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CN-122024300-A - L-based2Low-rank representation face clustering method with regular p-norm balance

CN122024300ACN 122024300 ACN122024300 ACN 122024300ACN-122024300-A

Abstract

The invention relates to a low-rank representation face clustering method based on L 2 and p norm equilibrium regularization, which relates to the field of data clustering and machine learning, and comprises the steps of obtaining a plurality of face data samples to be clustered, constructing a data matrix, and initializing a projection matrix and a label matrix; the method comprises the steps of constructing a first clustering objective function according to a data matrix, a projection matrix and a label matrix, obtaining a second clustering objective function according to the first clustering objective function, solving the second clustering objective function by adopting an alternate optimization strategy, gradually converging the second clustering objective function through iteratively updating the label matrix and related variables to obtain a final label matrix, and determining a clustering result of each face data sample according to the final label matrix. According to the invention, L 2 and p norm (p < 0) equalization regular terms are introduced into the label matrix, so that clustering categories with overlarge number of face data samples are adaptively restrained, the relatively reasonable face data sample scale is obtained by each clustering cluster, and the clustering result is more balanced.

Inventors

  • LI FANGFANG
  • GAO QUANXUE
  • CUI KAI
  • XUE XINGYU
  • DUAN YU

Assignees

  • 西安电子科技大学

Dates

Publication Date
20260512
Application Date
20260413

Claims (10)

