An incomplete multi-view clustering method fusing consensus and discrepancy information
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- OCEAN UNIV OF CHINA
- Filing Date
- 2026-03-24
- Publication Date
- 2026-06-05
AI Technical Summary
Existing multi-view clustering methods exhibit significant performance degradation when data is incomplete, making it difficult to effectively uncover deep-seated potential relationships within the data.
By constructing a cross-order neighborhood tensor, the Markov random walk principle is used to extract multi-order neighborhood information. Combined with the non-convex tensor rank approximation constraint and adaptive weight mechanism, the complete similar tensor is restored, a consensus affinity matrix is generated, and consensus and difference information are integrated.
It significantly improves clustering performance under conditions of missing data, maintains consensus information between views, suppresses information redundancy, and achieves more efficient clustering results.
Smart Images
Figure CN122156694A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of multi-view clustering methods, and in particular to an incomplete multi-view clustering method that integrates consensus and difference information. Background Technology
[0002] In recent years, multi-view clustering methods have made significant progress and achieved excellent performance. However, most traditional algorithms are based on the ideal assumption of "view completeness," which assumes that the data for all samples is complete in each view. This assumption is often difficult to hold in real-world applications, as noise during data acquisition, equipment malfunctions, or privacy protection issues frequently lead to information loss. For example, data obtained by web crawlers often lacks text or image features, and medical image data often cannot be matched one-to-one due to differences in the detection items.
[0003] This data incompleteness disrupts the natural alignment properties of multi-view data, exacerbating information imbalances between views and leading to a significant decline in the clustering performance of existing techniques. To address this challenge, researchers have proposed a series of solutions, such as reconstructing missing data by completing similarity maps or utilizing complementary information across views. Nevertheless, existing methods remain insufficient in uncovering deep, potential relationships within the data. Therefore, developing robust and efficient clustering methods for incomplete multi-view data, capable of achieving accurate clustering even with missing views, has become a crucial and urgent task. Summary of the Invention
[0004] This invention addresses the technical problems existing in the background art by proposing an incomplete multi-view clustering method that integrates consensus and difference information. It utilizes the cross-order neighbor structure of the data to construct an incomplete graph, thereby providing complementary information. Furthermore, it introduces tensor completion technology, fully leveraging cross-view graph information to construct a fine-grained neighborhood tensor with a complex similarity structure, effectively representing and inferring the relationships between missing samples. It employs a logarithm-based tensor rank approximation, which is more efficient than the Schatten-p norm, and fuses different view information through an adaptive weighting mechanism. The core lies in directly encoding the diverse features of cross-views into the weights, ensuring that the generated consistency affinity matrix can both integrate complementary information from multiple views and retain the unique differences of each view, thus significantly improving the robustness of data representation. An efficient optimization algorithm was designed and developed to solve the computational difficulties in the model solving process, making it practically operable and achieving better performance and computational efficiency than existing state-of-the-art incomplete multi-view clustering methods.
[0005] To solve the technical problem, the technical solution of the present invention is as follows:
[0006] An incomplete multi-view clustering method that integrates consensus and difference information includes the following steps:
[0007] Step S1: Obtain the non-missing samples of each view, and construct an initial similarity map of each view based on the non-missing samples; based on the Markov random walk principle, extract multi-order neighborhood information from the initial similarity map, and fuse the multi-order neighborhood information to construct an incomplete cross-order neighborhood tensor containing information from multiple views.
[0008] Step S2: Based on the non-convex tensor rank approximation constraint, the incomplete cross-order neighborhood tensor is recovered to obtain the complete similar tensor; wherein, the non-convex tensor rank approximation constraint is based on the definition of the singular value logarithm function of the similar tensor in the frequency domain representation;
[0009] Step S3: Introduce learnable adaptive weights to each view slice of the similar tensor, and apply difference constraints to the adaptive weights based on the similarity between views, and obtain the fused consistency affinity matrix through learning.
[0010] This application introduces low-rank constraints and view difference constraints simultaneously during the multi-view fusion process to achieve collaborative modeling of the common consistent structure and view-specific structure in multi-view data. This maintains consensus information among views while suppressing interference from redundant views, ultimately learning a consistency affinity matrix that reflects the common structure of multiple views.
[0011] Furthermore, step S1 includes:
[0012] S101: For the v-th view, calculate the initial similarity matrix based on the non-missing samples;
[0013] S102: Based on the initial similarity matrix, calculate the corresponding Markov transition probability moments;
[0014] S103: Based on the Markov transition probability matrix, calculate the transition probability matrix from order 1 to order T, as the multi-order neighborhood information, where T is an integer greater than 1;
[0015] S104: Fuse the transition probability matrices from order 1 to order T to obtain the fine-grained neighborhood matrix of the view;
[0016] S105: Stack the fine-grained neighborhood matrices of all views to form the incomplete cross-order neighborhood tensor.
