopted for different generation tasks, thereby improving the overall quality of generated samples.

[0026] 4. Instead of using a fixed ratio to divide the generation task into three parts: boundary-aware generation, topology-sensitive enhancement, and random supplementation generation, this invention establishes a collaborative enhancement strategy around boundary-aware generation, topology-sensitive enhancement, and random supplementation generation to adaptively allocate enhancement resources. This ensures that the generated resources cover the real boundary transition area, the topology-vulnerable area, and the remaining areas to be supplemented, thereby improving the allocation effect. Attached Figure Description

[0027] Figure 1 A flowchart of an industrial imbalance data augmentation method based on topology analysis and manifold sampling provided in an embodiment of the present invention;

[0028] Figure 2 A flowchart of topology boundary analysis provided for embodiments of the present invention;

[0029] Figure 3 A flowchart of boundary reconstruction and progressive enhancement provided for embodiments of the present invention;

[0030] Figure 4 This is a flowchart of manifold geodesic sampling provided in an embodiment of the present invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] like Figure 1 As shown, this invention employs an industrial imbalance data augmentation method based on topology analysis and manifold sampling, comprising:

[0033] S1. Obtain the industrial dataset, preprocess the industrial dataset to obtain the preprocessed industrial dataset; the preprocessed industrial dataset includes sample sets of multiple categories;

[0034] The industrial dataset consists of one sample per row, and each sample includes: industrial tabular data. and category labels Preprocessing of industrial data includes:

[0035] To eliminate the impact of dimensional differences on neighborhood construction and subsequent topological analysis, the industrial tabular data in each sample were first analyzed. Standardize the numerical features x in the data: .in, The mean of the corresponding feature. is the standard deviation of the corresponding feature.

[0036] Category Labels The same samples are aggregated to obtain sample sets of multiple categories; among them, the categories with a sample number lower than a preset sample number threshold are minority classes.

[0037] S2. Perform topological boundary analysis on the sample sets of each minority class c to obtain the topological summary of each minority class c.

[0038] A topological summary should include at least the following: a set of topological features, the persistence of each topological feature, a set of supporting samples for each topological feature, a sample-level topological boundary sensitivity index, the confidence level of boundary candidates, the final set of boundary candidates, a set of similar neighborhoods, local density, and statistical information on category-level topological complexity.

[0039] like Figure 2 As shown, for each minority class c, the topological boundary analysis of its sample set includes:

[0040] S21. Construct a multi-scale neighborhood topological complex sequence for the minority class c based on the sample set of the minority class c; extract multiple topological features of the minority class c from the multi-scale neighborhood topological complex sequence of the minority class c. Its appearance scale parameter, disappearance scale parameter, and simplex set;

[0041] For mixed industrial data that contains both numerical and categorical features, in order to take into account both numerical differences and categorical attribute differences, this invention uses a hybrid distance to calculate the distance between two samples: ;in, For the sample Normalized numerical distance For the sample Category attribute difference measure The balancing parameter is used to adjust the relative influence of numerical and categorical features. This processing method preserves the continuous variation information of numerical features while taking into account the influence of categorical attributes on local structure partitioning, thus providing a more stable input basis for subsequent topological boundary analysis.

[0042] Specifically, constructing a neighborhood topological complex includes:

[0043] Set scale parameters If the distance between any two samples in the sample set (mixed distance) does not exceed the scale parameter Then, each pair of samples is a neighbor of the other;

[0044] Two samples that are mutually adjacent generate an edge (1-dimensional simplex), and multiple samples that are mutually adjacent generate higher-dimensional simplexes such as triangles and tetrahedrons.

[0045] By aggregating all simplexes, the current scale parameters can be obtained. The neighborhood topological complex below;

[0046] By continuously changing the scale parameter, a nested, incremental multi-scale neighborhood topological complex sequence is generated.

[0047] As the scale parameter gradually changes, a topological representation describing the evolution of local connectivity can be obtained, namely a multi-scale neighborhood topological complex sequence. This representation can reflect the changes in connectivity of samples at different scales, thus providing a basis for the structural analysis of boundary regions.

[0048] In one embodiment, to avoid a significant increase in computational complexity due to excessively large complex size, this invention selects an appropriate range of scale parameters based on the distance distribution between samples, so as to maintain the main local topological relationships without destroying the computational overhead. The purpose of this step is to transform the local neighborhood relationships in the original data into a structural representation that can be used for multi-scale topological analysis.

[0049] Topological features include connected components, loops, and holes, which are the overall topological configurations formed after the aggregation of simplexes. The scale parameter for the appearance of a topological feature is the scale parameter when the topological feature appears, and the scale parameter for the disappearance of a topological feature is the scale parameter when the topological feature disappears. The set of simplexes constituting a topological feature is the set of all simplexes that make up the topological feature.

[0050] S22. For each topological feature The persistence is calculated based on the appearance scale parameter and the disappearance scale parameter. The supporting sample set is selected from the sample set of a few classes c based on the simplex set. The class heterogeneity and normalized local sparsity are calculated based on the supporting sample set.

[0051] Computational persistence ;in, Representing topological features The scale parameter at which it appears. Representing topological features The persistence parameter is the scale parameter at which the topology disappears. A higher persistence indicates greater stability of the corresponding topology across multiple scales; a lower persistence indicates that the structure is more likely to correspond to a vulnerable boundary region or a locally perturbed region. This step compresses the originally dispersed local connectivity relationships across different scales into stability features that can be used for boundary analysis. These persistence features then serve as the basis for calculating the topological boundary sensitivity index.

[0052] Based on topological features The simplex set selects topological features from a sample set of minority class c. The supporting sample set includes: selecting samples from the minority class c sample set that participate in the construction of any simplex in the simplex set to obtain the supporting sample set.

[0053] Calculate topological features Category heterogeneity and local sparsity include:

[0054] S221, Based on topological features The supporting sample set selects topological features from the sample sets of all categories. Find the k nearest neighbor samples to obtain the nearest neighbor sample set. Topological features The local neighborhood;

[0055] Selecting topological features The k nearest neighbor samples include: the set of supporting samples for the topological feature v, denoted as . Each sample in the sample set of all categories To topological features Minimum mixing distance of the supporting sample set Alternatively, the average distance can be used, i.e. ,in express Mid-range Several recent supporting samples; in the sample set of all categories, according to Select k samples from smallest to largest to obtain the nearest neighbor sample set. .

[0056] S222, Calculate topological features The degree of class heterogeneity in the local neighborhood and normalized local sparsity discreteness .

