Sparse Convolution Subspace Clustering

Abstract

The real-world high-dimensional data lie on low-dimensional manifolds embedded within the high-dimensional space. Therefore, clustering in high-dimensional spaces is a difficult problem. Subspace-based clustering methods are proposed to project the high dimensional data into a low-dimensional space, and then find clusters in this low-dimensional subspaces of the high dimensional data, instead of finding clusters in the entire feature space. In this work, we propose a subspace clustering method called Sparse Convolution Subspace Clustering (SCSC) which is inspired by Sparse Subspace Clustering (SSC). SSC is to find a sparse representations of a data point in terms of other points while SCSC tries to find a sparse convolutional representations of a data point in terms of other points. A group optimization method based alternating direction method of multipliers (ADMM) is used to solve the sparse convolutional representation problem. It should be pointed out that SSC is a special case of SCSC while the convolution kernel size is set as $1 \times 1$. The experimental results on face data show the effectiveness of the proposed SCSC.