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Proceedings Paper

The algebra and statistics of generalized principal component analysis
Author(s): Shankar Rao; Harm Derksen; Robert Fossum; Yi Ma; Andrew Wagner; Allen Yang
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Paper Abstract

We consider the problem of simultaneously segmenting data samples drawn from multiple linear subspaces and estimating model parameters for those subspaces. This "subspace segmentation" problem naturally arises in many computer vision applications such as motion and video segmentation, and in the recognition of human faces, textures, and range data. Generalized Principal Component Analysis (GPCA) has provided an effective way to resolve the strong coupling between data segmentation and model estimation inherent in subspace segmentation. Essentially, GPCA works by first finding a global algebraic representation of the unsegmented data set, and then decomposing the model into irreducible components, each corresponding to exactly one subspace. We provide a summary of important algebraic properties and statistical facts that are crucial for making GPCA both efficient and robust, even when the given data are corrupted with noise or contaminated by outliers. We demonstrate the effectiveness of GPCA using a large testbed of synthetic and real experiments.

Paper Details

Date Published: 29 January 2007
PDF: 15 pages
Proc. SPIE 6508, Visual Communications and Image Processing 2007, 65080G (29 January 2007); doi: 10.1117/12.707527
Show Author Affiliations
Shankar Rao, Univ. of Illinois at Urbana-Champaign (United States)
Harm Derksen, Univ. of Michigan (United States)
Robert Fossum, Univ. of Illinois at Urbana-Champaign (United States)
Yi Ma, Univ. of Illinois at Urbana-Champaign (United States)
Andrew Wagner, Univ. of Illinois at Urbana-Champaign (United States)
Allen Yang, Univ. of California at Berkeley (United States)


Published in SPIE Proceedings Vol. 6508:
Visual Communications and Image Processing 2007
Chang Wen Chen; Dan Schonfeld; Jiebo Luo, Editor(s)

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