[0057] Category heterogeneity For the nearest neighbor sample set The proportion of outlier samples within the minority class c, i.e., the proportion of samples that do not belong to the minority class c. ;in, As a sample, For the sample The tag, This is an indicator function.

[0058] Normalized local sparsity discreteness Original local sparsity According to the current few categories Reference local distance scale The result is obtained after normalization and truncation; where the original local sparsity is... For the nearest neighbor sample set Samples within Average mixing distance between Reference local distance scale For a minority of categories All samples Local average mixing distance The median, normalized local sparsity dispersion , It is a very small positive number.

[0059] sample Local average mixing distance , For the sample The set of nearest neighbor samples of the same type.

[0060] S23. Calculate the topological boundary sensitivity index of each topological feature based on its persistence, class heterogeneity, and normalized local sparsity. ; Calculate the topological boundary sensitivity index of each sample in the minority class c sample set based on each topological feature. topological boundary sensitivity index ; Select samples from the minority class c sample set whose topological boundary sensitivity index exceeds the preset topological boundary sensitivity threshold (range [0,1], can be 0.6) to obtain the topological sensitive sample set of minority class c.

[0061] To avoid determining the fragility of a boundary solely based on its persistence magnitude, this invention further constructs a topological boundary sensitivity index. :

[0062]

[0063] in, This is the persistence balance parameter, which is the median of the persistence of all topological features of the minority class c; , As weight, Considering that the degree of category mixing directly affects the identification of boundary regions, the preferred value can be set to , If the sparsity of minority class sampling is more pronounced, then... , .

[0064] This index considers not only the stability of the topological features themselves, but also the degree of heterogeneity in their boundary neighborhoods and the degree of local sparsity and dispersion after normalization. Therefore, it is more suitable for describing boundary-sensitive regions in imbalanced data. When the value is large, it indicates that the region has characteristics such as weak persistence, highly mixed boundaries, or insufficient local support, and should be given priority in the subsequent boundary reconstruction and sample generation process.

[0065] Persistence balance parameters It can be obtained from the median, mean, or specified quantile of the persistence of all topological features of the current few classes c, with the addition of very small positive numbers to avoid division by zero.

[0066] Calculate samples topological boundary sensitivity index Includes: Acquisition and Samples The associated topological features will be related to the sample Topological boundary sensitivity index of each associated topological feature Perform weighted aggregation to obtain samples topological boundary sensitivity index ; where, if the sample Belongs to topological features The supporting sample set, then the topological features With sample Related; associated with the sample The weights of the associated topological features can be derived from the samples. The minimum mixing distance to the supporting sample set of each topological feature is determined, for example, the normalized value of the minimum mixing distance.

[0067] S24. Calculate the global nearest neighbor set, the same-class nearest neighbor set, and the different-class nearest neighbor set for each sample in the minority class c sample set; calculate the degree of neighborhood class mixing for each sample in the minority class c sample set based on the global nearest neighbor set.

[0068] sample The global nearest neighbor set is based on the mixture distance among all classes of sample sets. The set is constructed by selecting the k nearest neighbors.

[0069] sample The set of nearest neighbor samples of the same type is in relation to the sample Based on the mixture distance in the same category of sample set The set is constructed by selecting the k nearest neighbors.

[0070] sample The set of out-of-class nearest neighbors is the set of samples that are removed from the sample set of all classes. The sample set of the same category is used to obtain the remaining sample set. The remaining sample set is then analyzed based on the mixture distance. The set is constructed by selecting the k nearest neighbors.

[0071] The degree of mixing of neighboring categories represents the sample The percentage of outliers in the neighborhood; For the sample The global nearest neighbor sample set; The larger the sample size, the better. The higher the proportion of outlier samples in the neighborhood, the more likely the sample is to be located near the class transition region.

[0072] S25. Calculate the local density of each sample in the minority class c sample set in the neighborhood of the same class and the neighborhood of different classes based on the neighborhood of the same class and the neighborhood of different classes. Calculate the local density transition features of each sample based on the local density of each sample in the neighborhood of the same class and the neighborhood of different classes.

[0073] Local density transition features are used to characterize samples. The degree of boundary mixing in terms of the density of neighborhoods of the same and different types; among which... Indicates sample Local density in the same neighborhood, It is a very small positive number, used to avoid the denominator being 0. For the sample The set of nearest neighbor samples of the same type, that is, in relation to the sample The k nearest neighbor samples selected from a set of samples of the same type; Indicates sample Local density in heterogeneous neighborhoods For the sample The set of out-of-class nearest neighbors, that is, in all other classes (except for sample 1) Select the k nearest neighbor samples from a set of samples of the same type. This indicates that the average value is taken. When the density of similar-class neighborhoods is relatively close to the density of dissimilar-class neighborhoods, it suggests that the sample is more likely to be in the transition region between the true and false classes. Larger values ​​indicate a greater likelihood of a sample being biased towards a particular neighborhood; conversely, smaller values ​​indicate a greater likelihood of a sample being biased towards a particular neighborhood. The value is relatively small.

[0074] S26. Calculate the boundary candidate confidence of each sample in the sample set of minority class c based on the degree of mixing of neighborhood categories, the topological boundary sensitivity index and the local density transition characteristics. Construct an initial boundary candidate set for minority class c based on the samples whose boundary candidate confidence exceeds the preset boundary threshold.

[0075] Boundary threshold can be taken ;in, It is more focused on recall and is suitable for scenarios with sparse boundary samples. It prioritizes accuracy and is suitable for scenarios with a sufficient number of candidate points.

[0076] For minority samples This invention no longer determines whether a point is a boundary point solely based on the ratio of dissimilar neighbors, but comprehensively considers the degree of mixing of neighborhood categories, the sensitivity of topological boundaries, and the characteristics of local density transitions.

[0077] Construct the boundary candidate confidence function: ;in, As weight, and Preferably, At the same time, it preserves topological sensitivity and density transition information. Sensitivity to topological boundaries, representing the sample The normalized result of the topological boundary sensitivity index is used to reflect the degree of instability of the topological structure of the sample region. The larger the value, the better the sample size. It is more likely to be located in a topologically sensitive area.

[0078] The three components characterize the boundary attributes of the sample from three perspectives: neighborhood category composition, topological boundary sensitivity, and local density transition state. Their combined use can reduce the misidentification of noise points or isolated points when relying on only a single criterion.

[0079] The candidate set of boundaries further serves as the basic input for subsequent boundary constraint interpolation generation and enhancement task allocation.

