A data classification system based on support vector machines

Abstract

The application discloses a data classification system based on a support vector machine, and relates to the technical field of machine learning.The system constructs an approximate nearest neighbor graph to calculate the local density of samples, adaptively determines the kernel bandwidth, generates a kernel function which is a weighted compound of a local Gaussian kernel and a global polynomial kernel, divides the samples into strongly connected subgraphs with overlapping boundaries based on graph Laplacian spectrum embedding and distributes the samples to distributed nodes, fuses the dual variables of the boundary sharing samples through an augmented Lagrange iteration, and performs low-rank approximation on the kernel matrix based on leverage score sampling landmark points, so that the storage and calculation overhead is compressed to an approximate linear level.The application can adaptively generate a kernel function according to the data manifold structure, maintains the integrity of the classification boundary in distributed training, reduces the memory and calculation overhead in a large-scale high-dimensional data scenario, and is suitable for data classification scenarios such as financial risk control and medical diagnosis.

Description

Technical Field

[0001] This invention relates to the field of machine learning technology, specifically to a data classification system based on support vector machines. Background Technology

[0002] Support Vector Machine (SVM) is a supervised learning classification algorithm based on statistical learning theory and aiming at maximizing the margin. Its training process is essentially solving a quadratic programming problem with the kernel matrix as the core operation object. With its rigorous theoretical foundation of margin maximization and excellent generalization ability, SVM has important application value in fields with high interpretability requirements, such as financial risk control, medical diagnosis, and fault detection. SVM maps the original data to a high-dimensional feature space through the kernel function, and solves the classification hyperplane that maximizes the margin in this space. Theoretically, it has a globally optimal solution.

[0003] A typical solution currently used in the industry to address the problem of training support vector machines on large-scale data is as follows: the original training dataset is randomly split or simply sharded based on hashing, and the data is evenly distributed to multiple computing nodes. Each computing node independently solves the local support vector machine quadratic programming subproblem on its local data subset based on a pre-defined unified kernel function, and obtains local support vectors and local decision hyperplane parameters. The local model results of each node are then aggregated through voting fusion or parameter averaging to obtain an approximate global classification model. The types of kernel functions, penalty factors, kernel parameters and other hyperparameters are optimized by traversing the pre-defined parameter space through grid search and cross-validation, and the parameter combination with higher accuracy on the validation set is selected as the final model configuration.

[0004] The above scheme has the following shortcomings: Because the scheme randomly splits or simply hashes the data, the key support vectors that were originally near the global classification boundary are randomly scattered to different computing nodes or even split into regions with ambiguous boundaries. This further leads to each node independently solving local subproblems without complete boundary information, resulting in a systematic deviation between the local decision boundary and the global optimal boundary. Ultimately, this causes a decrease in the model classification accuracy in large-scale data scenarios, and the nodes generate high communication overhead due to repeated exchange of support vector information.

[0005] Meanwhile, because the scheme uses a globally uniform and pre-fixed kernel function, the kernel function cannot perceive the differences in density and geometric structure of the dataset in different local regions. This leads to the dual risks of overfitting in data-dense regions and underfitting in data-sparse regions. The grid search method that eliminates this risk requires traversing a large number of parameter combinations and repeatedly training the model, which further exacerbates the consumption of computational resources. To address this, we propose a data classification system based on support vector machines. Summary of the Invention

[0006] The purpose of this invention is to provide a data classification system based on support vector machines.

[0007] The technical problems to be solved by this invention include two aspects: First, when traditional support vector machines process large-scale datasets, the storage and computational complexity of the kernel matrix increases with the square and cube of the number of samples, respectively, leading to a sharp increase in memory overhead and computation time. Existing random sampling or simple distributed segmentation schemes often sacrifice key support vectors, resulting in a decrease in classification accuracy. Second, the kernel function of existing support vector machine systems is usually a pre-defined fixed form, and its hyperparameters depend on human experience or grid search for determination, making it difficult to adapt to the complex nonlinear manifold structure inherent in the dataset. This leads to underfitting or overfitting of the model in sparse or dense regions of the data, making it difficult to guarantee classification accuracy.

