Fast multi-view image clustering method guided by implicit anchor points

Abstract

The present application discloses a fast multi-view image clustering algorithm guided by implicit anchor points, which specifically relates to the field of image processing. It includes: obtaining the sub-view sample matrix of each view and randomly generating a sample label matrix; constructing an anchor feature matrix and an anchor indicator matrix; constructing a feature structure graph and a reconstruction consensus graph for each view; determining the loss error between the feature structure graph and the reconstruction consensus graph of all views, and establishing an objective function based on the loss error; updating the anchor feature matrix, anchor indicator matrix and sample label matrix in the objective function until the objective function meets the preset conditions and outputs the optimal sample label matrix. The anchor feature matrix and anchor indicator matrix are introduced to construct a structural graph loss function to realize the propagation of sample features to label information, and the anchor information is implicitly updated during the optimization process to streamline the optimization process, accelerate the solution optimization, and reduce the calculation time.

Description

Technical Field

[0001] The present application relates to the field of image classification, and in particular to a fast multi-view image clustering method guided by implicit anchor points. Background Art

[0002] With the improvement of image acquisition equipment performance and the refinement of image signal processing theory, multi-view image parsing technology, driven by both hardware foundations and software algorithms, can provide image data with richer details and a wider range of feature sources, thus being widely used in the field of multimedia data mining. As a key component of image parsing technology, multi-view image clustering algorithms aim to learn the consistent distribution of samples across views and ultimately use it to extract sample labels. However, the expansion of data sources inevitably leads to a surge in the dimensionality of multi-view data, further resulting in algorithmic efficiency failing to meet application requirements.

[0003] Existing methods include: integrating global structure graph learning and label learning into a unified framework, taking into account both diversity feature extraction and consistent distribution mining; reconstructing structured graphs through global orthogonal indicator matrices and public fuzzy label matrices, and combining them with singular value decomposition to accelerate algorithm optimization; extracting consensus graph matrices using view structure loss functions, and overcoming information loss caused by post-processing by learning continuously distributed indicator matrices. Although these modular multi-view clustering algorithms can enhance the effectiveness of consensus features and obtain labels without post-processing, high-dimensional data can lead to a sharp increase in the computational time required by the algorithms. Summary of the Invention

[0004] The main purpose of this application is to provide a fast multi-view image clustering method under the guidance of implicit anchor points, aiming to solve the problem in the existing technology that high-dimensional data causes a sharp increase in the computational time cost required for the algorithm.

[0005] To achieve the above objectives, the present application provides a fast multi-view image clustering method under implicit anchor guidance, including: obtaining a sub-view sample matrix of each view and randomly generating a sample label matrix; extracting the anchor points of the sub-view sample matrix, constructing an anchor feature matrix and an anchor indicator matrix; constructing a feature structure graph of each view based on the sub-view sample matrix and the anchor feature matrix; constructing a reconstruction consensus graph based on the sample label matrix and the anchor indicator matrix; determining the loss error between the feature structure graph and the reconstruction consensus graph of all views, and establishing an objective function based on the loss error; updating the anchor feature matrix, anchor indicator matrix and sample label matrix in the objective function until the objective function meets the preset conditions and outputs the optimal sample label matrix.

[0006] Optionally, the objective function is:

[0007]

[0008] In the formula, ||·|| F represents the norm of matrix F, represents the subview sample matrix under the vth subview, represents the anchor feature matrix under the v-th subview, represents the transposed matrix of the anchor feature matrix, m represents the number of global anchor points, d v Represents the number of sample feature dimensions under the vth subview, G∈R m×c represents the anchor point indicator matrix, G T ∈R c×m Represents the transposed matrix of the anchor indicator matrix; F∈R n×c Indicates that the sample label matrix satisfies the constraints F∈Ind, F T represents the transposed matrix of the sample indicator matrix, c represents the number of sample labels, and the matrix I c ∈R c×c Represents the identity matrix of dimension c×c.

