Multi-view Clustering Method and Device Based on Self-paced Learning

Abstract

A multi-view clustering method and device based on self-paced learning can effectively avoid the deficiencies of traditional methods, can effectively improve the robustness of the model to noise points and outliers, and ensure the maximization of consistent information sharing among perspectives while effectively utilizing the intrinsic differential information of each perspective. The method includes: (1) The input is a multi-view data set. For each perspective and each sample, a node is corresponding. Centering on each node, an adaptive graph learning method is used to learn the similarity between nodes to construct edges, thereby completing the construction of the graph for each perspective; (2) Construct a multi-graph clustering model based on the consistency and personalized information separation strategy; (3) Use a self-paced learning weight matrix to measure the complexity of each node in the graph, transition from fewer simple nodes to more and more complex nodes, and gradually participate in the multi-graph learning until the model converges; (4) Output the clustering result.

Description

Technical Field

[0001] The present invention relates to the technical field of computer vision, and in particular to a multi-view clustering method based on self-paced learning, and a multi-view clustering device based on self-paced learning. Background Art

[0002] Cluster analysis, especially the spectral clustering method for multi-view data, has attracted extensive attention in the fields of data mining and computer vision in recent years. Without the guidance of prior knowledge, cluster analysis uses the Euclidean distance to measure the similarity between samples, and divides similar samples into the same cluster. Multi-view data clustering (MVC) is one of the most popular topics in the field of data mining recently, aiming to classify N objects with V views into K classes. By integrating the redundant information of multiple views, multi-view clustering can obtain better performance than single-view clustering. Compared with the data sampled from a single view, the multi-view data obtained from different angles or in different ways for the same thing has rich redundant information, and there are complementarity and differences between different views.

[0003] For the clustering task of multi-view data, the first problem of multi-view data clustering is how to maximize the sharing of consistent information among multiple views while separating and utilizing the personalized information specific to each view, and making use of the consistency and difference information. And how to process the unevenly distributed noise points and outliers that can appear in practical applications to improve the clustering performance is the second problem of the multi-view data clustering task. Summary of the Invention

[0004] To overcome the defects of the prior art, the technical problem to be solved by the present invention is to provide a multi-view clustering method based on self-paced learning, which can effectively avoid the deficiencies of traditional methods, can effectively improve the robustness of the model to noise points and outliers, and ensure the maximization of the sharing of consistent information among views while effectively utilizing the internal differences of each view.

[0005] The technical solution of the present invention is as follows: This multi-view clustering method based on self-paced learning includes the following steps:

[0006] (1) The input is a multi-view data set. For each view and each sample, a node is corresponding. Taking each node as the center, an adaptive graph learning method is used to learn the similarity between nodes to construct edges, thereby completing the construction of the graph for each view;

[0007] (2) Construct a multi-graph clustering model based on the consistency and personalized information separation strategy;

[0008] (3) Use the self-paced learning weight matrix to measure the complexity of each node in the graph, transition from fewer simple nodes to more and more complex nodes, gradually participate in multi-graph learning until the model converges;

[0009] (4) Output the clustering result.

[0010] The present invention introduces the idea of self-paced learning, which can effectively improve the robustness of the model to noise points and outliers; uses the adaptive graph learning method to construct a graph corresponding to the data of each perspective, which is conducive to accurately characterizing the connection strength between samples under each perspective; uses the separation strategy to ensure the maximization of the shared consistency information between perspectives while effectively utilizing the internal differential information of each perspective; combines the Laplacian rank constraint to ensure further learning of a similarity matrix that accurately reflects the similarity between samples; therefore, it can effectively avoid the deficiencies of traditional methods, effectively improve the robustness of the model to noise points and outliers, ensure the maximization of the shared consistency information between perspectives while effectively utilizing the internal differential information of each perspective.

[0011] Also provided is a multi-view clustering device based on self-paced learning, and the device includes:

[0012] An initial graph construction module, whose input is a multi-perspective data set, corresponding to each perspective and each sample with a node, centered on each node, using the adaptive graph learning method to learn the similarity between nodes to construct edges, thereby completing the construction of the graph for each perspective;

[0013] A learning model construction module, which constructs a multi-graph clustering model based on the consistency and personalized information separation strategy;

[0014] A multi-graph learning module, which uses the self-paced learning weight matrix to measure the complexity of each node in the graph, transitions from fewer simple nodes to more and more complex nodes, gradually participates in multi-graph learning until the model converges;

[0015] A clustering module, which outputs the clustering result. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Shows a flowchart of the multi-view clustering method based on self-paced learning according to the present invention.

