Sparse Subspace Clustering via Diffusion Process

Subspace clustering refers to the problem of clustering high-dimensional data that lie in a union of lowdimensional subspaces. State-of-the-art subspace clustering methods are based on the idea of expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with `1, `2 or nuclear norms for a sparse solution. `1 regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no connections between points from different subspaces) under broad theoretical conditions, but the clusters may not be fully connected. `2 and nuclear norm regularization often improve connectivity, but give a subspace-preserving affinity only for independent subspaces. Mixed `1, `2 and nuclear norm regularization could offer a balance between the subspace-preserving and connectedness properties, but this comes at the cost of increased computational complexity. This paper focuses on using `1 norm and alleviating the corresponding connectivity problem by a simple yet efficient diffusion process on subspace affinity graphs. Without adding any tuning parameter , our method can achieve state-of-the-art clustering performance on Hopkins 155 and Extended Yale B data sets.