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Nonnegative Matrix Factorization (NMF) has been a popular representationmethod for pattern classification problem. It tries to decompose a nonnegativematrix of data samples as the product of a nonnegative basic matrix and anonnegative coefficient matrix, and the coefficient matrix is used as the newrepresentation. However, traditional NMF methods ignore the class labels of thedata samples. In this paper, we proposed a supervised novel NMF algorithm toimprove the discriminative ability of the new representation. Using the classlabels, we separate all the data sample pairs into within-class pairs andbetween-class pairs. To improve the discriminate ability of the new NMFrepresentations, we hope that the maximum distance of the within-class pairs inthe new NMF space could be minimized, while the minimum distance of thebetween-class pairs pairs could be maximized. With this criterion, we constructan objective function and optimize it with regard to basic and coefficientmatrices and slack variables alternatively, resulting in a iterative algorithm.

Max-Min Distance Nonnegative Matrix Factorization