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CVPR
2004
IEEE

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

14 years 5 months ago
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...
Kun Huang, René Vidal, Yi Ma
Added 12 Oct 2009
Updated 29 Oct 2009
Type Conference
Year 2004
Where CVPR
Authors Kun Huang, René Vidal, Yi Ma
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