Minimum Effective Dimension for Mixtures of Subspaces: A Robust GPCA Algorithm and Its Applications

In this paper, we propose a robust model selection criterion for mixtures of subspaces called minimum effective dimension (MED). Previous information-theoretic model selection criteria typically assume that data can be modelled with a parametric model of certain (possibly differing) dimension and a known error distribution. However, for mixtures of subspaces with different dimensions, a generalized notion of dimensionality is needed and hence introduced in this paper. The proposed MED criterion minimizes this geometric dimension subject to a given error tolerance (regardless of the noise distribution). Furthermore, combined with a purely algebraic approach to clustering mixtures of subspaces, namely Generalized PCA (GPCA), the MED is designed to also respect the global algebraic and geometric structure of the data. The result is a non-iterative algorithm called robust GPCA that estimates from noisy data an unknown number of subspaces with unknown and possibly different dimensions subj...

• Type: Conference
• Year: 2004
• Where: CVPR
• Authors: Kun Huang, René Vidal, Yi Ma
• Keywords: Computer Vision, CVPR 2004, Maximum Error Bound, Model Selection Criterion, Robust Gpca, Subspaces Called Minimum, Synthetic Noisy Data