IEEE Trans Image Process - A convex model for nonnegative matrix factorization and dimensionality reduction on physical space.

Tópicos

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Resumo

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, 8) 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 noise-free data. We also show how to relax the restriction-to- 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.

Resumo Limpo

collabor convex framework factor data matrix x nonneg product spars coeffici matrix s propos restrict column dictionari matrix coincid certain column data matrix x therebi guarante physic meaning dictionari dimension reduct use l regular select dictionari data show lead exact convex relax l case distinct noisefre data also show relax restrictionto x constraint initi altern minim approach solut convex model obtain dictionari close necessarili x focus applic propos framework hyperspectr endmemb abund identif also show applic blind sourc separ nuclear magnet reson data

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