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.
In this paper, based on ideas from lossy data coding and compression, we present a simple but surprisingly effective
technique for segmenting multivariate mixed data that are drawn from a mixture of Gaussian distributions
or linear subspaces. The goal is to find the optimal segmentation that minimizes the overall coding length of
the segmented data, subject to a given distortion. We show that deterministic segmentation minimizes an upper
bound on the (asymptotically) optimal solution. The proposed algorithm does not require any prior knowledge of
the number or dimension of the groups, nor does it involve any parameter estimation. Simulation results reveal
intriguing phase-transition behaviors of the number of segments when changing the level of distortion or the
amount of outliers. Finally, we demonstrate how this technique can be readily applied to segment real imagery
and bioinformatic data.
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