[0017] Furthermore, in step S103, the T-order transition probability matrix is obtained by calculating the T-th power of the Markov transition probability matrix.
[0018] Furthermore, in step S104, the fine-grained neighborhood matrix is obtained by weighted summation of the transition probability matrices from order 1 to order T and then symmetric processing.
[0019] Furthermore, in step S2, the non-convex tensor rank approximation constraint is a logarithmic tensor rank approximation constraint; the logarithmic tensor rank approximation constraint is defined as follows: the similar tensor is subjected to a Fourier transform along the third dimension to obtain a frequency domain tensor, and a penalty term based on a logarithmic function is applied to the singular values of each front slice of the frequency domain tensor.
[0020] Furthermore, in step S2, when recovering the incomplete cross-order neighborhood tensor, the complete similar tensor obtained by constraint recovery satisfies the following conditions: each view slice of the complete similar tensor is a symmetric matrix, and each element of each view slice is a non-negative value.
[0021] Furthermore, step S3 is achieved by jointly optimizing the objectives corresponding to the following constraints:
[0022] The first term is the non-convex tensor rank approximation constraint applied to the complete similar tensor;
[0023] The second step is to minimize the fusion error constraint between the consistency affinity matrix and each weighted post-view slice based on the adaptive weights.
[0024] The third item is to apply differential constraints to the adaptive weights based on the similarity between view slices, which is used to suppress the weights of information-redundant views.
[0025] Furthermore, the augmented Lagrange multiplier method is used for the joint optimization, and the complete similarity tensor, the consistency affinity matrix and the adaptive weights are updated alternately and iteratively until convergence.
[0026] Specifically, the overall optimization objective consists of three types of constraints: the first type of constraint is the non-convex tensor rank approximation constraint applied to the similarity tensor, which is used to characterize the low-rank consistent structure of the multi-view data; the second type of constraint is the consistency fusion constraint based on adaptive weights, which is used to minimize the fusion error between the consistency affinity matrix and each view slice; and the third type of constraint is the difference constraint based on the similarity between views, which is used to suppress the weights of information-redundant views.
[0027] This application has the following advantages:
[0028] This application proposes an incomplete multi-view clustering method that integrates consensus and discrepancy information. First, it constructs an incomplete graph using the cross-rank neighborhood relationships of samples without missing data to mine potential comprehensive and complementary neighborhood information within the data. Then, a logarithmic tensor rank approximation model is introduced to perform low-rank recovery on the tensor constructed from the incomplete graph, thereby obtaining a complete, fine-grained affinity tensor. Building upon this, the patent further proposes an adaptive weight fusion mechanism that learns the weights of different views to extract a consistency affinity matrix from the recovered tensor. This mechanism effectively leverages the discrepancies and consensus across views, effectively solving the clustering challenge caused by missing multi-view data. Attached Figure Description
[0029] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0030] Figure 1 Six datasets with a missing rate of 10% were compared: clustering results of NGs, WebKB, 100Leaves, Caltech101-7, ProteinFold, and CCV across 12 contrastive methods, including accuracy, mutual information, purity, F-score, and adjusted RAND index.
[0031] Figure 2 Clustering visualizations of the NGs dataset with 50% and 90% missing values;
[0032] Figure 3 Bar chart showing the sensitivity of Caltech 101-7, 100Leaves, and NGs data to two missing rate parameters under the accuracy metric.
[0033] Figure 4 Line graphs of ablation experiments on the impact of local neighbors on clustering performance for the 100Leaves and Caltech101-7 datasets under three missing rates and five clustering metrics.
[0034] Figure 5 Flowchart for implementing an incomplete multi-view clustering method that integrates consensus and difference information. Detailed Implementation
[0035] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0036] Example 1:
[0037] like Figure 5 As shown, this application proposes an incomplete multi-view clustering method that integrates consensus and difference information, achieving collaborative learning of consensus and difference. Specifically, this method mines a consensus affinity matrix representing the global consistency structure of multiple views from fine-grained neighborhood tensors. At the same time, it explicitly encodes heterogeneous information across views using adaptive weight parameters, avoiding the loss of complementary information in traditional fusion processes.
[0038] Step 1: Recover potential similar tensors by constructing cross-order neighborhood tensors of the data.
[0039] Specifically: For each view, an initial similarity map is constructed using existing non-missing samples. Based on the Markov random walk principle, a Markov transition probability matrix is defined and constructed. in This represents the operation of calculating the row sums of the input matrix and constructing a diagonal matrix whose diagonal elements are the sum of the elements of the corresponding rows. This represents a similarity graph.
