Multi-view concept decomposition clustering method based on consensus learning and double graph regularization

Abstract

The application discloses a multi-view concept decomposition clustering method based on consensus learning and double-graph regularization, and belongs to the technical field of data processing, and comprises the following steps: S1, generating a consensus base matrix for all views, and constructing a first target function; S2, constructing a sample similarity graph for each view, taking the sample similarity graph as a regularization constraint, and constructing a second target function based on the first target function; S3, constructing a multi-view concept decomposition clustering model based on direct consensus learning and double-graph regularization according to the second target function; and S4, solving the multi-view concept decomposition clustering model to obtain a classification result. By directly learning a unified consensus representation matrix, the application discards a complex multi-view alignment process in a traditional method, significantly simplifies a model structure, reduces a calculation complexity, and makes optimization solving more efficient.

Description

Technical Field

[0001] This invention belongs to the field of data processing technology, specifically relating to a multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization. Background Technology

[0002] In recent years, multi-view clustering methods have been extensively researched and developed. Among them, concept decomposition-based models, by seeking non-negative low-dimensional representations for data, can intuitively reveal the hidden cluster structure in the data, and have become an important and effective method. To integrate complementary information from multiple views, existing techniques generally follow a mainstream paradigm: first, construct a unique representation matrix for each view, and then, by introducing additional consensus constraints or alignment terms, encourage these view-specific representations to converge towards a unified consensus matrix. This "separate representations, posterior alignment" approach aims to uncover consistent clustering structures across views and has achieved good performance in many applications. Building on this, to further improve representation quality, research has begun to introduce graph regularization techniques into the model to maintain the inherent geometric structure of the data. For example, the bi-graph regularized concept decomposition method, by simultaneously constructing data sample graphs and feature graphs, constrains the smoothness of low-dimensional representations in the sample space and feature space respectively, enabling the model to capture richer structured information, which represents an important technological advancement in this direction. However, despite the continuous development of the above methods, their core framework still relies on the complex path of generating independent representations for each view and then fusing them. This results in numerous model parameters and a complex structure. Furthermore, it may make it difficult to directly and efficiently utilize the inherent consistency information of multi-view data during the fusion process. Therefore, exploring simpler and more compact consensus representation learning mechanisms within the framework of concept decomposition, and making fuller use of the geometric structure of data to enhance clustering discriminative power, remains a direction worthy of in-depth research.

[0003] The existing technical solution aims to achieve multi-view clustering through an integrated framework. Its core is to learn a set of view-specific representation matrices for each view's data, including coefficient and basis matrices, and obtain low-dimensional representations of each view by minimizing reconstruction errors. To improve clustering discriminative power, the model introduces a clustering diversity constraint, aiming to maximize the differences between different cluster centers to avoid trivial solutions. For multi-view fusion, a global consensus matrix is ​​set, and a weighted Frobenius norm regularization term is used to constrain all view-specific basis matrices to align with this consensus matrix. The view weights are adaptively learned through maximum entropy regularization to ensure balance. The entire model is solved using an alternating iterative optimization algorithm, which guarantees that the objective function does not monotonically increase after each update, thus achieving convergence and ultimately completing the clustering task based on the learned representations. However, the existing technology has the following drawbacks: First, the model structure is complex: it requires maintaining an independent representation matrix for each view and fusing them through additional alignment terms, resulting in many parameters and low optimization efficiency; Second, information utilization is insufficient: it does not simultaneously mine and maintain the geometric structure of the data in the sample space and feature space, which limits the discriminative power of the representation; Third, the fusion strategy is not refined: the learning of view weights is not fully linked to the representation quality and structure preservation ability of each view, which affects the robustness of fusion. Summary of the Invention

[0004] To address the above problems, this invention proposes a multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization.

[0005] The technical solution of this invention is: a multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization, comprising the following steps:

[0006] S1. Generate a consensus basis matrix for all views and construct the first objective function;

[0007] S2. Construct sample similarity maps for each view, use the sample similarity maps as regularization constraints, and construct a second objective function based on the first objective function;

[0008] S3. Based on the second objective function, construct a multi-view concept decomposition and clustering model based on direct consensus learning and dual-graph regularization;

[0009] S4. Solve the multi-view concept decomposition clustering model to obtain the classification results.

[0010] Furthermore, in S1, the expression for the first objective function is:

[0011] ;

[0012] in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views.

[0013] Furthermore, in S2, the expression for the second objective function is:

[0014] ;

[0015] in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. This represents the second equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views. Describes the rank of a matrix. This represents the Laplacian matrix of each data plot.

[0016] Furthermore, in S3, the expression for the multi-view concept decomposition clustering model is:

[0017] ;

[0018] in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. This represents the second equilibrium parameter. This represents the third equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views. Describes the rank of a matrix. This represents the Laplacian matrix of each data plot. This represents the Laplacian matrix of each feature map.