[0080] S27. The initial boundary candidate set of minority class c is filtered using a coverage-first filtering strategy and a quality-first filtering strategy to obtain the final boundary candidate set of minority class c. ;

[0081] The purpose of this step is to further purify the candidate set of boundaries, removing candidate samples with unstable local structures, insufficient boundary representativeness, or significant deviation from the real transition region, thereby improving the effectiveness of subsequent boundary constraint interpolation generation.

[0082] For the set of boundary candidate points, this invention provides two filtering strategies based on the application scenario. The first is a coverage-first filtering strategy, which is suitable for scenarios where boundary candidate points are relatively sparse. Under the premise of ensuring the spatial coverage of the boundary region, only samples with extremely high local structural anomalies are removed. The second is a quality-first filtering strategy, which is suitable for scenarios where boundary candidate points are relatively abundant. It comprehensively considers the local density anomaly, the confidence of the boundary candidate, and the local neighborhood coverage, and prioritizes retaining candidate samples that are more representative of the real boundary transition region.

[0083] The coverage-first filtering strategy includes: calculating the degree of local structural anomaly of the boundary candidate samples, which can be calculated by the local outlier factor or the degree of deviation of the local neighbor structure; when the local outlier factor of a sample is lower than the preset extreme outlier threshold or the degree of local structural anomaly is extremely high, it can be removed from the boundary candidate set. Before removing the sample, the regional coverage after removing the sample is calculated, and it is determined whether the regional coverage is lower than the preset coverage threshold. If so, it will cause a lack of coverage, so the removal is abandoned.

[0084] Calculating the region coverage after removing samples includes: Let the set of candidate boundary points before sample removal be... The boundary candidate set after removing samples is For sets For each boundary candidate sample in the set, calculate its path to the set. The average coverage distance is calculated by averaging the distances of the nearest neighbors in the dataset. The average coverage distance is then normalized using the average nearest neighbor distance of the removed samples as a reference scale to obtain the region coverage after sample removal. A smaller average coverage distance indicates that the removed dataset still covers the original boundary region well, resulting in higher coverage.

[0085] Local outlier factor is calculated by comparing the local density difference between a candidate sample at a boundary and its nearest neighbors of the same type. If the sample is significantly sparser than its surrounding samples of the same type, its outlier degree is considered high. Local neighbor structural deviation is calculated by determining the proportion of outlier samples among the candidate sample's neighbors and calculating its distance from the distribution center of its own type of samples. If almost all of the sample's neighbors are outliers and are significantly far from the distribution center of its own type of samples, it is also considered to have an extremely high degree of local structural anomaly.

[0086] The quality-first filtering strategy involves several steps. Instead of simple addition, it first calculates and normalizes each evaluation indicator separately before constructing a comprehensive quality score. Specifically: A number of the nearest neighboring samples of a boundary candidate sample are selected. The number of samples in the same category as the candidate sample is counted and divided by the total number of neighboring samples to obtain the proportion of similar neighbors, i.e., the degree of local support. A higher proportion indicates sufficient support from similar samples around the candidate sample, resulting in a more stable local structure; a lower proportion indicates a lack of similar neighborhood support, making the sample more likely to be an isolated point, noise point, or anomalous boundary point. The distance between the boundary candidate sample and its similar neighboring samples is calculated to obtain the degree of local neighborhood coverage. A weighted sum of the local density anomaly, boundary candidate credibility, and local neighborhood coverage of the boundary candidate sample is used to obtain the comprehensive quality score. Candidate samples with scores exceeding a preset threshold or with high rankings are prioritized for retention. Example weights can be set to 0.4, 0.3, and 0.3.

[0087] After the above processing, the retained samples constitute the final candidate set of boundaries.

[0088] S28. Combining all topological features, we obtain the topological feature set of minority class c; combining the neighborhood sample set of each sample in the sample set of minority class c and the local density of each sample in the neighborhood, we obtain the local structural statistics of minority class c; combining the topological feature set of minority class c, the persistence of each topological feature in the topological feature set, the local structural statistics, the topological sensitive sample set, the boundary candidate set, the topological boundary sensitivity index of each sample in the sample set, and the boundary candidate credibility of each sample in the sample set, we obtain the topological summary of minority class c.

[0089] After completing the boundary candidate filtering, the topological analysis results of each category at different scales are summarized to form a category-level topological summary that can be used for subsequent enhanced decision-making, reflecting the boundary complexity, structural stability and candidate sample distribution of each category.

[0090] The topology summary further serves as the basic input for subsequent augmentation task allocation and augmentation intensity adjustment, enabling the sample generation strategy to no longer rely solely on fixed empirical proportions, but to adaptively adjust based on the topological state of different categories.

[0091] S3. Based on the topological summary of each minority class c, perform topological boundary reconstruction and progressive enhancement on the sample set of each minority class c to obtain candidate enhanced samples for each minority class c.

[0092] like Figure 3 As shown, the topological boundary reconstruction and progressive enhancement of the sample set of minority class c includes:

[0093] S31. Calculate the imbalance ratio of minority class c in the preprocessed industrial dataset. According to the unbalanced proportion To obtain enhanced requirements for a minority of classes c; among which, Let c be the number of samples in the minority class c. The number of samples in the category with the most samples;

[0094] The process of determining category enhancement requirements is divided into two parts: "determining the number of enhancements" and "selecting the generation location." For each minority class c, the calculation of its enhancement requirements includes:

[0095] S311. Calculate the imbalance ratio of the minority class c based on the number of samples in all classes of the preprocessed industrial dataset. Based on the imbalance ratio, select the enhancement strategy for the minority class c;

[0096] For mild imbalance, a minimum enhancement strategy (IR < 2) is adopted; for moderate imbalance, a conservative enhancement strategy (IR 2 to 5) is adopted; for severe class imbalance, a boundary-first enhancement strategy (IR greater than 5) is adopted.

[0097] S312. Determine the target number of minority class c based on the enhancement strategy for minority class c. Subtract the number of minority class c samples from the target number of minority class c to obtain the number of enhanced samples that need to be generated for minority class c, i.e., the enhancement requirement.

[0098] The target number of minority class c is determined based on the enhancement strategy: If the minimum enhancement strategy is adopted, only a small number of samples are added, that is, the number of added samples does not exceed 20% of the current number of minority class samples, and does not exceed 30% of the difference between the number of minority class samples and the number of majority class samples; if the conservative enhancement strategy is adopted, a medium number of samples are added, that is, the number of added samples does not exceed 50% of the current number of minority class samples, and does not exceed 60% of the difference between the number of minority class samples and the number of majority class samples; if the boundary priority enhancement strategy is adopted, the minority class is enhanced to a certain proportion (65% to 80%) close to the majority class (i.e., the class with the most samples), but it is not directly forced to be added to the number of majority class samples. The specific proportion can be adaptively determined according to the overall imbalance: when the imbalance is low, it is close to 80%, and when the imbalance is high, it is close to 65%, so as to enhance the samples in the boundary area while avoiding over-generation.