[0040] To capture deeper, underlying topological relationships between samples, this application defines Transition probability matrix of order, For one The transition probability matrix of order 1 reveals the transition probability matrix of order 2 at the 1st order. Two non-missing samples in each view The probability of a random walk, i.e., the probability of a random walk, reflects the number of steps taken from a given sample. The step to reach another sample.
[0041] therefore, Defined as: It can be seen It reveals higher-order local information, containing basic and complementary information about the data, thus providing deeper potential relationships.
[0042] in, : indicates the first In each view, from one non-missing sample to another non-missing sample The transition probability matrix of a random walk. Indicates the index of the current view. Represents a specific view. : indicates the first In each view, the transition probability matrix of a one-step random walk from one non-missing sample to another non-missing sample. :express Multiplied by itself repeatedly Second-rate. : indicates the first The first view and the first The Markov transition probability matrix between views describes the transition probability from one sample to another in the sample set. : Represents a matrix of The exponentiation is the product of the matrix itself and itself. Next, used for calculation The transition probability of a random walk.
[0043] To fully utilize the comprehensive and complementary cross-order neighborhood information mentioned above, this application introduces a multi-order fusion mechanism. Different orders (from 1 to the highest order) are fused together. The transition probability matrices of ) are weighted and fused to construct the first Fine-grained neighborhood matrix of each view Its construction formula is: Further, we obtain the incomplete cross-order neighborhood tensor. This includes both observable and missing data.
[0044] Step 2: Since the convex nuclear norm rank approximation cannot accurately approximate the true rank of the matrix, and existing non-convex rank approximation tensors with the Schatten-p norm suffer from low optimization efficiency and poor performance of the closed-form solutions, this application utilizes a logarithm-based tensor rank approximation model to recover the entire neighborhood tensor. :
[0045]
[0046] Wherein, Ω represents the observation index set, which is used to identify the position of the element in the cross-order neighborhood tensor corresponding to the non-missing sample; (·) represents an operator that applies a consistency constraint to the observation index set Ω, which is used to retain the values at the observed positions and ignore the unobserved positions; This represents the logarithmic tensor rank constraint. This represents the constructed incomplete cross-order neighborhood tensor. The subscript o indicates that the tensor contains unobserved elements due to missing samples, and the subscript A indicates that the tensor is composed of multi-view neighborhood information. It is a tensor with lines and Columns, and Each dimension (layer).
[0047] The logarithmic tensor rank approximation (LTRA) is defined as follows:
[0048]
[0049] Let be the i-th largest singular value of the input matrix. This represents the front slice matrix corresponding to the v-th frequency component in the frequency domain after performing a Fourier transform on the tensor Z along the third dimension; specifically, first along the tensor... The third dimension is used to perform a Fourier transform (FFT) to convert the frequency domain representation of the tensor from the time domain. Then, in the frequency domain, the singular values of each front slice of the transformed tensor are calculated and summed. The front slice refers to a two-dimensional matrix obtained by fixing the index along the third dimension of the tensor. For the similarity map, this application expects... The frontal slices are non-negative and symmetrical, which is a natural property of similarity maps, leading to the further development of models:
[0050]
[0051] Step 3: To address the problem of existing technologies simply averaging all views while ignoring view specificity, this application proposes an adaptive weighted fusion mechanism. By introducing an adaptive weighting mechanism, the recovered tensor... Nonlinear fusion is performed on different view slices to learn a consistency affinity matrix that best reflects the common structure of multiple views and is robust to noise. Further development of the model:
[0052]
[0053] in, This represents a balance parameter of the model. This represents the adaptive weight vector, used to measure the importance of each view in the fusion process. This represents the square root of the sum of the squares of all elements in the matrix; This represents the adaptive weight of each view, used to adjust the relative importance of each view during the merging process; The target consistency affinity matrix is the matrix that is ultimately desired. Furthermore, this application extends this norm to the tensor dimension, where, for the input tensor, it is also defined as the square root of the sum of the squares of all elements within the tensor.
[0054] Step 4: In the multi-view fusion process, if the similarity matrices of two views show high similarity (i.e., significant information redundancy), then these two views should not be assigned large weights simultaneously. To address this, this application introduces a cross-view diversity embedding term to enhance model differential learning, aiming to suppress the simultaneous increase of weights for highly correlated views, thereby forcing the model to focus on views that provide complementary information. Therefore, the final model is:
[0055]
[0056] in, For balancing parameters, It is an introduced cross-view diversity embedding that represents the similarity between different views, measured in a weighted manner. The trace operation is used to calculate the sum of the features of a matrix. The above model is named Incomplete Multi-View Clustering (IM4C), which integrates consensus and discrepancy information.
[0057] Step 5: For the optimization part, alternating optimization will be performed using the Augmented Lagrange Multiplier (ALM) method. Specifically, subproblems related to a single variable will be selectively solved while keeping other variables constant; this process will be repeated until convergence and a minimum value is obtained.