[0017] Figure 2 Displays the original graphs of different perspectives and the similarity graphs learned by the SPMGC model. DETAILED DESCRIPTION OF THE INVENTION

[0018] As Figure 1 shown, this multi-view clustering method based on self-paced learning includes the following steps:

[0019] (1) The input is a multi-view dataset. For each view and each sample, a node is corresponding. Centered on each node, an adaptive graph learning method is used to learn the similarity between nodes to construct edges, thereby completing the construction of the graph for each view;

[0020] (2) Construct a multi-graph clustering model based on the consistency and personalized information separation strategy;

[0021] (3) Use a self-paced learning weight matrix to measure the complexity of each node in the graph, transition from fewer simple nodes to more and more complex nodes, and gradually participate in multi-graph learning until the model converges;

[0022] (4) Output the clustering result.

[0023] The present invention introduces the idea of self-paced learning, which can effectively improve the robustness of the model to noise points and outliers; uses the adaptive graph learning method to construct the graph corresponding to the data of each view, which is beneficial to accurately describe the connection strength between samples under each view; uses the separation strategy to ensure that the perspective-sharing consistency information is maximized while effectively utilizing the internal differential information of each view; combines the Laplacian rank constraint to ensure further learning of a similarity matrix that accurately reflects the similarity between samples; therefore, it can effectively avoid the deficiencies of traditional methods, effectively improve the robustness of the model to noise points and outliers, and ensure that the perspective-sharing consistency information is maximized while effectively utilizing the internal differential information of each view.

[0024] Preferably, in the step (1), the multi-view data X = {X (1) , … X (M)} to be clustered is obtained. The multi-view data refers to a set of sample data extracted with M features. There are multiple samples under each view. Among them, the feature matrix d m and N are the feature dimension and the number of samples. According to the following adaptive graph method, the initial graph corresponding to each view of the dataset is constructed

[0025]

[0026] Adaptive graph learning learns the similarity matrix by adaptively assigning the optimal neighbor points to each sample point x i .

[0027] Preferably, in the step (1), there are N samples in the m-th view, which belong to K categories in total. Among them, respectively represent the i-th and j-th samples in the m-th view, represents The similarity of two samples, and then construct the initial graph of the m-th perspective For the initial graph A (m) , is its i, j-th node, is the edge connecting these two nodes.

[0028] Preferably, in the step (2), with the initial multi-graph data where A (m) ∈R N×N , construct the following multi-graph learning model MGC:

[0029]

[0030]

[0031] where α (m) = 1 / ||C⊙D (m) -A (m) || F· , which is determined by the current C and D (m) .

[0032] Preferably, in the step (2), N and K are the number of input images and the number of categories to which the images belong under the m-th perspective, c i , represents the i-th row of the shared consistency similarity graph matrix C, L C represents the Laplacian matrix of C, rank(·) represents the rank of the matrix, c i，j and d i，j (m) represent the i, j-th elements of C and D (m) respectively, set the lower bound d i，j ≥δ, ⊙ represents the element-wise multiplication of matrices, represents the squared Frobenius norm, and the trade-off factor γ ranges from {10 -4 , 10 -3 , 10 -2 , 10 -1 , 10 0 , 10 1 , 10 2 , 10 3}.

[0033] Preferably, in the step (3), measure the complexity of each edge in the graph through the weight matrix to construct the self-paced learning based multi-graph clustering model SPLMGC.

[0034] Preferably, in the step (3), the greater the weight , the more the edge in the m-th graph The greater the possibility of being selected to enter the multi-graph learning model MGC; the SPLMGC model is:

[0035]

[0036] where l ij represents the loss function of the i-th edge, θ are the MGC model parameters, including D (m) , C, weight v ij represents the complexity of the i-th edge, and the weight parameter λ controls the self-paced learning speed;

[0037] The weight regularization term is adopted in the following soft weighting manner:

[0038]

[0039] The range of the weight value is within [0, 1]. When the multi-graph learning model parameters are fixed, the optimal weight of the i-th edge is:

[0040]

[0041] Preferably, in the step (4), for C * and D (m)* learned by the model, the final clustering result is obtained by implementing a standard clustering method on the following association matrix

[0042]

[0043] Preferably, the standard clustering method in the step (4) is the Normalized Cut method.

[0044] The technical solution of the present invention will be described in more detail below.