[0008] To address the aforementioned technical problems, this invention provides a data classification system based on support vector machines, comprising a data manifold-aware dynamic composite kernel generation module, a topology-preserving graph partitioning module, a distributed consensus training module, a memory-compressed solution module, and a global decision function generation module.

[0009] The data manifold-aware dynamic composite kernel generation module is used to construct an approximate nearest neighbor graph based on the original training dataset. It calculates the local density index of each sample point based on the approximate nearest neighbor graph, adaptively determines the kernel function bandwidth parameter for each sample point based on the local density index, and generates a composite kernel function composed of local Gaussian kernel components and global polynomial kernel components with density-adaptive weighting coefficients based on the kernel function bandwidth parameter.

[0010] The topology-preserving graph partitioning module is connected to the data manifold-aware dynamic composite kernel generation module. It is used to construct a graph Laplacian matrix based on the approximate nearest neighbor graph, perform eigenvalue decomposition on the graph Laplacian matrix to obtain the spectral embedding matrix, divide all sample points in the spectral embedding space into multiple non-overlapping core subsets, and for each core subset, include the external nodes connected to the sample points in the core subset in the approximate nearest neighbor graph into the core subset to form a strongly connected subgraph with overlapping boundary nodes. Multiple strongly connected subgraphs are distributed to multiple distributed computing nodes.

[0011] The distributed consensus training module is connected to the topology-preserving graph partitioning module. It controls each distributed computing node to independently solve the local support vector machine dual optimization subproblem on the local strongly connected subgraph according to the composite kernel function to obtain local dual variables. The central coordination node then uses the augmented Lagrange iteration method to perform consistency fusion on the local dual variables corresponding to the overlapping boundary nodes based on the local dual variables uploaded by each distributed computing node. The global consensus variables are then updated and distributed to each distributed computing node for iteration until the preset convergence condition is met, resulting in the global consensus dual variables and the global support vector set.

[0012] The memory compression solution module is connected to the distributed consensus training module. It is used to estimate the leverage score of each sample point in the training dataset, construct a sampling probability distribution based on the leverage score, sample a set of landmark points with a number less than the total number of samples according to the sampling probability distribution, and construct a low-rank approximation matrix of the original kernel matrix based on the kernel matrix between the set of landmark points and all sample points, as well as the kernel sub-matrices between landmark points. This matrix is ​​then called by the distributed consensus training module when solving the dual optimization sub-problem of the local support vector machine.

[0013] The global decision function generation module is connected to the distributed consensus training module. It is used to construct a classification decision function based on the global consensus dual variable and the global support vector set, and output the category determination result of the sample to be classified.

[0014] Compared with the prior art, the beneficial effects of the present invention by adopting the above technical solution are as follows:

[0015] 1. This invention automatically generates composite kernel functions that adapt to the inherent geometric structure of the data through a data manifold-aware dynamic composite kernel generation module. It can achieve adaptive configuration of kernel functions without human experience or grid search, thereby improving the classification accuracy of complex nonlinear data.

[0016] 2. Since the kernel function bandwidth parameter is directly related to the local density index of the sample, the topology-preserving graph partitioning module further reuses the approximate nearest neighbor graph connection relationship on which the local density index depends for graph partitioning and boundary expansion. This makes the kernel function adaptive result and the distributed graph partitioning result based on the same density metric. This overcomes the technical bias of the prior art, where kernel function configuration and distributed data partitioning are independent of each other and do not perceive each other's internal structure, resulting in collaborative failure and double distortion of boundary support vectors and kernel parameters. This achieves the synergistic gain of kernel function adaptation and distributed boundary preservation.

[0017] 3. This invention uses a memory compression solution module to actively sample landmarks based on leverage fractions to perform a low-rank approximation of the kernel matrix. This reduces the kernel matrix storage overhead from the quadratic level of the number of samples to an approximately linear level, and the computational complexity from the cubic level of the number of samples to an approximately linear level. This enables the system to process large-scale high-dimensional datasets while balancing classification accuracy and processing efficiency. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall system flow in an embodiment of the present invention;

[0019] Figure 2 This is a schematic diagram of the composite kernel generation process in an embodiment of the present invention;

[0020] Figure 3This is a schematic diagram of the distributed training compression solution subprocess in an embodiment of the present invention. Detailed Implementation

[0021] The following is in conjunction with the appendix Figure 1-3 The specific embodiments of the present invention will be further described below. It should be noted that the description of these embodiments is for the purpose of helping to understand the present invention, but does not constitute a limitation of the present invention.

