Study On Sparse Subspace Clustering With K Nearest Neighbor Constraint

Cluster analysis is based on the information and their relationship of the objects to group or classify the data objects,so that the similarity of objects within the same group is high,and the similarity of objects within different groups is low.It is an important research content in the fields of data mining,machine learning,pattern recognition and so on.With the development of information technology,data collection and storage becomes easier,and at the same time,the scale and complexity of the data is increasing and so does the representation dimensionality of data.Dealing with high-dimensional data is a new challenge of clustering analysis since a lot of redundant data and the complex geometry structure caused by high-dimensional feature representation.However,in many practical problems,the data of one class in high-dimensional space is distributed in a low dimensional subspace.The data from multiple classes lies in several low-dimensional subspaces.According to this idea,the problem is that clustering can be transformed into subspace segmentation,hence the subspace clustering algorithm is acquired.In this paper,on the basis of the analysis and comparison of the subspace clustering algorithm,the k nearest neighbor constraint is introduced and the sparse subspace clustering with k nearest neighbor constrain is proposed.Sparse subspace clustering and low-rank subspace clustering are the proposed clustering algorithms for high-dimensional data in recent years,and they are spectral clustering-based subspace clustering methods.The key is to reveal the real subspace structure of high-dimensional data on the basis of sparse and low rank constraints.The similarity matrix is constructed according to the representation coefficients,and then the spectral clustering algorithm is used to obtain the clustering results of the data.In this paper,the model,algorithm of sparse subspace clustering and low-rank subspace clustering are described in detail,moreover,its extension algorithms is also introduced.For the case that the actual data do not completely satisfy the linear subspace model,in the subspace representation,the problem that the sample is linearly represented by other subspace data is prone to occur.This paper proposes a sparse subspace clustering algorithm with k-nearest neighbor constraint.The main purpose is to obtain better subspace representation.The proposed algorithm combines the subspace structure characteristics,k nearest neighbors and the distance information,and adds k nearest neighbor constraints into the sparse subspace model.The added intuitive recognition with the smaller corresponding distance of constraint term and the larger the similarity coefficient does not change the sparsity of coefficient matrix.In the experiment section,the proposed sparse subspace with k nearest neighbor constraint clustering algorithm and the classic subspace clustering algorithm are compared and analyzed by the clustering experiments on faced data sets Extended Yale B,ORL,AR,object image dataset COIL20 and handwritten digital image dataset USPS.The result shows that the proposed subspace representation model can reduce the case that a sample is linear represented by other subspace data,and the clustering algorithm has competitive performance.