Research On Robust Subspace Clustering Algorithm Based On Block Diagonal Representation

Mining high-dimensional data is a hot spot in the field of machine learning.However,high-dimensional data generally have the characteristics of high dimensionality,sparseness and noise,which lead to the "curse of dimensionality" in the recognition process.Sparse subspace clustering algorithm is an effective algorithm for clustering high-dimensional data.It first learns the coefficient matrix from the input high-dimensional data,then uses this coefficient matrix to construct the affinity matrix,and finally uses spectral clustering algorithm to get the clustering results.In recent years,many researchers are devoted to learning a suitable coefficient matrix,but they ignore the influence of noise on the subspace clustering and how to better construct the affinity matrix.(i)How to design a sparse subspace clustering model that is robust against high noise and(ii)how to construct a more effective affinity matrix are the focus of this paper.The subspace clustering algorithm based on block diagonal representation can directly constrain the coefficient matrix with a block diagonal structure,where data may contain some noise and outlier.In this paper,a robust subspace clustering algorithm(RBDR)based on block diagonal representation is proposed to deal with clustering in high noise data,and a robust block-diagonal-representation subspace clustering algorithm based on diffusion(RBDRD)is also proposed to construct a better affinity matrix.The main work of this article are summarized as follows:(1)RBDR model is proposed to solve unknown high noise in high-dimensional data clustering.We use a re-weighting matrix to constrain the reconstruction error of the data and design a convex optimization algorithm to compute the re-weighting matrix and its parameters.In this model,re-weighting the reconstruction error can effectively deal with high noise data in the clustering.It should be noted that this method does not require prior knowledge about the type of noise.Thus,it can be applied in practice.At the same time,the model optimization method carefully designed in this paper can reduce the model optimization complexity and parameter training time.Experiments show the proposed method gets a better performance than others.(2)RBDRD model is proposed to improve the affinity matrix learning.Diffusion is adopted to learn the affinity matrix.This model uses the diffusion process to iteratively make full use of the local neighborhood structure.Each pair of affinity is enhanced and re-evaluated by the affinity relationship with other affinity.Thereby we can get an affinity that can approximate to the true geometric shape of the data matrix.At the same time,the diffusion process can enhance the connectivity of the inner edge of the same subgraph,which is beneficial to cut graph and enhance the effect of spectral clustering.