[0022] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0023] The data classification system based on support vector machines provided by this invention generally includes a data manifold-aware dynamic composite kernel generation module, a topology-preserving graph partitioning module, a distributed consensus training module, a memory-compressed solution module, and a global decision function generation module. These modules are sequentially connected and work together to complete the entire process from input of the original training data to output of the final classification decision. After preprocessing, the original training dataset is first input into the data manifold-aware dynamic composite kernel generation module. The composite kernel function generation rules output by this module are input into the topology-preserving graph partitioning module along with the original training data. The strongly connected subgraph with overlapping boundaries output by the topology-preserving graph partitioning module is distributed to multiple distributed computing nodes. With the support of the memory-compressed solution module, each distributed computing node solves the local support vector machine dual optimization subproblem on its local subgraph. The output results of each distributed computing node are converged to the central coordinating node in the distributed consensus training module for consistent iterative optimization. After convergence, the global decision function generation module outputs a unified classification decision function.

[0024] (a) Data manifold-aware dynamic composite kernel generation module:

[0025] This module is designed to eliminate the reliance on preset static kernel functions and automatically generate locally adaptive composite kernel functions by mining the topological structure of the dataset itself.

[0026] Specifically, the module first calls the hierarchical approximate nearest neighbor graph construction unit to establish a set of k nearest neighbors and corresponding edge weights for each sample point in the training dataset. The edge weights are represented by the Euclidean distance between the sample points, thereby constructing an approximate nearest neighbor graph that reflects the local connectivity of the dataset. Optionally, the module can also use the shortest path algorithm on the graph to estimate the geodesic distance between any two sample points based on the approximate nearest neighbor graph, so as to more accurately reflect the intrinsic geometric relationship of the data on the curved manifold and provide a distance metric that is closer to the real structure of the data than the Euclidean distance for the subsequent kernel function construction.

[0027] Based on this, the module calculates the local density index of each sample point according to the approximate nearest neighbor graph, and the calculation method is as follows:

[0028] ;

[0029] in, Indicates the first Local density index of each sample point This indicates the preset number of nearest neighbors. Indicates the first sample points Nearest neighbor index set, Represents sample points With sample points The Euclidean distance between them;

[0030] Furthermore, this module adaptively determines the kernel function bandwidth parameter for each sample point based on the aforementioned local density index, calculated as follows:

[0031] ;

[0032] in, Indicates the first Adaptive bandwidth parameters for each sample point This represents the preset reference bandwidth constant. This represents the density-sensitive adjustment coefficient, used to control the degree to which bandwidth changes with density. The arithmetic mean of the local density index of all samples is given by the above formula. It can be seen that when the density of the region where the sample point is located is higher than the average level, its corresponding bandwidth is smaller and the kernel function has a stronger local resolution in the region. When the density of the region where the sample point is located is lower than the average level, the bandwidth is larger to ensure that the kernel function covers the sparse region sufficiently.

[0033] Subsequently, this module constructs a composite kernel function for sample pairs, calculated as follows:

[0034] ;

[0035] in, Represents sample points and The composite kernel function values ​​between Indicates by and The joint bandwidth obtained by arithmetic mean and Let represent the bias constant and order of the polynomial kernel, respectively, both of which are preset hyperparameters. The adaptive weighting coefficients between the local Gaussian kernel components and the global polynomial kernel components are calculated as follows:

[0036] ;

[0037] in, This represents the weight sensitivity coefficient, used to control the steepness of the change in the weighting coefficient with density difference. As shown in the formula above, when the density of the sample pair's region is significantly higher than the average level, Approaching 1, the composite kernel function is dominated by Gaussian kernel components that characterize the fine local structure. When the density of the sample pair in the region is low, Approaching 0, the composite kernel function mainly uses polynomial kernel components that characterize the global trend, thereby achieving adaptive matching of the kernel function to the data manifold structure;

[0038] This module iterates through sample pairs in the dataset, or calculates only sample pairs with actual connections according to the nearest neighbor graph to reduce the amount of computation, and outputs the compound kernel function generation rules and the corresponding kernel matrix calculation method for subsequent modules to call.

