Subspace clustering via structure-enforced dictionary learning

Abstract Many real world data, which we deal with today, often have very high dimensions. These high-dimensional data can be seen as collections of data points from a union of low-dimensional subspaces. Subspace clustering, one solution to the high-dimensional data problem, refers to a method by which a set of data points is divided into multiple clusters by finding multiple subspaces that fit each cluster. Most existing subspace clustering approaches construct an affinity matrix using the self-representation model, which can propagate disturbing noisy information because even noisy data points are used to represent the data; then, they perform spectral clustering on the obtained affinity matrix, which contains the irrelevant information about noise or outliers. This paper proposes a novel subspace clustering method based on the structured sparse PCA-based dictionary learning. Our proposed method learns the reduced dimensional dictionary and coefficient matrices using the structural information as well as sparsity of data. Then, the affinity matrix is constructed from inner product of the learned dictionary coefficient vectors, which shows the correlation among data points. The experimental results on three benchmark datasets verify that the proposed method outperforms state-of-the-art subspace clustering methods.