[0009] Optionally, the anchor feature matrix, anchor indicator matrix and sample label matrix in the objective function are updated until the objective function meets the preset conditions, and the optimal sample label matrix is ​​output, including: using an implicit optimization strategy to update the anchor feature matrix and anchor indicator matrix in the objective function, and converting the objective function into an objective function about the sample label matrix; adopting a coordinate descent strategy to optimize the converted objective function and determine the sample label matrix; when it is determined that the converted objective function meets the preset conditions, outputting the sample label matrix; when it is determined that the converted objective function does not meet the preset conditions, re-adopting the coordinate descent strategy to optimize the converted objective function and determine the sample label matrix.

[0010] Optionally, the converted objective function is:

[0011]

[0012] Where, represents the subview sample matrix under the vth subview, Represents the transposed matrix of the subview sample matrix.

[0013] Optionally, a coordinate descent strategy is adopted to optimize the converted objective function and determine the sample label matrix, including: solving the elements in each column vector in the sample label matrix to obtain a preliminary solution set with a preset number of labels; determining the preliminary solution set in each row of the preliminary solution set that can maximize the value of the converted objective function, and using it as the sample label matrix.

[0014] Optionally, the preset condition is that the improvement value of the objective function is less than a convergence threshold.

[0015] Optionally, the improvement value of the objective function is determined according to the difference between the objective function value after the current round of iterative optimization and the objective function value after the previous round of iterative optimization.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] The fast multi-view image clustering method under implicit anchor guidance of the present invention introduces an anchor feature matrix and an anchor indicator matrix to construct a structural graph loss function to realize the propagation of sample features to label information, and implicitly updates the anchor information during the optimization process to streamline the optimization process, accelerate the solution and optimization, and reduce the calculation time; by imposing a discrete constraint F∈Ind, the sample label information can be directly obtained according to the sample label matrix F; the coordinate descent strategy is used to optimize the objective function, and the discrete label matrix learning can be realized without the help of post-processing means, thereby greatly improving the efficiency of multi-view clustering. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of the process of the fast multi-view image clustering method guided by implicit anchor points in this application;

[0019] Figure 2 This is a flowchart for solving the fast multi-view image clustering method guided by implicit anchor points in this application;

[0020] Figure 3 This is a graph showing the decrease in objective function value and the improvement in clustering index of an embodiment of the fast multi-view image clustering method guided by implicit anchor points in this application.

[0021] The realization of the objectives, functional features and advantages of this application will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0022] To make the objectives, technical solutions, and advantages of this application more clear, the technical solutions of this application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments of this application, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of this application.

[0023] The first embodiment of the present invention provides a fast multi-view image clustering method guided by implicit anchor points, such as Figure 1 As shown, the specific steps include:

[0024] Step S1: Get the subview sample matrix of each view Represents the features of all samples under the v-th subview, and the column vector corresponds to the information of a single image; and randomly generates a sample label matrix. Specifically, the sample label matrix can be completed by randomly assigning 1 to an element in the row vector and 0 to other elements.

[0025] Step S2: extract the anchor points of the subview sample matrix and construct the anchor feature matrix and anchor indicator matrix G∈R m×c Among them, in order to enhance the independence of anchor features and the irrelevance between anchor label clusters as much as possible, the anchor feature matrix construction can be completed by randomly initializing the row orthogonalization matrix, and the anchor indicator matrix construction can be completed by randomly initializing the column orthogonalization matrix.

[0026] Step S3: According to the subview sample matrix and anchor feature matrix Construct a feature structure graph of each view;

[0027] Step S4, constructing a reconstructed consensus graph based on the sample label matrix and the anchor point indicator matrix;

[0028] Step S5: determining the loss error between the feature structure graphs of all views and the reconstructed consensus graph, and establishing an objective function based on the loss error;

[0029]

[0030] In the formula, ||·|| F represents the norm of matrix F, represents the subview sample matrix under the vth subview, represents the anchor feature matrix under the v-th subview and represents the transposed matrix of the anchor feature matrix, m represents the number of global anchor points, d v Represents the number of sample feature dimensions under the vth subview, G∈R m×c Indicates that the anchor indicator matrix satisfies the orthogonal constraint GG T =I c And G T ∈R c×m represents the transposed matrix of the anchor indicator matrix, i.e., the potential anchor clusters are independent of each other; F∈R n×c Indicates that the sample label matrix satisfies the constraints F∈Ind, F T Represents the transposed matrix of the sample indicator matrix, that is, there is only one non-zero element in the matrix row vector that is 1 and the rest of the elements are 0. c represents the number of sample labels. Matrix I c ∈R c ×c Represents the identity matrix of dimension c×c.