  1. 1. The low-rank representation face clustering method based on L 2 and p-norm equalization regularization is characterized by comprising the following steps of: step 1, acquiring a plurality of face data samples to be clustered to construct a data matrix, initializing a projection matrix and a label matrix required by clustering, wherein the label matrix meets non-negative constraint and sample allocation normalization constraint; Step 2, constructing a first clustering objective function according to the data matrix, the projection matrix and the tag matrix, wherein L 2 is introduced into the tag matrix of the first clustering objective function, p norms are used as equilibrium regular terms, and p is less than 0; Step 3, obtaining a second clustering objective function according to the first clustering objective function, wherein the second clustering objective function comprises an equilibrium derivative matrix derived from an equilibrium regular term; and 4, solving the second aggregation target function by adopting an alternative optimization strategy, gradually converging the second aggregation target function by iteratively updating a label matrix and related variables to obtain a final label matrix, and determining a clustering result of each face data sample according to the final label matrix.
  2. 2. The low-rank representation face clustering method of claim 1, wherein obtaining a plurality of face data samples to be clustered to construct a data matrix comprises: obtaining a plurality of face data samples to be clustered, constructing the data matrix according to the face data samples to be clustered, , wherein, As a matrix of data, As a set of real numbers, For the feature dimension of the face data sample, Is the number of face data samples.
  3. 3. The low-rank representation face clustering method of claim 2, wherein initializing the projection matrix and the tag matrix required for clustering comprises: initializing the projection matrix and the label matrix required for clustering, , , , And is also provided with , wherein, In order to project the matrix of the light, In the form of a matrix of labels, For the dimensions of the projection subspace, For the number of cluster categories, Is a matrix of units which is a matrix of units, Is a transpose operation.
  4. 4. A low rank representation face clustering method according to claim 3, wherein the first clustering objective function is represented as: ; Wherein, the In order to share the base matrix of the matrix, , For a low rank to share the subspace dimension, In the case of a low-rank coefficient matrix, , In order to regularize the weight parameters, Is the Frobenius norm, For the sum of L 2 , p-norms, In order to minimize the number of the components, Is a constraint.
  5. 5. The low-rank representation face clustering method of claim 4, wherein the second aggregation objective function is represented as: ; ; Wherein, the In order to equalize the derivative matrix, As a trace of the matrix, In order to diagonalize the operator, For a matrix of labels I is greater than or equal to 1 and less than or equal to c, Is the L 2 norm.
  6. 6. The low-rank representation face clustering method according to claim 5, wherein the step 4 comprises: Step 4.1, fixing the label matrix in the second polymer objective function obtained by the j-1 th round of iteration in the j-th round of iteration Shared base matrix Low rank coefficient matrix Constructing and linearizing minimum optimization problems To obtain For a pair of Singular value decomposition is carried out to obtain a projection matrix of the jth round of iteration And utilize the projection matrix Updating a second aggregate objective function obtained by the j-1 th iteration, wherein, , A projection matrix for the j-1 th iteration; Step 4.2, fixing the projection matrix in the second polymer objective function updated in the step 4.1 Label matrix Low rank coefficient matrix According to the minimum optimization problem Obtaining a matrix equation To according to the matrix equation Obtaining a shared base matrix of the jth round of iteration And utilize the shared base matrix Updating the second aggregate target function updated in the step 4.1; Step 4.3, fixing the projection matrix in the second polymer objective function updated in the step 4.2 Label matrix Shared base matrix According to the minimum optimization problem Obtaining a matrix equation To according to the matrix equation Obtaining a low-rank coefficient matrix of the jth round of iteration And utilize the low rank coefficient matrix Updating the second aggregate target function updated in the step 4.2; Step 4.4, fixing the projection matrix in the second polymer objective function updated in the step 4.3 Shared base matrix Low rank coefficient matrix According to the minimum optimization problem Obtaining minimum optimization problem And according to the minimum optimization problem Obtaining a label matrix of the jth round of iteration , wherein, , , ; Step 4.5, judging If the label matrix is smaller than the preset threshold value, stopping iteration if the label matrix is smaller than the preset threshold value, and obtaining the label matrix And determining a clustering result of each face data sample to be clustered according to the final tag matrix, and if not, continuing iteration until an iteration stop condition is met.
  7. 7. The low-rank representation face clustering method according to claim 6, wherein the step 4.1 comprises: step 4.11, fixing the label matrix in the second polymer objective function obtained by the j-1 th round of iteration in the j-th round of iteration Shared base matrix Low rank coefficient matrix ; Step 4.12, constructing a projection matrix for the j-1 th round of iteration Minimum optimization problem of (2) ; Step 4.13 based on The minimum optimization problem is solved Conversion by linearization to ; Step 4.14, matrix alignment Singular value decomposition is carried out, and a left singular vector of the maximum singular value is taken as a projection matrix of the j-th round iteration And utilize the projection matrix of the jth round of iteration Substituting projection matrix in second-class objective function obtained through j-1 iteration 。
  8. 8. The low-rank representation face clustering method according to claim 6, wherein the step 4.2 comprises: Step 4.21, fixing the projection matrix in the second polymer objective function updated in the step 4.1 Label matrix Low rank coefficient matrix ; Step 4.22, constructing a matrix for the shared basis Minimum optimization problem of (2) ; Step 4.23, according to the minimum optimization problem Obtaining a matrix equation ; Step 4.24, according to the matrix equation Obtaining a shared base matrix of the jth round of iteration , And utilize the shared base matrix Replacing the shared base matrix in the second polymer objective function updated in the step 4.1 。
  9. 9. The low-rank representation face clustering method according to claim 6, wherein the step 4.3 comprises: Step 4.31, fixing the projection matrix in the second polymer objective function updated in the step 4.2 Label matrix Shared base matrix ; Step 4.32, constructing a matrix for the low rank coefficients Minimum optimization problem of (2) ; Step 4.33, according to the minimum optimization problem Obtaining a matrix equation ; Step 4.34, according to the matrix equation Obtaining a low-rank coefficient matrix of the jth round of iteration , And utilize the low rank coefficient matrix Replacing the low rank coefficient matrix in the second polymer objective function updated in the step 4.2 。
  10. 10. The low-rank representation face clustering method of claim 6, wherein the step 4.4 comprises: Step 4.41, fixing the projection matrix in the second polymer objective function updated in the step 4.3 Shared base matrix Low rank coefficient matrix ; Step 4.42, order 、 Then with respect to the tag matrix The minimum optimization problem of (1) is expressed as ; Step 4.43, developing and sorting the minimum optimization problem Obtaining the minimum optimization problem ; Step 4.44, when matrix Solving for said irreversible or numerical instability Obtaining a matrix And according to the matrix Obtaining a label matrix of the jth round of iteration 。

