Math @ Duke

Publications [#265120] of Guillermo Sapiro
Papers Published
 Esser, E; Möller, M; Osher, S; Sapiro, G; Xin, J, A convex model for nonnegative matrix factorization and dimensionality reduction on physical space.,
IEEE Transactions on Image Processing, vol. 21 no. 7
(July, 2012),
pp. 32393252 [22410332], [doi]
(last updated on 2017/12/15)
Abstract: A collaborative convex framework for factoring a data matrix X into a nonnegative product AS , with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We use l(1, ∞) regularization to select the dictionary from the data and show that this leads to an exact convex relaxation of l(0) in the case of distinct noisefree data. We also show how to relax the restrictionto X constraint by initializing an alternating minimization approach with the solution of the convex model, obtaining a dictionary close to but not necessarily in X. We focus on applications of the proposed framework to hyperspectral endmember and abundance identification and also show an application to blind source separation of nuclear magnetic resonance data.


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