Latent space sparse and low-rank subspace clustering

Vishal M. Patel, Hien Van Nguyen, René Vidal

Research output: Contribution to journalArticlepeer-review

86 Scopus citations


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.

Original languageEnglish (US)
Article number7039205
Pages (from-to)691-701
Number of pages11
JournalIEEE Journal on Selected Topics in Signal Processing
Issue number4
StatePublished - Jun 1 2015

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


  • Dimension reduction
  • kernel methods
  • low-rank subspace clustering
  • manifold clustering
  • sparse subspace clustering
  • subspace clustering


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