Description

L 2 -based p-norm equalization regularization low-rank representation face clustering method Technical Field The invention relates to the technical field of data clustering and machine learning, in particular to a low-rank representation face clustering method based on L 2 and p norm equalization regularization. Background Cluster analysis is an important research direction in the fields of machine learning and data mining, and aims to automatically divide samples into a plurality of categories according to similarity or potential structural characteristics among data samples, so as to reveal the inherent distribution rule of the data. However, in an actual application scene, there are often problems of uneven distribution, significant differences in category density, and the like of the data samples. Under the condition, the phenomenon of unbalanced scale of the clustering categories is easy to occur in the optimization process of the traditional clustering method, namely, part of the clustering categories contain a large number of samples, and the rest of the clustering categories only contain a small number of samples and even are ignored, so that the non-ideal conditions such as excessive concentration of the categories, isolated clusters or category degradation and the like of the clustering results are caused, and the stability, consistency and practical application value of the clustering results are seriously influenced. The above problems are particularly prominent in application scenarios such as large-scale face data analysis. Specifically, because the frequency difference of different individuals under the actual acquisition condition is large, the number of face data samples corresponding to the same identity often has obvious imbalance phenomenon, so that the condition that the clustering result is concentrated to a few high-frequency identities is easier to occur in the unsupervised face clustering process. Existing unsupervised clustering methods, such as k-means clustering, spectral clustering and subspace clustering methods, generally describe structural relationships among samples by constructing a distance relationship, a similarity matrix or a low-rank representation model among the samples, and finish sample division according to the structural relationships. However, such methods focus mainly on inter-sample similarity, structural consistency, or low rank characteristics in the design of objective functions, and do not impose explicit constraints on sample size distribution for different cluster categories. When the class distribution deflection exists in the data or the structure is complex, the method is easy to form a clustering result with highly unbalanced sample distribution in the iterative optimization process. In order to improve the clustering structure, some researches try to introduce regularization constraint into a clustering model to adjust the structural characteristics of a clustering result, however, the main effect of the regularization mode is to enhance sparsity or selectivity, so that part of clustering categories are inhibited or disappeared, further aggravate the problem of clustering unbalance, and the practical requirement on cluster scale balance cannot be met. In addition, part of the existing methods can alleviate the problem of cluster category scale imbalance to a certain extent by additionally introducing manually set cluster scale constraint, priori proportion information or complex balance parameters. The method not only increases the complexity of model design and parameter selection, but also has poor applicability in actual application scenes lacking prior information. Therefore, how to realize the self-adaptive balanced adjustment of the cluster class scale through the constraint mechanism of the model on the premise of not depending on any label information or manual priori in the application scene of the unsupervised face cluster is still a technical problem to be solved in the existing unsupervised clustering technology. Disclosure of Invention In order to solve the problems in the prior art, the invention provides a low-rank representation face clustering method based on L 2 and p-norm equalization regularization. The technical problems to be solved by the invention are realized by the following technical scheme: The invention provides a low-rank representation face clustering method based on L 2 and p norm equalization regularization, which comprises the following steps: step 1, acquiring a plurality of face data samples to be clustered to construct a data matrix, initializing a projection matrix and a label matrix required by clustering, wherein the label matrix meets non-negative constraint and sample allocation normalization constraint; Step 2, constructing a first clustering objective function according to the data matrix, the projection matrix and the tag matrix, wherein L 2 is introduced into the tag matrix of the first clustering objec