[0039] (ii) Topology-preserving graph partitioning module:

[0040] This module is used to solve the problem of key support vectors being lost due to data splitting in distributed training;

[0041] Specifically, this module calculates the graph Laplacian matrix based on the aforementioned approximate nearest neighbor graph, and the calculation method is as follows:

[0042] ;

[0043] in, Represents the graph Laplace matrix. The degree matrix of the graph is a diagonal matrix, where the diagonal elements are the degrees of the corresponding sample points in the graph. This represents the adjacency weight matrix of a graph, where each element represents the connection weight of the edges between sample points.

[0044] This module performs eigenvalue decomposition on the graph Laplacian matrix, selects the eigenvectors corresponding to the first preset number of non-zero eigenvalues ​​after sorting by numerical value, and forms a spectral embedding matrix. The preset number is not less than the number of distributed computing nodes. This maps the original high-dimensional sample to a low-dimensional spectral embedding space, so that sample points with similar topological relationships in the original graph are also similar in distance in the spectral embedding space.

[0045] In the spectral embedding space, this module uses a clustering algorithm to divide all samples into non-overlapping core subsets, the same number as the number of distributed computing nodes. To avoid truncating key support vectors on the classification boundary in the subgraph partitioning, this module performs boundary expansion on each core subset: for any sample point in the core subset, if there is a connecting edge pointing to a node outside the subset in the original approximate nearest neighbor graph, then the outside node is included in the training set of the subset, forming a strongly connected subgraph with overlapping regions. This ensures that key samples near the classification boundary can be perceived by multiple adjacent computing nodes at the same time. The multiple overlapping subgraphs are then distributed to the corresponding distributed computing nodes.

[0046] (III) Distributed Consensus Training Module:

[0047] Each distributed computing node independently solves the local support vector machine quadratic programming subproblem based on the aforementioned composite kernel function. The dual optimization objective of the standard support vector machine is:

[0048] ;

[0049] The constraints are:

[0050] ;

[0051] in, Indicates the first The Lagrange multipliers corresponding to each sample Indicates the first The category label for each sample, with a value of either positive or negative one. This represents the penalty factor, used to balance maximizing the margin with tolerance for misclassification. This represents the number of samples in the current subgraph. Each distributed computing node solves for the set of local dual variables, denoted as... ,in Number the nodes;

[0052] The central coordination node collects the local dual variables uploaded by each distributed computing node, and optimizes the hierarchical consistency of the dual variables corresponding to shared samples in the overlapping areas of each node using an augmented Lagrangian approach. Specifically, the central coordination node constructs an augmented Lagrangian function:

[0053] ;

[0054] in, Indicates the first The negative form of the dual objective function of a local support vector machine for distributed computing nodes. This represents the total number of distributed computing nodes. This represents a preset penalty parameter used to control the strength of consistency constraints between local variables and global consensus variables. Represents a global consensus variable. Indicates the first The dual auxiliary variable corresponding to each node, superscript Indicates vector transpose;

[0055] During the iteration process, each distributed computing node solves the local update problem in parallel:

[0056] ;

[0057] Among them, subscript Indicates the iteration round number. Indicates the first In the first iteration The central coordinating node collects the updated local dual variables from each node and updates the global consensus variables.

[0058] ;

[0059] For shared samples within overlapping regions, their local dual variables in different nodes are weighted and consistent through this formula, thereby ensuring that the same sample has a unique and definite classification contribution in a global sense, avoiding information loss in boundary support vectors due to partitioning. Each distributed computing node then updates its local dual auxiliary variables:

[0060] ;

[0061] Determine whether both the original residual and the dual residual are less than the preset convergence threshold. If not, return to the local update problem and continue iterating. If they are satisfied, terminate the iteration and output a globally consistent set of support vectors and dual variables. After convergence, the central coordinating node merges the local support vector sets retained by each computing node and determines the bias term of the classification hyperplane by combining the global consensus variables.

