Correlation Adaptive Subspace Clustering And Its Application

Based on the fact that high-dimensional data usually lies in a union of several low-dimensional subspaces,subspace clustering is a method for revealing the low-dimensional structure underlying high-dimensional data.For a given datasets from high-dimensional space,subspace clustering aims to segment the high-dimensional datasets into several clusters,with each cluster corresponding to a subspace.Revealing the low-dimensional structure underlying high-dimensional data can better reflect the inherent quality of data,and it has important application in machine learning and computer vision.The spectral-clustering based method is a popular method for subspace clustering in recent years,which always need to construct an affinity matrix based on the subspace self-representation of the data points.The ideal affinity matrix should be inter-cluster sparse and intra-cluster uniform.The inter-cluster sparsity tends to group data from different subspaces into different clusters and the intra-cluster uniformity tends to group data from the same cluster together.Most previous methods partly satisfy these properties and cannot obtain ideal results,so we propose a data correlation adaptive regression method for the subspace representation.The proposed model essentially uses l₂norm on the coefficients of highly correlated data points while l₁norm on that of less correlated data points.The l₂norm tends to enforce the corresponding coefficients uniform while the l₁norm tends to enforce the corresponding coefficients sparse.So our method has self-adaptivity,and it can ensure the inter-cluster sparsity and intra-cluster uniformity of the affinity matrix.It also obtained the ideal experiment result.Additionally,based on the theory of sparsity and grouping effect,we also proposed two subspace clustering methods which explicitly enforce sparsity and grouping effect of the affinity matrix.One of it can even guarantee the affinity matrix is sparsity between clusters,and have grouping effect within clusters.The sparsity between clusters ensure the representation coefficients between clusters are zero and the grouping effect within clusters ensure the representation coefficients within clusters are uniform.We also used our method on several popular high-dimensional datasets and a standard image segmentation dataset for data clustering and image segmentation.Both data clustering results and image segmentation results is better than previous methods.