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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