[0062] (iv) Memory compression solution module:

[0063] This module reduces the storage and computational overhead of the kernel matrix. For kernel matrices processed by local computing nodes or central coordination nodes, this module does not directly construct and store the complete kernel matrix. Instead, it quickly estimates the statistical leverage score for each sample using a random projection approximation method. The calculation method is as follows:

[0064] ;

[0065] in, Indicates the first Leverage score of each sample, Represents the kernel matrix. This represents the regularization parameter, used to ensure the numerical stability of matrix inversion. Represents the identity matrix, subscript This means taking the first element on the diagonal of the matrix. One element;

[0066] Based on the leverage score of each sample, this module constructs a probability distribution with the normalized leverage score as the sampling probability. Sample points with a number less than the total number of samples are sampled without replacement according to this probability distribution as landmark points. Since samples with higher leverage scores contribute more to the low-rank structure of the kernel matrix and the classification decision boundary, this sampling mechanism prioritizes the selection of samples that have a key impact on the decision boundary, and has higher approximate accuracy compared to uniform random sampling.

[0067] Based on the selected landmarks, this module calculates the kernel matrix between landmarks and the kernel matrix between all samples and landmarks, which are transposes of each other. The module then performs eigenvalue decomposition on the landmark kernel matrix to construct a low-rank approximation of the original kernel matrix.

[0068] ;

[0069] in, Represents the original kernel matrix. The kernel matrix represents the relationship between samples and landmarks. This represents the inverse matrix of the landmark nucleus matrix. In actual calculations, a pseudo-inverse or regularization terms can be used to ensure numerical stability. express The transpose of the kernel matrix is ​​used to reduce the storage overhead of the kernel matrix from the square of the number of samples to the product of the number of samples and the number of landmarks. When the number of landmarks is much smaller than the total number of samples, it is approximately equivalent to the linear level. This module substitutes the above low-rank approximate kernel matrix into the support vector machine quadratic programming solver for iterative solution. Since the matrix operation scale is reduced from the square of the number of samples to the product of the number of samples and the number of landmarks and the square of the number of landmarks, the floating-point operation and memory usage required for the solution process are greatly reduced, and the computational complexity is reduced from the original cubic level to the approximately linear level.

[0070] (v) Global Decision Function Generation Module:

[0071] After completing the collaborative processing of the above modules, this module generates a unified classification decision function based on the globally converged set of support vectors and dual variables:

[0072] ;

[0073] in, Indicates the samples to be classified The classification results Represents the set of global support vector indices. , They represent the first The dual variables and class labels corresponding to each support vector This indicates that the kernel function determined by the aforementioned data manifold-aware dynamic composite kernel generation module is applied to the support vectors. With the sample to be classified The values ​​between, The bias term representing the classification hyperplane is determined by the convergence result of the global consensus optimization. This represents the symbolic function used to output the classification result. Specific Implementation

[0074] Taking a fault detection dataset for industrial equipment as an example, this dataset contains a large number of high-dimensional sensor samples. Each sample contains multiple features such as vibration, temperature, and current. After inputting this dataset into the system of this invention, the data manifold perception dynamic composite kernel generation module first constructs an approximate nearest neighbor graph and calculates the local density index of each sample, automatically generating a composite kernel function without the need for manual setting of fixed kernel parameters. The topology-preserving graph partitioning module divides the sample set into several strongly connected subgraphs and distributes them to several distributed computing nodes. Each subgraph retains a certain proportion of overlapping samples at the partition boundary. With the support of the memory compression solution module, each computing node compresses the local kernel matrix into a landmark kernel matrix to participate in the calculation and solve the local subproblems. The distributed consensus training module converges after several rounds of augmented Lagrange iterations and outputs a globally consistent set of support vectors and classification hyperplane parameters. Compared with the traditional distributed scheme that uses random partitioning and fixed Gaussian kernels, this invention can more completely retain the key support vectors near the classification boundary while maintaining similar training time. At the same time, it keeps the storage occupation of the kernel matrix at a level that is approximately linear with the number of samples, enabling the system to complete the training and classification of large-scale high-dimensional data under limited memory conditions.

[0075] It should be noted that, in other embodiments of the present invention, the topology-preserving graph partitioning module can also use a community detection algorithm based on modularity optimization instead of the spectral clustering method based on graph Laplacian matrix eigenvalue decomposition for subgraph partitioning. This can also identify the community structure of the data and form overlapping subgraphs by combining boundary expansion strategies. The memory compression solution module can also use an explicit mapping method of kernel function based on random Fourier features instead of the low-rank approximation method based on leverage fractional sampling. By mapping the kernel function to an inner product approximation in a low-dimensional random feature space, the memory and computational overhead of kernel matrix operations can also be reduced. The above alternative implementation methods can achieve similar technical effects to the foregoing embodiments and are all within the protection scope of the present invention.

