Latent Space Sparse and Low-Rank Subspace Clustering

• Published in: IEEE journal of selected topics in signal processing Vol. 9; no. 4; pp. 691 - 701
• Main Authors: Patel, Vishal M., Van Nguyen, Hien, Vidal, Rene
• Format: Journal Article
• Language: English
• Published: IEEE 01-06-2015
• Subjects: Clustering algorithms; Clustering methods; Cost function; Dimension reduction; Kernel; kernel methods; low-rank subspace clustering; manifold clustering; Signal processing algorithms; Sparse matrices; sparse subspace clustering; subspace clustering
• ISSN: 1932-4553; 1941-0484
• DOI: 10.1109/JSTSP.2015.2402643

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.