[0019] Furthermore, S4 includes the following sub-steps:

[0020] S41. Initialize parameters;

[0021] S42, Update the coefficient matrix of each view and the consensus basis matrix shared by all views, and proceed to S43;

[0022] S43, Update the learnable view weights;

[0023] S44. Repeat S42-S43, and when the convergence condition is met or the maximum number of iterations is reached, determine the cluster labels and output the classification results.

[0024] Furthermore, in S41, the initialization parameters include the coefficient matrix of each view, the consensus basis matrix shared by all views, the Laplacian matrix of each data graph, the Laplacian matrix of each feature graph, and the learnable view weights.

[0025] The beneficial effects of this invention are as follows: By directly learning a unified consensus representation matrix, this invention eliminates the complex multi-view alignment process in traditional methods, significantly simplifying the model structure, reducing computational complexity, and making optimization more efficient. The simultaneous introduction of dual regularization terms for the data graph and feature graph forces the model to maintain the manifold structure of both the sample space and feature space during the learning process, thereby learning a more discriminative low-dimensional consensus representation. This lays a better foundation for subsequent clustering tasks, and its effectiveness has been demonstrated through extensive experiments. Attached Figure Description

[0026] Figure 1 A flowchart of a multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization;

[0027] Figure 2 The clustering results for six datasets—NGs, 3Scoure, BBC, Wikipedia-test, Reuters, and Wikipedia—are presented using eight comparative methods.

[0028] Figure 3 Example plot of sequence error convergence curves for 3Scources and Wikipedia-test data;

[0029] Figure 4 Visualizations of three views and clustering results for the BBC dataset;

[0030] Figure 5 Figures showing the results of ablation experiments on the 3Sources and BBC datasets. Detailed Implementation

[0031] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0032] like Figure 1 As shown, this invention provides a multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization, comprising the following steps:

[0033] S1. Generate a consensus basis matrix for all views and construct the first objective function;

[0034] S2. Construct sample similarity maps for each view, use the sample similarity maps as regularization constraints, and construct a second objective function based on the first objective function;

[0035] S3. Based on the second objective function, construct a multi-view concept decomposition and clustering model based on direct consensus learning and dual-graph regularization;

[0036] S4. Solve the multi-view concept decomposition clustering model to obtain the classification results.

[0037] This invention aims to address the problems of complex models and low efficiency in existing methods by designing a model framework for directly learning a unified consensus representation matrix. This framework abandons the complex process of constructing and aligning independent representation matrices for each view, instead directly capturing the inherent consistency of cross-view data with a simpler structure, thereby effectively reducing model complexity.

[0038] In the consensus representation learning process, this invention innovatively introduces dual regularization constraints on the data graph and the feature graph simultaneously, enabling the model to maintain the geometric manifold structure of both the data sample space and the feature space, thereby uncovering a deeper and more discriminative data structure to enhance the discriminative power of the final cluster representation.

[0039] This invention integrates a unified consensus representation with dual-graph regularization constraints to form an efficient multi-view clustering objective function and provides a matching stable optimization algorithm, aiming to achieve more accurate and stable multi-view clustering performance.

[0040] In this embodiment of the invention, in S1, for a single view data matrix Its conceptual decomposition model aims to find two non-negative matrices: the coefficient matrix and the non-negative matrix. With basis matrix , making .

[0041] When extending the above framework to multi-view scenarios, this invention proposes a more direct and compact extension method: directly establishing a shared consensus basis matrix for all views. This ensures consistency between views at the source, resulting in the following objective function:

[0042] The expression for the first objective function is:

[0043] ;

[0044] in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views.

[0045] Learnable view weights satisfy This design adaptively balances the importance of different views. This allows the model to learn a consistent clustering structure across views more efficiently and directly, without needing to first generate and then align multiple intermediate representations.

[0046] To further improve the quality of this consensus representation, two key constraints are imposed: 1) on the coefficient matrix Apply F-norm regularization Under orthogonality constraints, it is equivalent to the constraint affinity matrix. 1) Low rank to facilitate the generation of a clear block-like diagonal structure; 2) For the consensus matrix Apply orthogonal constraints This enhanced The physical significance of its role as an orthonormal basis is that its row vectors are more suitable as input features for subsequent clustering algorithms.

[0047] In this embodiment of the invention, in S2, in order to maintain the local manifold structure of the data in the sample space, a sample similarity graph is constructed for each view and introduced as a regularization constraint into the objective function, thus proposing an objective function model.

[0048] The expression for the second objective function is:

[0049] ;

[0050] in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. This represents the second equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views. Describes the rank of a matrix. This represents the Laplacian matrix of each data plot.

[0051] regularization term An objective function is introduced. This term forces the consensus representation of neighboring samples in the original feature space to be optimized after dimensionality reduction. They are also close to each other, thus effectively preserving the local geometry of the sample space.

[0052] In this embodiment of the invention, in S3, a similarity graph is constructed on the feature dimension for each view to mine the correlation between features, thereby capturing and maintaining the geometric structure of the feature space, and the following complete objective function model is proposed.