[0076] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications without departing from the spirit and scope of the present invention. Therefore, any modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope defined by the claims of the present invention.

Claims

1. A data classification system based on support vector machines, characterized in that, include: The data manifold-aware dynamic composite kernel generation module is used to construct an approximate nearest neighbor graph based on the original training dataset, calculate the local density index of each sample point according to the approximate nearest neighbor graph, adaptively determine the kernel function bandwidth parameter for each sample point according to the local density index, and generate a composite kernel function composed of local Gaussian kernel components and global polynomial kernel components according to the kernel function bandwidth parameter with density adaptive weighting coefficients. The topology-preserving graph partitioning module, connected to the data manifold-aware dynamic composite kernel generation module, is used to construct a graph Laplacian matrix based on the approximate nearest neighbor graph, perform eigenvalue decomposition on the graph Laplacian matrix to obtain a spectral embedding matrix, divide all sample points in the spectral embedding space into multiple non-overlapping core subsets, and for each core subset, include the external nodes connected to the sample points in the approximate nearest neighbor graph into the core subset to form a strongly connected subgraph with overlapping boundary nodes, and distribute multiple strongly connected subgraphs to multiple distributed computing nodes; The distributed consensus training module, connected to the topology-preserving graph partitioning module, controls each distributed computing node to independently solve the local support vector machine dual optimization subproblem on the local strongly connected subgraph according to the composite kernel function, obtaining local dual variables. The central coordination node then uses the augmented Lagrange iteration method to perform consistency fusion on the local dual variables corresponding to overlapping boundary nodes based on the local dual variables uploaded by each distributed computing node, updates the global consensus variables, and distributes them to each distributed computing node for iteration until the preset convergence condition is met, resulting in the global consensus dual variables and the global support vector set. The memory compression solution module, connected to the distributed consensus training module, is used to estimate the leverage score of each sample point in the training dataset, construct a sampling probability distribution based on the leverage score, sample a set of landmark points with a number less than the total number of samples according to the sampling probability distribution, and construct a low-rank approximation matrix of the original kernel matrix based on the kernel matrix between the set of landmark points and all sample points, as well as the kernel sub-matrices between landmark points, for the distributed consensus training module to call when solving the dual optimization sub-problem of the local support vector machine; The global decision function generation module, connected to the distributed consensus training module, is used to construct a classification decision function based on the global consensus dual variable and the global support vector set, and output the category determination result of the sample to be classified.

2. The data classification system based on support vector machine according to claim 1, characterized in that: The local density index is calculated as follows: ； in, Indicates the first Local density index of each sample point This indicates the preset number of nearest neighbors. Indicates the first sample points Nearest neighbor index set, Represents sample points With sample points The Euclidean distance between them; The kernel function bandwidth parameter is determined as follows: ； in, Indicates the first Kernel function bandwidth parameter for each sample point Indicates the preset reference bandwidth constant. This represents the density-sensitive adjustment coefficient. This represents the arithmetic mean of the local density indices for all sample points.

3. The data classification system based on support vector machine according to claim 1, characterized in that: The composite kernel function is constructed as follows: ； in, Represents sample points With sample points The composite kernel function values ​​between Indicates by At The joint bandwidth obtained by arithmetic mean and These represent the preset polynomial kernel bias constant and order, respectively. The adaptive weighting coefficients between the local Gaussian kernel components and the global polynomial kernel components are calculated as follows: ； in, This represents the preset weight sensitivity coefficient.

4. A data classification system based on support vector machines according to claim 1, characterized in that: The topology-preserving graph partitioning module is specifically used to perform eigenvalue decomposition on the graph Laplacian matrix, select the eigenvectors corresponding to the first preset number of non-zero eigenvalues ​​after sorting by numerical value to form the spectral embedding matrix, the preset number being no less than the number of distributed computing nodes, and use a clustering algorithm to divide all sample points in the spectral embedding space into a core subset with the same number as the number of distributed computing nodes.