[0099] After the above processing, the overall sample generation requirements for each minority class in the subsequent enhancement stage can be obtained.

[0100] S32. Based on the topology summary of minority class c, adaptive enhancement allocation is performed on the enhancement requirements of minority class c to obtain the target number of multi-class generation tasks for minority class c; among which, the multi-class generation tasks include: boundary-aware generation task, topology-sensitive enhancement task, and random supplementation generation task.

[0101] For each minority class c, this invention no longer uses a fixed ratio to divide the generation task into three parts: boundary-aware generation, topology-sensitive enhancement, and random supplementation generation. Instead, it uses an adaptive enhancement allocation function based on the degree of class imbalance, boundary complexity, and topology sensitivity, specifically including:

[0102] Enhancement tendency of computational boundary-aware generation tasks :

[0103]

[0104]

[0105]

[0106] in, The unbalanced proportion of the minority class c; This represents the average confidence level of the boundary candidates for the minority class c, i.e., the set of boundary candidates for the minority class c. All samples Boundary candidate credibility The average value; This represents the topological boundary sensitivity average index of the minority class c, i.e., the boundary candidate set of the minority class c. All samples topological boundary sensitivity index The average value.

[0107] The augmentation tendency of computation topology-sensitive augmentation tasks :

[0108]

[0109]

[0110] in, The topological complexity is for a minority of classes c; The set of topological features of a minority class c The number of topological features reflects the topological complexity of the sample distribution for that category. The Betti number of the minority class c in the d-th dimension (the Betti number is used to represent the number of topological features in a certain dimension, where the 0-dimensional Betti number represents the number of connected components, the 1-dimensional Betti number represents the number of ring structures, and the 2-dimensional Betti number represents the number of cavity structures). For a minority The average durability is used to characterize the retention requirements of stable topologies in this category. The larger the value, the more stable the topological features of this category are across multiple scales, and the more likely it is to correspond to a real connected structure, ring structure, or cavity structure. Therefore, it is more important to maintain its topological morphology during subsequent generation. For a minority The proportion of fragile topological features is used to characterize the reinforcement needs of short-persistence, unstable topological structures; therefore, and These correspond to two aspects: preservation of stable structures and reinforcement of vulnerable regions, which together constitute the topological complexity. It is a set of topological features for a minority class c; Topological features Durability, This is the normalization function; The persistence threshold is between 0 and 1, consistent with the default persistence threshold in the current implementation. It can also be adaptively determined based on the persistence distribution of the current class or all samples, for example, taking the 25th percentile of the persistence distribution. The values ​​are weights, ranging from 0 to 1, and the sum of the three is equal to 1. Preferably, they are set to 0.3, 0.3, and 0.4 respectively, which can appropriately increase the impact of the proportion of fragile topological features on topological complexity while comprehensively considering the number of topological features and average durability.

[0111] The augmentation tendency of computationally supplemented tasks :

[0112]

[0113] when When the value is larger, it indicates that this category needs to prioritize allocating generation resources to the boundary areas; when... When the value is large, it indicates that this category needs more reinforcement of topology-sensitive regions; As a basic element, it is used to ensure that the random supplementary generation retains a necessary proportion in the overall allocation.

[0114] Further, the allocation ratio of the three types of tasks was obtained. , :

[0115]

[0116] Through the above normalization process, the three types of enhancement tendencies can be uniformly converted into the allocation ratio of boundary-aware generation tasks, topology-sensitive enhancement tasks, and random supplementation generation tasks.

[0117] The target generation quantity for the boundary-aware generation task, the topology-sensitivity enhancement task, and the random supplementation generation task is determined based on the allocation ratio. , and :

[0118]

[0119] in, This indicates the enhanced requirements of a minority class c. This indicates rounding down to the nearest integer.

[0120] S33. Generate candidate samples for various generation tasks of the minority class c based on the topological summary of the minority class c and the target generation number of each generation task.

[0121] Boundary-aware generation task:

[0122] This step involves the boundary candidate set. Constraint interpolation is performed to generate candidate samples for the target number of samples to be generated in the boundary-aware generation task. The aim is to prioritize the sample generation task allocated to the boundary-aware generation branch towards the real boundary transition region, thereby improving the relevance and effectiveness of boundary sample enhancement.

[0123] The target number of boundary awareness generation tasks The present invention is based on the boundary candidate set. Within the filtered candidate boundary set (step S27), samples with high candidate boundary confidence are selected, and constrained interpolation is performed between them to generate the target number of candidate samples. Unlike random supplementation, this step emphasizes that the generated samples should be concentrated near the real boundary transition region to enhance the supporting ability of the boundary samples in the original data.

[0124] Topology-sensitive augmentation task:

[0125] like Figure 4 As shown, this step involves the boundary candidate set. Manifold structure learning is performed on the topology-sensitive sample set to generate candidate samples for the target number of topology-sensitive enhancement tasks. The aim is to direct the sample generation task assigned to the topology-sensitive enhancement task towards regions with high topology boundary sensitivity indices, thereby enhancing the support capability of vulnerable boundary regions in the original data. The target number of samples generated for the topology-sensitive enhancement task is... This step prioritizes generating reinforcement samples near regions with high topological boundary sensitivity indices and unstable local structures. Specifically, candidate samples for a few class c topological sensitivity enhancement tasks are generated, including:

[0126] S331. Construct a manifold representation of the sample set of minority class c based on the topological summary of minority class c; the manifold representation includes: neighborhood graph. Geodesic distance matrix and manifold space coordinate matrix;

[0127] The purpose of this step is to establish a manifold representation for minority class samples that can reflect the continuity of local structure and neighborhood reachability, thereby providing a basis for subsequent path reliability assessment and constraint interpolation generation.

[0128] For minority class samples, this invention no longer relies solely on Euclidean linear relationships in the original feature space to describe the similarity between samples. Instead, it constructs geodesic neighborhood representations based on local neighborhood connectivity relationships between samples, specifically including:

[0129] Step 1: Treat each sample in the minority class c sample set as a node, obtain the neighborhood sample set of each sample in the topological summary of minority class c, and establish direct connections (i.e., edges) between each sample and samples in its neighborhood sample set to form a neighborhood graph. ;

[0130] Step 2, in the neighborhood graph The shortest path distance between each node is calculated as the geodesic distance, and the geodesic distance matrix is ​​obtained.

