Math @ Duke

Publications [#264734] of Guillermo Sapiro
Papers Published
 Elhamifar, E; Sapiro, G; Vidal, R, Finding exemplars from pairwise dissimilarities via simultaneous sparse recovery,
Advances in Neural Information Processing Systems, vol. 1
(December, 2012),
pp. 1927, ISSN 10495258
(last updated on 2019/06/24)
Abstract: Given pairwise dissimilarities between data points, we consider the problem of finding a subset of data points, called representatives or exemplars, that can efficiently describe the data collection. We formulate the problem as a rowsparsity regularized trace minimization problem that can be solved efficiently using convex programming. The solution of the proposed optimization program finds the representatives and the probability that each data point is associated with each one of the representatives. We obtain the range of the regularization parameter for which the solution of the proposed optimization program changes from selecting one representative for all data points to selecting all data points as representatives. When data points are distributed around multiple clusters according to the dissimilarities, we show that the data points in each cluster select representatives only from that cluster. Unlike metricbased methods, our algorithm can be applied to dissimilarities that are asymmetric or violate the triangle inequality, i.e., it does not require that the pairwise dissimilarities come from a metric. We demonstrate the effectiveness of the proposed algorithm on synthetic data as well as realworld image and text data.


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