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See all by looking at a few: Sparse modeling for finding representative objects

9 years 2 months ago
See all by looking at a few: Sparse modeling for finding representative objects
We consider the problem of finding a few representatives for a dataset, i.e., a subset of data points that efficiently describes the entire dataset. We assume that each data point can be expressed as a linear combination of the representatives and formulate the problem of finding the representatives as a sparse multiple measurement vector problem. In our formulation, both the dictionary and the measurements are given by the data matrix, and the unknown sparse codes select the representatives via convex optimization. In general, we do not assume that the data are lowrank or distributed around cluster centers. When the data do come from a collection of low-rank models, we show that our method automatically selects a few representatives from each low-rank model. We also analyze the geometry of the representatives and discuss their relationship to the vertices of the convex hull of the data. We show that our framework can be extended to detect and reject outliers in datasets, and to ef...
Ehsan Elhamifar, Guillermo Sapiro, René Vid
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where CVPR
Authors Ehsan Elhamifar, Guillermo Sapiro, René Vidal
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