[0053] The expression for the multi-view concept decomposition clustering model is:

[0054] ;

[0055] in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. This represents the second equilibrium parameter. This represents the third equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views. Describes the rank of a matrix. This represents the Laplacian matrix of each data plot. This represents the Laplacian matrix of each feature map.

[0056] In this embodiment of the invention, to efficiently solve the constructed objective function, an iterative optimization algorithm based on a multiplication update rule is designed. The core feature of this algorithm is that in each global iteration, the consensus matrix and the coefficient matrices of all views are updated synchronously, rather than sequentially depending on the latest values ​​of each other. This approach, while ensuring convergence, can potentially improve computational efficiency and better capture the relationships between variables. This process is repeated until convergence.

[0057] S4 includes the following sub-steps:

[0058] S41. Initialize parameters;

[0059] S42, Update the coefficient matrix of each view and the consensus basis matrix shared by all views, and proceed to S43;

[0060] S43, Update the learnable view weights;

[0061] S44. Repeat S42-S43, and when the convergence condition is met or the maximum number of iterations is reached, determine the cluster labels and output the classification results.

[0062] In this embodiment of the invention, in S41, the initialization parameters include the coefficient matrix of each view, the consensus basis matrix shared by all views, the Laplacian matrix of each data graph, the Laplacian matrix of each feature graph, and the learnable view weights.

[0063] In an embodiment of the present invention, Figure 2 The results are clustering of six datasets (NGs, 3Scoure, BBC, Wikipedia-test, Reuters, and Wikipedia) across eight comparative methods, including accuracy, mutual information, purity, precision, and F-score.

[0064] Figure 3 This is an example graph showing the sequence error convergence curves for the 3Scources and Wikipedia-test data.

[0065] Figure 4 It includes three views of the BBC dataset and visualization of clustering results.

[0066] Figure 5 These are ablation experiments on the 3Sources and BBC datasets, showing a comparison of the experimental results with only feature map regularization, only data map regularization, and no dual-map regularization.

[0067] This invention presents a model framework for directly learning a unified consensus representation. It abandons the complex process of generating independent representations for each view and then aligning them in traditional methods. Instead, it proposes a new framework for directly learning a shared consensus representation matrix for all views, thereby simplifying the model and improving efficiency.

[0068] This invention integrates a dual-graph regularization method that simultaneously incorporates the geometric structure of the data and feature space. To fully exploit the inherent structure of the data, this invention introduces both data graph regularization, which preserves local relationships between samples, and feature graph regularization, which preserves feature correlations, into the model, making the learned consensus representation more discriminative.

[0069] This invention designs an automatically learnable view weight that can dynamically adjust the importance of each view based on its reconstruction quality and structural preservation, thus achieving robust and intelligent fusion of multi-view information.

[0070] The effectiveness has been verified through extensive experiments. Experimental results on multiple public datasets show that the method of this invention significantly outperforms mainstream comparative methods in core metrics such as accuracy and normalized mutual information, verifying its effectiveness and advancement.

[0071] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization, characterized in that, Includes the following steps: S1. Generate a consensus basis matrix for all views and construct the first objective function; S2. Construct sample similarity maps for each view, use the sample similarity maps as regularization constraints, and construct a second objective function based on the first objective function; S3. Based on the second objective function, construct a multi-view concept decomposition and clustering model based on direct consensus learning and dual-graph regularization; S4. Solve the multi-view concept decomposition clustering model to obtain the classification results.

2. The multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization according to claim 1, characterized in that, In S1, the expression for the first objective function is: ； in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views.

3. The multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization according to claim 1, characterized in that, In S2, the expression for the second objective function is: ； in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. This represents the second equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views. Describes the rank of a matrix. This represents the Laplacian matrix of each data plot.

4. The multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization according to claim 1, characterized in that, In S3, the expression for the multi-view concept decomposition clustering model is: ； in, Indicates the first The coefficient matrix of each view. Represents learnable view weights. This represents the consensus basis matrix shared by all views. Indicates the first Data matrix of views, Represents the transpose of a matrix. Indicates the first equilibrium parameter. This represents the second equilibrium parameter. This represents the third equilibrium parameter. Represents an identity matrix of appropriate size. Indicates the total number of views. Describes the rank of a matrix. This represents the Laplacian matrix of each data plot. This represents the Laplacian matrix of each feature map.

5. The multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization according to claim 1, characterized in that, S4 includes the following sub-steps: S41. Initialize parameters; S42, Update the coefficient matrix of each view and the consensus basis matrix shared by all views, and proceed to S43; S43, Update the learnable view weights; S44. Repeat S42-S43, and when the convergence condition is met or the maximum number of iterations is reached, determine the cluster labels and output the classification results.

6. The multi-view concept decomposition and clustering method based on consensus learning and dual-graph regularization according to claim 5, characterized in that, In step S41, the initialization parameters include the coefficient matrix of each view, the consensus basis matrix shared by all views, the Laplacian matrix of each data graph, the Laplacian matrix of each feature graph, and the learnable view weights.

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