29 January 2007 The algebra and statistics of generalized principal component analysis
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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.
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Shankar Rao, Shankar Rao, Harm Derksen, Harm Derksen, Robert Fossum, Robert Fossum, Yi Ma, Yi Ma, Andrew Wagner, Andrew Wagner, Allen Yang, Allen Yang, } "The algebra and statistics of generalized principal component analysis", Proc. SPIE 6508, Visual Communications and Image Processing 2007, 65080G (29 January 2007); doi: 10.1117/12.707527; https://doi.org/10.1117/12.707527

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