IEEE Trans Image Process - Manifold regularized discriminative nonnegative matrix factorization with fast gradient descent.

Tópicos

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Resumo

Nonnegative matrix factorization (NMF) has become a popular data-representation method and has been widely used in image processing and pattern-recognition problems. This is because the learned bases can be interpreted as a natural parts-based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole. For practical classification tasks, however, NMF ignores both the local geometry of data and the discriminative information of different classes. In addition, existing research results show that the learned basis is unnecessarily parts-based because there is neither explicit nor implicit constraint to ensure the representation parts-based. In this paper, we introduce the manifold regularization and the margin maximization to NMF and obtain the manifold regularized discriminative NMF (MD-NMF) to overcome the aforementioned problems. The multiplicative update rule (MUR) can be applied to optimizing MD-NMF, but it converges slowly. In this paper, we propose a fast gradient descent (FGD) to optimize MD-NMF. FGD contains a Newton method that searches the optimal step length, and thus, FGD converges much faster than MUR. In addition, FGD includes MUR as a special case and can be applied to optimizing NMF and its variants. For a problem with 165 samples in R(1600), FGD converges in 28 s, while MUR requires 282 s. We also apply FGD in a variant of MD-NMF and experimental results confirm its efficiency. Experimental results on several face image datasets suggest the effectiveness of MD-NMF.

Resumo Limpo

nonneg matrix factor nmf becom popular datarepresent method wide use imag process patternrecognit problem learn base can interpret natur partsbas represent data interpret consist psycholog intuit combin part form whole practic classif task howev nmf ignor local geometri data discrimin inform differ class addit exist research result show learn basi unnecessarili partsbas neither explicit implicit constraint ensur represent partsbas paper introduc manifold regular margin maxim nmf obtain manifold regular discrimin nmf mdnmf overcom aforement problem multipl updat rule mur can appli optim mdnmf converg slowli paper propos fast gradient descent fgd optim mdnmf fgd contain newton method search optim step length thus fgd converg much faster mur addit fgd includ mur special case can appli optim nmf variant problem sampl r fgd converg s mur requir s also appli fgd variant mdnmf experiment result confirm effici experiment result sever face imag dataset suggest effect mdnmf

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