[0058] Figure 1 The paper presents a comparison of the proposed method with twelve existing multi-view clustering methods in terms of accuracy, mutual information, purity, F-score, and adjusted RAND index, under the conditions of six publicly available multi-view datasets and a 10% missing sample rate. It can be seen that the proposed method achieves superior clustering performance on most datasets and evaluation metrics.
[0059] Figure 2 The diagram illustrates the clustering results with missing sample rates of 50% and 90% in the NGs dataset. It can be seen that even under conditions of high or even extreme missing sample rates, the method of this invention can still maintain a relatively clear clustering structure, demonstrating good robustness to missing sample conditions.
[0060] Figure 3 The accuracy variations of the proposed method on the Caltech101-7, 100Leaves, and NGs datasets under different parameter settings are shown. The results demonstrate that the proposed method is insensitive to parameter changes under varying missing rates, exhibiting good stability and feasibility.
[0061] Figure 4The results show the impact of varying local neighbor counts on the clustering performance of the 100Leaves and Caltech101-7 datasets under different missing counts. The results demonstrate that appropriately incorporating multi-order neighborhood information can significantly improve clustering performance, validating the effectiveness of the cross-order neighborhood modeling mechanism employed in this invention.
[0062] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.
[0063] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.
Claims
1. An incomplete multi-view clustering method that integrates consensus and difference information, characterized in that, Includes the following steps: Step S1: Obtain the non-missing samples of each view, and construct an initial similarity map of each view based on the non-missing samples; Based on the Markov random walk principle, multi-level neighborhood information is extracted from the initial similarity graph, and the multi-level neighborhood information is fused to construct an incomplete cross-level neighborhood tensor containing multiple view information. Step S2: Based on the non-convex tensor rank approximation constraint, the incomplete cross-order neighborhood tensor is recovered to obtain the complete similar tensor; wherein, the non-convex tensor rank approximation constraint is based on the definition of the singular value logarithm function of the similar tensor in the frequency domain representation; Step S3: Introduce learnable adaptive weights to each view slice of the similar tensor, and apply difference constraints to the adaptive weights based on the similarity between views, and obtain the fused consistency affinity matrix through learning.
2. The incomplete multi-view clustering method that integrates consensus and difference information according to claim 1, characterized in that, Step S1 includes: S101: For the v-th view, calculate the initial similarity matrix based on the non-missing samples; S102: Based on the initial similarity matrix, calculate the corresponding Markov transition probability matrix; S103: Based on the Markov transition probability matrix, calculate the transition probability matrix from order 1 to order T, as the multi-order neighborhood information, where T is an integer greater than 1; S104: Fuse the transition probability matrices from order 1 to order T to obtain the fine-grained neighborhood matrix of the view; S105: Stack the fine-grained neighborhood matrices of all views to form the incomplete cross-order neighborhood tensor.
3. The incomplete multi-view clustering method that integrates consensus and difference information according to claim 2, characterized in that, In step S103, the T-order transition probability matrix is obtained by calculating the T-th power of the Markov transition probability matrix.
4. The incomplete multi-view clustering method that integrates consensus and difference information according to claim 2, characterized in that, In step S104, the fine-grained neighborhood matrix is obtained by weighted summation of the transition probability matrices from order 1 to order T and then symmetric processing.
5. The incomplete multi-view clustering method integrating consensus and difference information according to claim 1, characterized in that, In step S2, the non-convex tensor rank approximation constraint is a logarithmic tensor rank approximation constraint. The logarithmic tensor rank approximation constraint is defined as follows: the similar tensor is subjected to a Fourier transform along the third dimension to obtain a frequency domain tensor, and a penalty term based on a logarithmic function is applied to the singular values of each front slice of the frequency domain tensor.
6. The incomplete multi-view clustering method that integrates consensus and difference information according to claim 1, characterized in that, In step S2, when recovering the incomplete cross-order neighborhood tensor, the complete similar tensor obtained by constraint recovery satisfies the following conditions: each view slice of the complete similar tensor is a symmetric matrix, and each element of each view slice is a non-negative value.
7. The incomplete multi-view clustering method that integrates consensus and difference information according to claim 1, characterized in that, Step S3 is achieved by jointly optimizing the objectives corresponding to the following constraints: The first term is the non-convex tensor rank approximation constraint applied to the complete similar tensor; The second step is to minimize the fusion error constraint between the consistency affinity matrix and each weighted post-view slice based on the adaptive weights. The third item is to apply differential constraints to the adaptive weights based on the similarity between view slices, which is used to suppress the weights of information-redundant views.
8. The method according to claim 7, characterized in that, The augmented Lagrange multiplier method is used for the joint optimization, which involves iteratively updating the complete similarity tensor, the consistency affinity matrix, and the adaptive weights until convergence.