Math @ Duke

Publications [#265104] of Guillermo Sapiro
Papers Published
 Elhamifar, E; Sapiro, G; Vidal, R, See all by looking at a few: Sparse modeling for finding representative objects,
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
(2012),
pp. 16001607, ISSN 10636919 [doi]
(last updated on 2018/03/21)
Abstract: 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 lowrank models, we show that our method automatically selects a few representatives from each lowrank 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 efficiently deal with new observations and large datasets. The proposed framework and theoretical foundations are illustrated with examples in video summarization and image classification using representatives. © 2012 IEEE.


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