[0045] The input is a multi-view dataset. First, for each view, each sample corresponds to a node. Centered on each node, the similarity between nodes is learned using an adaptive graph learning method to construct edges, thereby completing the construction of the graph for each view; then a multi-graph clustering model is constructed based on the consistency and personalized information separation strategy; then a self-paced learning weight matrix is used to measure the "complexity" of each node in the graph, transitioning from fewer "simple" nodes to more and more "complex" nodes, gradually participating in the multi-graph learning until the model converges; finally, the clustering result is output. The specific steps are as follows:

[0046] Step 1: Initial graph construction based on adaptive graph learning

[0047] Obtain the multi-view data χ = {X (1) , … X (M)}, where the multi-view data refers to a set of sample data with M features, and there are multiple samples under each view. Among them, the feature matrix under the m-th view d m and N are the feature dimension and the number of samples. The first thing to do is to construct the initial graph corresponding to each view according to the following adaptive graph method for the dataset Construct the initial graph corresponding to each view

[0048]

[0049] Adaptive graph learning learns the similarity matrix by adaptively assigning the optimal nearest neighbor points to each sample point x i . Specifically, there are N samples in the m-th view, belonging to K categories in total. Among them, represent the i-th and j-th samples in the m-th view respectively, represents the similarity between two samples, and then constructs the initial graph of the m-th view For the initial graph A (m) , we call its i-th and j-th nodes, the edge connecting these two nodes.

[0050] Step 2: Construction of the multi-graph learning model based on the separation strategy

[0051] With the initial multi-graph data where A (m) ∈R N×N , in order to learn a shared consistent similarity graph, two aspects should be considered: on the one hand, different graphs are descriptions of the same set of samples from different angles, and the consistent information they share should be maximized; on the other hand, each graph has its own unique information, and these discriminative information is not possessed by other graphs. To address the above problems, the present invention constructs the following multi-graph learning model MGC:

[0052]

[0053]

[0054] where α (m) = 1 / ||C⊙D (m) -A (m) || F. , which is determined by the current C and D (m) .

[0055] Specifically, N and K are the number of input images and the number of categories to which the images belong in the m-th view. c i，· represents the i-th row of the shared consistent similarity graph matrix C, LC The Laplacian matrix of C is denoted as, and rank(·) represents the rank of a matrix, where c i，j and d i，j (m) represent the i-th and j-th elements of C and D respectively (m) respectively. Set the lower bound d i，j ≥δ to avoid the situation where C⊙D i，j = 0, which will lead to C⊙D (m) = 0, thus causing the graph C to lose its constraints. ⊙ represents the element-wise multiplication of matrices represents the squared Frobenius norm, and the trade-off factor γ takes values in the range {10 -4 , 10 -3 , 10 -2 , 10 -1 , 10 0 , 10 1 , 10 2 , 10 3}.

[0056] Through multi-graph learning, the consistency similarity graph C can be used as a template to extract the consistency information in multiple graphs. Different D (m) ensures that the personalized information of different graphs can be correctly utilized, and the Laplacian rank constraint ensures the diagonal block structure of graph C, thereby improving the clustering effect

[0057] Step 3: Multi-graph learning process based on self-paced learning

[0058] Considering that outliers or noise will have a negative impact on learning, a weight matrix is introduced to measure the "complexity" of each instance (edge) in the graph, thereby constructing a self-paced learning based multi-graph clustering model SPLMGC. Specifically, the larger the weight , the greater the possibility that the edge in the m-th graph is selected to enter the multi-graph learning model MGC. The SPLMGC model includes a weighted loss term for instances (edges) and a regularization term for the corresponding weights

[0059]

[0060] where l ij represents the loss function of the i-th edge. Specifically θ are the parameters of the MGC model, including D (m) , C. The weight v ij represents the "complexity" of the i-th edge, and the weight parameter λ controls the self-paced learning speed

[0061] Considering the uneven distribution of noise data in practical applications, the weight regularization term adopts the following soft weighting (the weight value ranges from [0, 1]) method

[0062]

[0063] When the parameters of the multi-graph learning model are fixed, the optimal weight of the i-th instance (edge) is calculated by the following formula:

[0064]

[0065] It can be seen that when the weight parameter λ controlling the number of selected instances is small, a small number of "simple" instances with small losses will be considered in learning. As λ increases, more and more "complex" instances with larger losses will be selected for learning. Therefore, the self-paced learning model starts from fewer "simple" instances and gradually involves more instances until the model converges. For the noisy data and outliers that are more likely to cause larger model errors, they are more likely to be defined as "complex" instances and do not participate in the model training and learning. Therefore, the robustness of the model is improved.

[0066] Step Four: Clustering Task

[0067] For C * and D (m)* learned by the model, the final clustering results are obtained by implementing standard clustering methods, such as Normalized Cut (NCUT), on the following association matrix.

[0068]

[0069] The present invention has experimentally verified the above method and achieved obvious effects. Two artificial data set experiments were conducted to evaluate the clustering performance of SPMGC. In the double-moon synthetic data set, there are two clusters of 200 data points distributed in the shape of the moon. Each class has 100 samples, and 0.12% and 0.14% of noise are added to obtain a two-view data set. In the three-circle data set containing 300 data points in three classes, each class has 100 samples. 0.14% and 0.16% of noise are added respectively to obtain a three-view data set.