5. A data classification system based on support vector machines according to claim 1, characterized in that: The distributed consensus training module is specifically used to construct the augmented Lagrange function: ； in, Indicates the first The dual objective function of a local support vector machine for distributed computing nodes. This represents the total number of distributed computing nodes. This indicates the preset penalty parameters. Represents a global consensus variable. Indicates the first The dual auxiliary variables corresponding to each distributed computing node; Each distributed computing node solves the local update problem in parallel to obtain the updated local dual variables. The central coordination node then updates the global consensus variables based on the updated local dual variables from each distributed computing node, as follows: ； Each distributed computing node updates its dual auxiliary variable based on the updated global consensus variable, and repeats the above iterative process until both the original residual and the dual residual are less than the preset convergence threshold.

6. A data classification system based on support vector machines according to claim 1, characterized in that: The memory compression solving module is specifically used to estimate the leverage fraction of the i-th sample point in the following manner: ； in, Indicates the first Leverage score for each sample point Represents the kernel matrix. This indicates the preset regularization parameters. Represent the identity matrix, and construct a low-rank approximation matrix as follows: ； in, This represents the kernel matrix between all sample points and landmark points. This represents the nucleus matrix between landmarks. express The transpose of .

7. A data classification system based on support vector machines according to claim 1, characterized in that: The sampling probability distribution is obtained by normalizing the leverage fraction of each sample point, and the set of landmark points is obtained by sampling without replacement according to the sampling probability distribution.

8. A data classification system based on support vector machines according to claim 1, characterized in that: The topology-preserving graph partitioning module is specifically used to partition the entire sample points into subgraphs using a community detection algorithm based on modularity optimization, thereby obtaining multiple core subsets.

9. A data classification method based on support vector machines, characterized in that, include: An approximate nearest neighbor graph is constructed based on the original training dataset. The local density index of each sample point is calculated based on the approximate nearest neighbor graph. The kernel function bandwidth parameter is adaptively determined for each sample point based on the local density index. A composite kernel function is generated based on the kernel function bandwidth parameter, which is composed of local Gaussian kernel components and global polynomial kernel components with density adaptive weighting coefficients. A graph Laplacian matrix is ​​constructed based on the approximate nearest neighbor graph. The graph Laplacian matrix is ​​decomposed into an eigenvalue matrix to obtain a spectral embedding matrix. All sample points are divided into multiple non-overlapping core subsets in the spectral embedding space. For each core subset, the external nodes connected to the sample points in the approximate nearest neighbor graph are included in the core subset to form a strongly connected subgraph with overlapping boundary nodes. Multiple strongly connected subgraphs are distributed to multiple distributed computing nodes. Each distributed computing node independently solves the local support vector machine dual optimization subproblem on its local strongly connected subgraph according to the composite kernel function, obtaining local dual variables. The central coordination node then uses the augmented Lagrange iteration method to perform consensus fusion on the local dual variables corresponding to overlapping boundary nodes based on the local dual variables uploaded by each distributed computing node, updates the global consensus variables, and distributes them to each distributed computing node for iteration until the preset convergence condition is met, resulting in the global consensus dual variables and the global support vector set. Estimate the leverage score of each sample point in the training dataset, construct a sampling probability distribution based on the leverage score, sample a set of landmarks with a number less than the total number of samples according to the sampling probability distribution, construct a low-rank approximation matrix of the original kernel matrix based on the kernel matrix between the set of landmarks and all sample points and the kernel sub-matrices between landmarks, and call the low-rank approximation matrix when solving the dual optimization sub-problem of the local support vector machine. A classification decision function is constructed based on the global consensus dual variable and the global support vector set, and the category determination result of the sample to be classified is output.

10. A data classification method based on support vector machines according to claim 9, characterized in that: The local density index is calculated as follows: ； The kernel function bandwidth parameter is determined as follows: ； in, Indicates the first Local density index of each sample point This indicates the preset number of nearest neighbors. Indicates the first sample points Nearest neighbor index set, Represents sample points With sample points The Euclidean distance between them Indicates the first Kernel function bandwidth parameter for each sample point Indicates the preset reference bandwidth constant. This represents the density-sensitive adjustment coefficient. This represents the arithmetic mean of the local density indices for all sample points.

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