Latent Space Sparse and Low-Rank Subspace Clustering

We propose three novel algorithms for simultaneous dimensionality reduction and clustering of data lying in a union of subspaces. Specifically, we describe methods that learn the projection of data and find the sparse and/or low-rank coefficients in the low-dimensional latent space. Cluster labels are then assigned by applying spectral clustering to a similarity matrix built from these representations. Efficient optimization methods are proposed and their non-linear extensions based on kernel methods are presented. Various experiments show that the proposed methods perform better than many competitive subspace clustering methods.