Research And Application Of Sparse Subspace Clustering Method Based On Non-convex Constraint

Sparse subspace clustering algorithm can cluster high-dimensional data,which is widely used in face clustering,image processing,motion segmentation and other fields.The special feature of this algorithm is to solve an optimization problem based on sparse penalty term.Most scholars use the convex norm of l₀ norm as penalty term to solve the representation coefficient,but the representation coefficient solved by convex norm is not sparse enough.Therefore,in this paper,a general algorithm for sparse subspace clustering based on non-convex constraints is proposed to overcome the shortcomings of sparse subspace clustering algorithms.On this basis,in order to explore the influence of non-convexity degree on clustering results,the general form of sparse subspace clustering algorithm based on progressive non-convexity is given and the improved algorithm is applied to human datasets and face datasets.The innovation of this paper is reflected in the following contents:1.In the optimization problem of sparse subspace clustering algorithm,the l₁ norm is used as the sparsity penalty term,which can not well describe the sparsity of the representation coefficients.A non-convexψ_αenergy functional is introduced to constrain the objective function,the general algorithm of sparse subspace clustering based on non-convex constraints is given and the reweighted ADMM algorithm is used to solve the problem.Where a³0 is a parameter that regulates the degree of non-convex constraint.Compared with the traditional l₁ norm,the non-convexψ_αenergy functional is closer to the l₀ norm and the representation coefficients obtained are more sparse.In addition,the improved algorithm is applied to artificial datasets and face datasets to illustrate the performance of the algorithm.2.Based on the fact that the non-convex energy functional can promote the sparsity of the representation coefficients,In this paper,l₁ norm and non-convexψ_q energy functional are introduced to constrain the objective function in sparse subspace clustering model,gives the general model of sparse subspace clustering based on progressive non-convex and solves it.In addition,in order to explore the influence of the non-convex degree on the clustering results,this paper adopts the progressive non-convex strategy for the two non-convex energy functional in the face clustering experiment and takes the non-convex ψ_qenergy functional as an example to analyze the influence of the change of the non-convex degree q on the clustering results.The results show that with the decrease of the non-convex degree q,the sparsity of the coefficient matrix is enhanced,but the clustering error is not reduced.It also shows that the introduction of non-convex energy functional enhances the sparsity of representation coefficients,but excessive sparsity will affect the performance of the algorithm.