[0131] Step 3: Using a manifold dimensionality reduction method that preserves geodesic distance structure, all samples in the sample set are mapped from the original feature space to the low-dimensional manifold representation space to obtain the manifold space coordinate matrix; where each row of the manifold space coordinate matrix corresponds to the coordinates of a sample in the low-dimensional manifold representation space;

[0132] Manifold dimensionality reduction methods that preserve geodesic distance structure retain the neighborhood structure, local connectivity, and variation trends along the manifold direction among samples.

[0133] Step 4: Combine the neighborhood graph, geodesic distance matrix, and manifold spatial coordinate matrix to form a manifold representation of the minority class c.

[0134] This expression can more accurately characterize the reachability of samples along the distribution direction of local structures, enabling samples that are close to each other but located in different local structural regions to be treated differently in subsequent processing.

[0135] S332. Construct multiple candidate paths for minority class c and their basic structural features based on the topological summary and manifold representation of minority class c. The basic structural features include: distance along the path, degree of local density change, node jump complexity, and straight-line distance.

[0136] This step is performed after the manifold representation is constructed. Its purpose is to establish candidate connection paths between minority class samples that can be used for interpolation generation, providing a basis for subsequent path reliability evaluation. Specifically, it includes:

[0137] Step 1: Obtain the candidate boundary set for minority class c from the topological summary of minority class c. From the boundary candidate set Multiple samples are selected from the union of the topology-sensitive sample set as source points. It prioritizes samples that belong to both the boundary candidate set and the topology-sensitive sample set; and selects each source point based on the manifold representation. target point Multiple source-target point pairs were obtained. Where n is the index of the source point;

[0138] For each source point Select target point based on manifold representation Includes: excluding source points in the neighborhood graph G For nodes that are unreachable, select nodes from the remaining nodes in the neighborhood graph G that are connected to the source node. The nodes with the smallest geodesic distances are selected as candidate target points, and the source point is obtained from the topology summary. Calculate the source point based on the local density of each candidate target point. Based on the difference in local density between the source and each candidate target point, the candidate target point with the smallest difference is selected as the source point. target point .

[0139] Step 2: Construct each set of source-target point pairs in the neighborhood graph G. Candidate paths This allows candidate paths to reflect the connectivity of samples along local structural directions, rather than just the linear proximity relationships in the original feature space; where, As the source point, For the target point, Candidate paths The number of sides in;

[0140] Step 3: For each group of source-target point pairs The candidate paths are further extracted to determine their distances along the paths. Degree of local density change Node jump complexity and straight-line distance , used to describe the basic structural features of a path.

[0141] The distance along the candidate path is obtained by accumulating the edge weights between adjacent nodes in the path. Specifically, the source-target point pairs are calculated for each group. Distance along the candidate path ;in, Indicates adjacent nodes The distance between manifold coordinates in the manifold space coordinate matrix, where r is the index of a node in the candidate path;

[0142] The degree of local density variation along the path is calculated based on the local density differences between adjacent path nodes. Specifically, the source-target point pairs are calculated. The degree of local density variation of candidate paths ;in, Represents path nodes The local density of the corresponding sample in the same neighborhood is obtained from the topological summary.

[0143] The node jump complexity is calculated using normalized calculation based on the number of edges contained in the candidate path. Specifically, it calculates the complexity of each source-target pair. The node jump complexity of the candidate path ;in, For all source-target point pairs The maximum value among the number of edges in the candidate paths or the preset maximum number of hops;

[0144] The straight-line distance is calculated based on the distance between the manifold spatial coordinates of the source and target points. Specifically, it is calculated for each set of source-target point pairs. The source and target points of the candidate paths are their manifold space coordinates in the manifold space coordinate matrix. Distance between .

[0145] The role of the candidate path construction step is to transform the local connectivity relationships in the manifold representation space into path objects that can be evaluated and filtered later.

[0146] S333. Calculate the manifold interpolation reliability of each candidate path of minority class c based on the basic structural characteristics, and filter the candidate paths whose manifold interpolation reliability exceeds the preset reliability threshold to obtain the candidate paths after filtering of minority class c.

[0147] The purpose of this step is to evaluate the availability of candidate paths and select those that are more suitable for subsequent sample generation.

[0148] A preset reliability threshold is used to filter candidate paths that can be used for subsequent interpolation generation, and its value ranges from 0 to 1. Since the reliability of manifold interpolation is a normalized score, the larger the value, the more stable, continuous, and suitable the path is for interpolation generation. Therefore, the preferred value can be set to 0.5, that is, retaining candidate paths with a reliability of not less than 0.5.

[0149] Construct the manifold interpolation reliability function: in, Indicates candidate paths, Indicate candidate path Path curvature; The values ​​for each item are weights, ranging from 0 to 1. Preferably, the values ​​are 0.3, 0.4, and 0.3 respectively.

[0150] For ease of implementation, the path bend degree can be further expressed as: .in, Indicate candidate path The straight-line distance. The larger the value, the more circuitous the path. The larger the value, the worse the continuity of the local structure along the path; The larger the value, the higher the complexity of the path jump. Therefore, The larger the value, the more stable, continuous, and suitable the candidate path is for subsequent constraint interpolation generation. After reliability evaluation, candidate paths that meet the requirements are retained.

[0151] S334. Interpolate each candidate path after filtering for minority class c to obtain multiple candidate points for minority class c.

[0152] The purpose of this step is to generate candidate points along the candidate paths that have passed the reliability assessment, so that the generation process can follow the local structural orientation, rather than simply interpolating along the straight lines in the original feature space.

[0153] For the candidate paths retained after screening, this invention selects appropriate interpolation positions along the path direction to generate candidate points. The selection of interpolation positions comprehensively considers the path length distribution and local structural continuity, so that the generated candidate points can be located in the effective transition region between the source point and the target point, without being excessively biased towards either endpoint.

[0154] The interpolation of the filtered candidate paths specifically includes:

[0155] Calculate the cumulative distance of each node in the filtered candidate path P to obtain the cumulative path distance sequence. ;in, As the source The cumulative distance, To start from the source To the target point The cumulative distance, Let P be the number of edges in the candidate path P;

[0156] Selecting the interpolation ratio Interpolation ratio The value range is from 0 to 1. =0 corresponds to the source point. When =1 corresponds to the target point, to avoid generating samples that are too close to the two endpoints, it is preferable to take the value in the middle region. ∈[0.3,0.7];

[0157] Determine the cumulative position of the target along the path In the path cumulative distance sequence The path into which the cumulative position s of the target falls is found, i.e., the path that satisfies... ; r is the index of a node in the candidate path P;

[0158] Perform local linear interpolation on the found path, that is, obtain the nodes corresponding to the found path. , At these two adjacent path nodes , Linear interpolation is performed between the coordinates of the manifold space to obtain candidate points in the manifold space.

