Research On Subspace Clustering Algorithm Based On Sparse, Adaptive And Hypergraph

Clustering analysis is an important data mining technique for unsupervised learning in machine learning,which groups a set of research samples into relatively homoge-neous clusters.Owing to science and technology,information collection has become increasingly convenient and diverse,and high-dimensional data is widely present in various industries.Clustering analysis of high-dimensional data has become an im-portant research direction and technical difficulty in clustering.Subspace clustering is a very effective method for solving high-dimensional data clustering problems,and it is an extension of traditional clustering methods in high-dimensional data spaces.Subspace clustering achieves clustering tasks by discovering and utilizing potential low-dimensional representations of high-dimensional data.Among them,a class sub-space clustering method based on the self-expression properties of data and spectral clustering is widely popular due to its advantages of simple operation,less prior infor-mation required,outstanding clustering effect,and various applicability.This research mainly studies such methods and focuses on their sparsity requirements,ideal structure requirements for affinity matrices,and representation requirements for more complex data relationships.The specific research results obtained are as follows:1.A k-sparse LSR（KSLSR）subspace clustering method via 0-1 integer pro-gramming is proposed in this research.This method provides a solution to address the problem of lacking sparsity in the classical least squares-based subspace cluster-ing method（LSR）by introducing an adjustable sparsity of k-sparsity,where k is the sparsity parameter.Although the classical LSR method has the advantages of a simple explicit solution and the grouping effects that tend to cluster highly correlated data into a group,it lacks sparsity,which may lead to its sensitivity to noise and data dimensions.Adding the constraint based on（?）₀norm is the most direct way to increase sparsity,but the optimization problem with（?）₀norm constraint is often tricky to solve.To address this issue,the proposed method converts the（?）₀norm constraint into the equivalent intersection of two continuous constraints with the help of a 0-1 integer constraint instead of performing any relaxation on the（?）₀norm constraint.Then,the resultant optimization problem can be solved effectively by the alternating direction multiplier method（ADMM）.The proposed method adds k-sparsity to LSR but also maintains the advantages of grouping effect of LSR.The performance of the proposed method KSLSR was tested on multiple image datasets,and the experimental results showed that the proposed method not only improves the clustering performance to achieve higher clustering accuracy but also has a certain robustness to data noise and dimensionality.2.An adaptive affinity sparse subspace clustering method（AASSC）is proposed in this research.This method can adaptively learn an affinity matrix that meets the requirements of an ideal structure and provides corresponding clustering results simul-taneously.The quality of the affinity matrix is crucial for spectral clustering-based subspace clustering methods and impacts their clustering performance significantly.However,the traditional affinity matrix calculated in some deterministic manners is only a feasible result rather than the most suitable result for displaying data structures.Besides,the post-processing of the coefficient matrix typically affects the quality of the affinity matrix.In addition,the calculation of the affinity matrix,optimization of the coefficient matrix,and implementation of spectral clustering are three independent processes that cannot guarantee the overall optimality of the final result.To this end,this research proposes a new method,AASSC,by adding the Laplace rank constraint into the subspace sparse-representation model.Due to the addition of new constraints,the proposed method can adaptively learn a high-quality affinity matrix with c con-nected components from the sparse coefficient matrix without post-processing,where c represents the category.In addition,by relaxing the Laplace rank constraint to trace minimization,the proposed method can naturally integrate the operations on coefficient matrix,affinity matrix,and spectral clustering into a unified optimization and alternately solve them to ensure the final overall optimality result.Multiple com-parative experimental results indicate that the proposed method has advantages in improving the quality of the affinity matrix and clustering accuracy.3.An adaptive iterative reweighted hypergraph subspace clustering framework（AIRHSC）is proposed in this research.This framework can be directly applied to multiple existing subspace clustering methods,replacing the traditional graph with the hypergraph to describe more complex representation relationships between data,thereby improving clustering accuracy.In subspace clustering problems setting,it is usually assumed that there is a pairwise relationship between clustering objects and can be represented by a graph.However,in the real world,the relationships between objects are often more complex,and using pairwise relationships alone is not enough to reflect the correlation between data,which also limits the clustering performance of such methods.With the development and application of hypergraphs,many sub-space clustering methods based on hypergraphs have been proposed.They usually design unique hypergraph construction methods based on specific subspace represen-tation models to improve clustering accuracy.However,to our knowledge,no unified method exists to introduce hypergraphs into traditional graph-based subspace cluster-ing methods and improve their clustering performance.To this end,this research pro-poses a unified hypergraph subspace clustering framework AIRHSC,whose hypergraph is constructed unified based on representation coefficients.Among them,hyperedges are generated by a coefficient-based neighborhood strategy,where each data point is treated as a centroid vertex and linked to the K nearest neighbors adaptively selected through the energy ratio rule;the weight is calculated through an iteratively reweighted method,which continuously modifies the weight until the best result is obtained.The adjustable ratioθand steadily revised weights make the proposed framework AIRHSC suitable for multiple subspace clustering methods and provide some improvement ef-fects.The experimental results show that the proposed hypergraph-based method significantly improves the clustering performance of classic sparse subspace clustering methods（SSC）,low-rank representation-based subspace clustering methods（LRR）,and least squares-based subspace clustering methods（LSR）.