[0070] Figure 2 Shows the original graphs from different perspectives and the similarity graphs learned by the SPMGC model. The connecting lines represent the similarity between two corresponding points. The first row is the double-moon data set, successively the original graph of the first perspective, the original graph of the second perspective, and the graph learned by SPMGC; the second row is the three-circle data set, successively the original graph of the first perspective, the original graph of the second perspective, and the graph learned by SPMGC.

[0071] It can be observed that in the original graph, there are even connecting lines between some data points of different classes. After learning, the original data is successfully divided into two (three) classes, proving the effectiveness of the proposed method.

[0072] The above are only the preferred embodiments of the present invention, and do not impose any form of limitation on the present invention. Any simple modifications, equivalent changes and decorations made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the technical solution of the present invention.

Claims

1. A multi-view clustering method based on self-paced learning, characterized in that: The method includes the following steps: (1) The input is a multi-view dataset. For each view and each sample, a node is corresponding. Centering on each node, the adaptive graph learning method is used to learn the similarity between nodes so as to construct edges, thereby completing the construction of the graph for each view; (2) Construct a multi-graph clustering model based on the consistency and personalized information separation strategy; (3) Use the self-paced learning weight matrix to measure the complexity of each node in the graph, transition from fewer simple nodes to more and more complex nodes, and gradually participate in the multi-graph learning until the model converges; (4) Output the clustering result; In the step (1), multi-view data χ = {X (1) , …, X (M)} to be clustered is obtained. The multi-view data refers to a set of sample data with M features extracted. There are multiple samples under each view. Among them, the feature matrix d m under the m-th view, where d and N are the feature dimension and the number of samples respectively. According to the following adaptive graph method, for the data set construct the initial graph Adaptive graph learning learns the similarity matrix by adaptively assigning the optimal nearest neighbor points to each sample point x i and adaptively allocating the optimal nearest neighbor points to learn the similarity matrix; In the step (1), there are N samples in the m-th perspective, which belong to K categories in total. Among them, respectively represent the i-th and j-th samples in the m-th perspective, represents the similarity between two samples, and then construct the initial graph of the m-th perspective In the step (2), with the initial multi-graph data where A (m) ∈R N×N , construct the following multi-graph learning model MGC: where α (m) = 1 / ||C⊙D (m) -A (m) || F· , which is determined by the current C and D (m) ; In the step (2), N and K are the number of input images and the number of categories to which the images belong under the m-th perspective, c i，· represents the i-th row of the shared consistency similarity graph matrix C, L C represents the Laplacian matrix of C, rank(·) represents the rank of the matrix, c i，j and d i，j (m) respectively represent the elements in the i-th row and j-th column of C and D (m) , set the lower bound d i，j ≥δ, ⊙ represents the element-by-element multiplication of the matrices, represents the square F norm, and the value range of the weighting factor γ is {10 -4 ，10 -3 ，10 -2 ，10 -1 ，10 0 ，10 1 ，10 2 ，10 3}； In the step (3), a weight matrix is used to measure the complexity of each edge in the graph, so as to construct a multi-graph clustering model SPLMGC based on self-paced learning; In the said step (3), the weight The larger it is, it means that the edge in the m-th graph has a greater possibility of being selected to enter the multi-graph learning model MGC; The SPLMGC model is: where \(l\) ij represents the loss function of the \(i\)-th edge, \(\theta\) are the MGC model parameters, including \(D\) (m) , \(C\), and the weight \(v\) ij represents the complexity of the \(i\)-th edge, and the weight parameter \(\lambda\) controls the self-paced learning rate; The weight regularization term adopts the following soft weighting method: The range of the weight value is within [0, 1]. When the parameters of the multi-graph learning model are fixed, the optimal weight of the i-th edge is:

2. The multi-view clustering method based on self-paced learning according to claim 1, characterized in that: In the step (4), for C * and D (m)* learned by the model, the final clustering result is obtained by implementing a standard clustering method on the following association matrix 3. The multi-view clustering method based on self-paced learning according to claim 2, characterized in that: The standard clustering method in the step (4) is the Normalized Cut method.

4. A multi-view clustering device based on self-paced learning, the device executes the method according to claim 1, characterized in that: The device includes: An initial graph construction module, whose input is a multi-view dataset. For each view and each sample, a node is corresponding. Centering on each node, the adaptive graph learning method is used to learn the similarity between nodes so as to construct edges, thereby completing the construction of the graph for each view; A learning model construction module, which constructs a multi-graph clustering model based on the consistency and personalized information separation strategy; A multi-graph learning module, which uses the self-paced learning weight matrix to measure the complexity of each node in the graph, transitions from fewer simple nodes to more and more complex nodes, and gradually participates in the multi-graph learning until the model converges; A clustering module, which outputs the clustering result.

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