[0159] The candidate points obtained through the above method can better reflect the sample distribution characteristics of the boundary region while maintaining path continuity and local structural consistency.

[0160] S335. Perform local consistency reconstruction mapping on each candidate point of the minority class c to obtain multiple reconstruction samples of the minority class c, i.e., candidate samples.

[0161] The purpose of this step is to approximate the mapping of candidate points generated along the candidate path from the manifold representation space back to the original feature space, thereby obtaining reconstructed samples that can be used for subsequent quality assessment and data merging.

[0162] Since candidate samples in the manifold space usually cannot be directly mapped one-to-one with samples in the original feature space, this invention uses a locally consistent reconstruction mapping for approximate recovery, specifically including:

[0163] For each candidate point, in the manifold representation (i.e., the neighborhood graph) Select from ) Calculate the normalized reconstruction weights for each nearest neighbor node: Based on this, the reconstructed sample in the original space is obtained: ;in, , Indicate the candidate point and its first The distance between the nearest neighbors in the manifold space , Let be the coordinates of the candidate point in the manifold space. For the first The coordinates of the nearest neighbor nodes in the manifold space Indicates the first The samples corresponding to the nearest neighbor nodes in the original feature space , Indicate the candidate point and its first The consistency coefficient of the m nearest neighbors in the local neighborhood structure, that is, the consistency coefficient between the candidate point and its m nearest neighbors. The normalized result of the reciprocal of the distance between the nearest neighbors in the manifold space. The closer the distance, the stronger the local consistency and the greater the weight. This is the distance decay parameter, used to control the impact of nearest neighbor distance on the reconstruction weights. The range of values ​​is The value >0 is preferred as the median of the manifold distances between a candidate point and its k nearest neighbors. The closer the neighbors are and the more consistent their local structures, the greater their corresponding weight.

[0164] Compared to simple inverse distance weighting, this mapping method not only considers the distance relationship between candidate points and their nearest neighbors, but also the consistency of local structure, thus better maintaining the consistency between generated samples and local real structure.

[0165] This step places greater emphasis on providing local support to regions with fragile topological structures, thereby improving the distribution stability of this type of sample near complex boundaries.

[0166] Randomly generated tasks:

[0167] The purpose of this step is to supplement the areas not covered by boundary-aware generation and topology-sensitive region enhancement, so as to maintain the overall balance of intra-class sample distribution.

[0168] For the number of randomly replenished targets This invention performs appropriate supplementary sampling on the remaining region without significantly interfering with the main directions of boundary enhancement and topology enhancement. Specifically, this includes: excluding the minority class c's boundary candidate set from the minority class c's sample set. The set of topology-sensitive samples is used to obtain the remaining sample set of minority class c; constrained interpolation is performed on the remaining sample set of minority class c to generate candidate samples for the target number of random supplementary generation tasks.

[0169] This step primarily serves to balance distribution and supplement regional needs, and is not intended as a major direction for increasing resource investment.

[0170] If the remaining sample set is empty or the number of samples is insufficient, it degenerates into selecting samples with low boundary candidate confidence and low topological boundary sensitivity index from all samples of the minority class as supplementary seeds.

[0171] S34. Perform unified quality control and filtering on candidate samples of various generation tasks for minority class c to obtain candidate augmentation samples for minority class c.

[0172] This step is performed after boundary constraint interpolation generation, topology sensitive region enhancement, and random supplementation generation are completed. Its purpose is to uniformly screen the candidate samples generated by different branches and remove samples that are of insufficient quality or are significantly inconsistent with the original local structure.

[0173] To avoid generating samples that are only geometrically reasonable but distorted in boundary properties or numerical stability, this invention constructs a unified sample credibility evaluation function for candidate samples of various generation tasks in a minority class c:

[0174]

[0175] in, Candidate samples The rationality of its geometric position Candidate samples Consistency of boundary attributes Candidate samples The continuity of local structure, Candidate samples Numerical stability, the value is stable at Intervals are used to facilitate unified comparisons and weighted combinations; , , , Let be the weight parameters, and let the weight parameters satisfy . and .

[0176] Computational geometric position rationality include:

[0177]

[0178] in, , These represent the generated candidate samples. The two samples, i.e., the two samples used for interpolation, if the candidate samples If interpolation is performed between two path nodes in the manifold space, then... , These are two samples corresponding to two nodes; Candidate samples and samples The distance between them Candidate samples and samples The distance between them For two samples , The distance between them It is a local minimum. Used to evaluate the reasonableness of the sample's geometric location; when a candidate sample is closer to a reasonable transition region between the source and target points, The value is larger.

[0179] Retrieving candidate samples from topology summary For the corresponding minority class c, the boundary candidate set is used. The average confidence of the boundary candidates for class c is obtained by averaging the confidence scores of all samples in the boundary candidate set for class c. ;

[0180] Calculate candidate samples The degree of mixing of neighborhood categories and the characteristics of local density transition; the calculation process is consistent with steps S24 and S25;

[0181] Generate candidate samples Two samples , The candidate samples are obtained by weighting and combining the topological boundary sensitivity indices. The topological boundary sensitivity index; based on candidate samples The topological boundary sensitivity index is used to calculate candidate samples. Sensitivity to topological boundaries;

[0182] Based on candidate samples The candidate samples are calculated based on the degree of mixing of neighborhood categories, sensitivity to topological boundaries, and local density transition features. Boundary candidate credibility Then the boundary attribute consistency for:

[0183]

[0184] Used to evaluate the consistency between the boundary attributes of a sample and the target class; when the boundary attributes of a candidate sample are closer to the typical boundary features of the target class, The value is larger.

[0185] Calculate candidate samples Set of nearest neighbor samples of the same type and local density in the same neighborhood Calculate the set of nearest neighbor samples of the same type. Each sample Local density in the same neighborhood Calculate the set of nearest neighbor samples of the same type. The average local density of all samples in their similar neighborhood. ; Calculate candidate samples Local structural continuity for:

[0186]

[0187]

[0188]

[0189] in, Candidate samples The set of k nearest neighbors in the sample set of its class c, i.e., candidate samples The set of nearest neighbor samples of the same type Candidate samples With sample distance, It is a local minimum.