[0031] Step S6: the anchor feature matrix Z in the objective function v , anchor point indicator matrix G∈R m×c And the sample label matrix F∈R n×c Update until the objective function reaches the preset conditions and outputs the optimal sample label matrix. The specific steps are as follows: Figure 2 shown.

[0032] Step S61, using an implicit optimization strategy to update the anchor point feature matrix and the anchor point indicator matrix in the objective function;

[0033] Specifically, in step S611, since the anchor feature matrix Z under each view v The updates are independent of each other, and the anchor feature matrix Z under a specific view v The optimization problem can be written as:

[0034]

[0035] For the anchor feature matrix Z v Taking the derivative and setting it to 0 can further yield:

[0036]

[0037] Will Substituting back into formula (2), the anchor feature matrix Z under a specific view is v The optimization problem can be rewritten as:

[0038]

[0039] Among them, the optimization problem of the anchor feature matrix can be transformed into the optimization problem of the anchor indicator matrix and the sample label matrix. T =I c , formula (4) can be finally transformed into the following form:

[0040]

[0041] In step S612, the above strategy is adopted in each view to update the implicit anchor point information. Then the objective function (Formula (1)) can be converted to:

[0042]

[0043] In step S62, a coordinate descent strategy is adopted to update the sample label matrix in the converted objective function to obtain the optimal sample label matrix. The specific solution method is as follows.

[0044] In step S621, since the sample label matrix satisfies the discrete constraint F∈Ind, there is only one non-zero element in the row vector of the matrix F and the value of the element is 1, so formula (6) can be converted into the following form:

[0045]

[0046] Among them, f l ∈ n×1 Represents the lth column vector in the sample label matrix. If the i-th element in the vector is non-zero, it means that the i-th class sample belongs to the l-th data cluster; if the i-th element in the vector is zero, it means that the i-th class sample does not belong to the l-th data cluster.

[0047] Based on this, the problem of solving formula (7) can be transformed into n sub-problems, that is, solving n row vectors, and the solution space of each sub-problem contains c preliminary solution sets f l (k) ∈ n×1 (k=1,2,...,c), that is, the c elements in each row vector. The difference between different preliminary solution sets is f l (k) The position of the non-zero element of the i-th element in the , usually specifies the first preliminary solution set f1 (1) ∈ n×1 The i-th element is 1 and the remaining sample label matrix column vector f l (1) ∈ n×1 The i-th element in (l≠1) is 0, and the second preliminary solution set f2 (2) ∈ n×1 The i-th element is 1 and the remaining sample label matrix column vector f l (2) ∈ n×1 The i-th element in (l≠2) is 0, and so on, c preliminary solution sets are obtained. The specific solution method of formula (7) is:

[0048] Step S622: Solve the elements in each column vector of the sample label matrix F to obtain c preliminary solution sets f l (k) ∈ n×1 (k=1,2,...,c);

[0049] Step S623, determine the preliminary solution set f for each row l ∈ n×1 The set of preliminary solutions f (l=1,2,...,c) that can maximize the value of the converted objective function l (k) , and use it as the optimal sample label matrix F;

[0050] Step S63: Determine the objective function improvement value and compare the objective function improvement value with the convergence threshold. If the objective function improvement value is less than the convergence threshold, stop the optimization and output the sample label matrix F; otherwise, return to step S62. The objective function improvement value is determined based on the difference between the objective function value after the current round of iterative optimization and the objective function value after the previous round of iterative optimization, and is expressed as:

[0051] loss i =|obj i -obj i-1 |

[0052] Among them, loss i Indicates the improvement value of the objective function corresponding to the i-th round of iterative optimization, obj i represents the objective function value after the i-th round of iterative optimization, ||·|| F Represents absolute value operation.