[0190] Used to evaluate local structural continuity; when the local density around the candidate sample is closer to the reference neighborhood. The value is larger.

[0191] Calculate numerical stability include:

[0192]

[0193] in, Indicates candidate samples The The safe range of values ​​allowed for each feature Indicates candidate samples The total number of features, Candidate samples The number of features that fall within the allowed safe range of values.

[0194] Let the minimum value of the f-th feature in the preprocessed industrial dataset be... The maximum value is The range of values ​​is: Then the safe range of values ​​allowed for the f-th feature is: Where 0.2 represents the safety margin coefficient, which is used to allow the generated samples to expand slightly near the original value range, avoiding overly strict rejection of reasonable boundary samples.

[0195] Used to evaluate numerical stability and the reasonableness of the feature range; when more features fall within the corresponding safe interval... The value is larger.

[0196] The larger the value, the more consistent the candidate samples are in terms of geometric location, boundary properties, local structure, and numerical stability, making them more suitable as final retained samples. Only when... Only samples generated when the threshold is exceeded are retained.

[0197] Candidate samples whose credibility evaluation exceeds a preset credibility threshold are selected to obtain candidate enhanced samples for minority class c. The credibility threshold ranges from 0 to 1, preferably from 0.3 to 0.5; in one embodiment, the credibility threshold is 0.5; when the number of minority class samples is small or the candidate sample filtering is strict, the credibility threshold can be 0.3.

[0198] This unified quality control process ensures that samples from different generation branches maintain consistent retention criteria, thereby preventing low-quality samples from entering the final augmented dataset and retaining augmented samples that are more representative of boundary regions and local structural features.

[0199] S4. Combining the preprocessed industrial dataset with all candidate augmentation samples of the minority class c, we obtain the augmented industrial dataset.

[0200] This step merges the retained generated samples with the original data to form an augmented dataset that can be directly used for subsequent model training.

[0201] Upon completion of sample merging, the retained augmented samples and the original samples are uniformly organized into an augmented training dataset, maintaining consistency between their class labels and source information. Simultaneously, this application records statistical information such as the number of generated samples, filtering ratio, and average confidence level to reflect the overall effect of the current augmentation process. These statistical results can be further used for subsequent parameter tuning, strategy optimization, and model training configuration.

[0202] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for industrial imbalance data augmentation based on topology analysis and manifold sampling, characterized in that, include: S1. Obtain the industrial dataset, preprocess the industrial dataset, and obtain the preprocessed industrial dataset. The preprocessed industrial dataset includes sample sets from multiple categories; S2. Perform topological boundary analysis on the sample sets of each minority class c to obtain the topological summary of each minority class c. S3. Based on the topological summary of each minority class c, perform topological boundary reconstruction and progressive enhancement on the sample set of each minority class c to obtain candidate enhanced samples for each minority class c. S4. Combining the preprocessed industrial dataset with all candidate augmentation samples of the minority class c, we obtain the augmented industrial dataset.

2. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 1, characterized in that, For each minority class c, topological boundary analysis of its sample set includes: S21. Construct a multi-scale neighborhood topological complex sequence of minority class c based on the sample set of minority class c; extract multiple topological features of minority class c and their occurrence scale parameter, disappearance scale parameter and simplex set from the multi-scale neighborhood topological complex sequence of minority class c respectively. S22. For each topological feature, calculate its persistence based on its appearance scale parameter and disappearance scale parameter, select its supporting sample set in the sample set of a few class c based on its simplex set, and calculate its class heterogeneity and normalized local sparsity based on its supporting sample set. S23. Calculate the topological boundary sensitivity index of each topological feature based on its persistence, class heterogeneity, and normalized local sparsity dispersion. Calculate the topological boundary sensitivity index of each sample in the minority class c sample set based on the topological boundary sensitivity index of each topological feature. Select samples in the minority class c sample set whose topological boundary sensitivity index exceeds a preset topological boundary sensitivity threshold to obtain the topological sensitive sample set of the minority class c. S24. Calculate the global nearest neighbor set, the same-class nearest neighbor set, and the different-class nearest neighbor set for each sample in the minority class c sample set; calculate the degree of neighborhood class mixing for each sample in the minority class c sample set based on the global nearest neighbor set. S25. Calculate the local density of each sample in the minority class c sample set in the neighborhood of the same class and the neighborhood of different classes based on the neighborhood of the same class and the neighborhood of different classes. Calculate the local density transition features of each sample based on the local density of each sample in the neighborhood of the same class and the neighborhood of different classes. S26. Calculate the boundary candidate confidence of each sample in the sample set of minority class c based on the degree of mixing of neighborhood categories, the topological boundary sensitivity index and the local density transition characteristics. Construct an initial boundary candidate set for minority class c based on the samples whose boundary candidate confidence exceeds the preset boundary threshold. S27. Filter the initial boundary candidate set of minority class c to obtain the final boundary candidate set of minority class c; S28. Combining all topological features, we obtain the topological feature set of minority class c; combining the neighborhood sample set of each sample in the sample set of minority class c and the local density of each sample in the neighborhood, we obtain the local structural statistics of minority class c; combining the topological feature set of minority class c, the persistence of each topological feature in the topological feature set, the local structural statistics, the topological sensitive sample set, the boundary candidate set, the topological boundary sensitivity index of each sample in the sample set, and the boundary candidate credibility of each sample in the sample set, we obtain the topological summary of minority class c.

3. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 2, characterized in that, Topological boundary sensitivity index for: in, This is the persistence balance parameter, which is the median of the persistence of all topological features of the minority class c; Topological features Durability, Representing topological features The degree of heterogeneity of categories; Representing topological features The degree of local sparsity and dispersion, , As weight.

4. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 1, characterized in that, The topological summary of minority class c includes: the set of topological features of minority class c, the persistence of each topological feature in the topological feature set, local structural statistics, the set of topologically sensitive samples, the set of boundary candidates, the topological boundary sensitivity index of each sample in the sample set, and the boundary candidate confidence of each sample in the sample set; the local structural statistics include: the set of similar neighborhood samples of each sample in the sample set of minority class c, and the local density of each sample in the similar neighborhood; the topological boundary reconstruction and progressive enhancement of the sample set of minority class c includes: S31. Calculate the imbalance ratio of minority class c in the preprocessed industrial dataset. According to the unbalanced proportion To obtain enhanced requirements for a minority of classes, such as C; S32. Based on the topology summary of minority class c, adaptive enhancement allocation is performed on the enhancement requirements of minority class c to obtain the target number of multi-class generation tasks for minority class c; among which, the multi-class generation tasks include: boundary-aware generation task, topology-sensitive enhancement task, and random supplementation generation task. S33. Generate candidate samples for various generation tasks of the minority class c based on the topological summary of the minority class c and the target generation number of each generation task. S34. Perform unified quality control and filtering on candidate samples of various generation tasks for minority class c to obtain candidate augmentation samples for minority class c.

5. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 4, characterized in that, Adaptive enhancement allocation for enhancement requirements of a minority class c includes: Enhancement tendency of computational boundary-aware generation tasks : in, The unbalanced proportion of the minority class c; This represents the average confidence level of the boundary candidates for the minority class c, i.e., the set of boundary candidates for the minority class c. All samples Boundary candidate credibility The average value; This represents the topological boundary sensitivity average index of the minority class c, i.e., the boundary candidate set of the minority class c. All samples topological boundary sensitivity index The average value; The augmentation tendency of computation topology-sensitive augmentation tasks : in, For a minority Topological complexity; For a minority topological feature set The number of topological features in the middle; For a minority Average durability; For a minority The proportion of fragile topological features; For a minority The set of topological features; Topological features Durability; This is the persistence threshold. This is the normalization function; As weight; The augmentation tendency of computationally supplemented tasks ; The allocation ratio of computational boundary-aware generation tasks, topology-sensitive enhancement tasks, and stochastic supplementation generation tasks. , : Calculate the target generation number for boundary-aware generation, topology-sensitive enhancement, and stochastic supplementation generation tasks. , , : in, This indicates an enhanced requirement for a minority class c.

6. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 4, characterized in that, Candidate samples for various generation tasks that generate minority class c include: In the boundary candidate set Constraint interpolation is performed to generate candidate samples of the target number of the boundary-aware generation task. In the boundary candidate set Manifold structure learning is performed on the topology-sensitive sample set to generate candidate samples for the target number of topology-sensitive enhancement tasks; Eliminate the boundary candidate set of minority class c from the sample set of minority class c. The set of topology-sensitive samples is used to obtain the remaining sample set of minority class c; constrained interpolation is performed on the remaining sample set of minority class c to generate candidate samples for the target number of random supplementary generation tasks.

7. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 6, characterized in that, Candidate samples for generating class c topology-sensitive augmentation tasks include: S331. Construct a manifold representation of the sample set of minority class c based on the topological summary of minority class c; the manifold representation includes: neighborhood graph. Geodesic distance matrix and manifold space coordinate matrix; S332. Construct multiple candidate paths for minority class c and their basic structural features based on the topological summary and manifold representation of minority class c. The basic structural features include: distance along the path, degree of local density change, node jump complexity, and straight-line distance. S333. Calculate the manifold interpolation reliability of each candidate path of minority class c based on the basic structural characteristics, and filter the candidate paths whose manifold interpolation reliability exceeds the preset reliability threshold to obtain the candidate paths after filtering of minority class c. S334. Interpolate each candidate path after filtering for minority class c to obtain multiple candidate points for minority class c. S335. Perform local consistency reconstruction mapping on each candidate point of the minority class c to obtain multiple reconstruction samples of the minority class c, i.e., candidate samples.

8. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 7, characterized in that, Multiple candidate paths and their basic structural features are constructed based on the topological summary and manifold representation of a minority class c, including: Multiple samples are selected from the union of the minority class c boundary candidate set and the topology-sensitive sample set as source points. Select each source point based on the manifold representation. target point Multiple source-target point pairs were obtained. Where n is the index of the source point; Construct each set of source-target point pairs in the neighborhood graph G. Candidate paths ,in, As the source point, For the target point, Candidate paths The number of sides in; Calculate the source-target point pairs for each group. Distance along the candidate path ;in, Indicates adjacent nodes The distance between manifold coordinates in the manifold space coordinate matrix, where r is the index of a node in the candidate path; Calculate the source-target point pairs for each group. The degree of local density variation of candidate paths ;in, Represents path nodes The local density of the corresponding sample in the same neighborhood. It is the minimum value; Calculate the source-target point pairs for each group. The node jump complexity of the candidate path ;in, For all source-target point pairs The maximum value among the number of edges of the candidate paths; Calculate the source-target point pairs for each group. The distance between the source and target points of the candidate paths in the manifold space coordinates of the manifold space coordinate matrix, i.e., the straight-line distance. .

9. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 7, characterized in that, Manifold interpolation reliability function , ;in, Indicates candidate paths, Indicate candidate path Path curvature, Indicate candidate path The degree of local density change Indicate candidate path The node jump complexity, Indicate candidate path The straight-line distance The distance along the line, Weight, It is a local minimum.

10. The industrial imbalance data augmentation method based on topology analysis and manifold sampling according to claim 6, characterized in that, Unified quality control and filtering of candidate samples for various generation tasks of a minority class c includes: Calculate candidate samples for each generation task of the minority class c. Geometric position rationality : ； in, , These represent the generated candidate samples. Two samples, Candidate samples and samples The distance between them Candidate samples and samples The distance between them For two samples , The distance between them It is the minimum value; Generate candidate samples Two samples , The candidate samples are obtained by combining the topological boundary sensitivity index. The topological boundary sensitivity index; based on candidate samples The topological boundary sensitivity index is used to calculate candidate samples. Sensitivity to topological boundaries; calculation of candidate samples The degree of mixing of neighborhood categories and the characteristics of local density transition; Based on candidate samples The candidate samples are calculated based on the degree of mixing of neighborhood categories, sensitivity to topological boundaries, and local density transition features. Boundary candidate credibility ; Calculate candidate samples Boundary property consistency : in, Candidate samples The corresponding minority class c boundary candidate set The average confidence level of the boundary candidates for all samples. Candidate samples The credibility of the boundary candidates; Calculate candidate samples Set of nearest neighbor samples of the same type and local density in the same neighborhood Calculate the set of nearest neighbor samples of the same type. Calculate the local density of each sample in its neighborhood and the set of nearest neighbors of the same type. The average local density of all samples in their similar neighborhood. ; Calculate candidate samples Local structural continuity : Calculate candidate samples Numerical stability : in, Indicates candidate samples The The safe range of values ​​allowed for each feature Indicates candidate samples The total number of features, Candidate samples The number of features that fall within the allowed safe value range. Let f be the minimum and maximum values ​​of the f-th feature in the preprocessed industrial dataset, respectively. The range of values; Calculate candidate samples for minority class c Credibility evaluation : in, , , , These are weight parameters; Candidate samples whose credibility evaluation exceeds the preset credibility threshold are selected to obtain a minority of candidate enhanced samples of class c.

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