[0053] Example 1

[0054] The proposed method is tested using the Hdigits dataset, which has 10,000 samples, two sub-view data, 784 and 256 feature dimensions for each view, and 10 image label types. The sample label matrix can be initialized by randomly assigning a value of 1 to an element in the row vector and 0 to the other elements. The convergence threshold is set to 1×10 -2 , get the optimal sample label matrix, and then get the predicted label Y according to the sample label matrix pre , by comparing the true label Y and the predicted label Y pre ,like Figure 3 As shown, the objective function steadily decreases with the increase in the number of iterations and converges at the 10th iteration. The three indicators of clustering accuracy (ACC), clustering normalized mutual information (NMI) and adjusted Rand index (ARI) all steadily increase with the progress of iterations. The clustering accuracy (ACC) reaches 95.95%, the clustering normalized mutual information (NMI) reaches 89.90%, and the adjusted Rand index (ARI) reaches 91.22%. The running time is reduced to 1.894 seconds, which significantly improves the clustering accuracy of multi-view image data. This shows that the method of the present invention can effectively extract consistent representation distribution in the latent space and accurately complete sample label learning.

[0055] The above are only preferred embodiments of the present application and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A fast multi-view image clustering method guided by implicit anchor points, characterized in that: include: Obtain the subview sample matrix of each view and randomly generate a sample label matrix; Extracting anchor points of the subview sample matrix, and constructing an anchor feature matrix and an anchor indicator matrix; The anchor feature matrix is ​​constructed by randomly initializing the row orthogonal matrix, and the anchor indicator matrix is ​​constructed by randomly initializing the column orthogonal matrix; constructing a feature structure graph of each view according to the sub-view sample matrix and the anchor point feature matrix; Constructing a reconstructed consensus graph based on the sample label matrix and the anchor point indicator matrix; Determine the loss error between the feature structure graph and the reconstructed consensus graph for all views, and establish an objective function based on the loss error; Update the anchor feature matrix, anchor indicator matrix, and sample label matrix in the objective function until the objective function meets the preset conditions and outputs the optimal sample label matrix; The objective function is: Where, represents the norm of matrix F, Indicates the The subview sample matrix under subviews, Indicates the The anchor feature matrix under each subview, represents the transposed matrix of the anchor feature matrix, represents the number of global anchor points, Indicates the The number of sample feature dimensions under each subview, represents the anchor point indicator matrix, represents the transposed matrix of the anchor indicator matrix; Indicates that the sample label matrix satisfies the constraint , represents the transposed matrix of the sample indicator matrix, Indicates the number of sample labels, matrix Indicates the dimension The identity matrix of The updating of the anchor feature matrix, the anchor indicator matrix, and the sample label matrix in the objective function until the objective function meets a preset condition and outputs an optimal sample label matrix includes: An implicit optimization strategy is used to update the anchor feature matrix and the anchor indicator matrix in the objective function, and the objective function is converted into an objective function related to the sample label matrix; The coordinate descent strategy is used to optimize the transformed objective function and determine the sample label matrix; When it is determined that the converted objective function meets the preset conditions, the sample label matrix is ​​output; when it is determined that the converted objective function does not meet the preset conditions, the coordinate descent strategy is re-adopted to optimize the converted objective function to determine the sample label matrix; The converted objective function is: Where, Indicates the The subview sample matrix under subviews, Represents the transposed matrix of the subview sample matrix.

2. The fast multi-view image clustering method guided by implicit anchor points according to claim 1, characterized in that: The coordinate descent strategy is adopted to optimize the converted objective function and determine the sample label matrix, including: Solve the elements in each column vector of the sample label matrix to obtain a preliminary solution set with a preset number of labels; Determine the set of preliminary solutions in each row of the preliminary solution set that can maximize the value of the converted objective function and use it as the sample label matrix.

3. The fast multi-view image clustering method guided by implicit anchor points according to claim 1, characterized in that: The preset condition is that the improvement value of the objective function is less than the convergence threshold.

4. The fast multi-view image clustering method guided by implicit anchor points according to claim 3, characterized in that: The improvement value of the objective function is determined according to the difference between the objective function value after the current round of iterative optimization and the objective function value after the previous round of iterative optimization.

Images