Max-Min Distance Nonnegative Matrix Factorization
This is an incremental improvement for pattern classification tasks, enhancing NMF's utility in supervised learning scenarios.
The paper tackles the problem of improving discriminative ability in Nonnegative Matrix Factorization (NMF) by incorporating class labels, proposing a supervised algorithm that minimizes within-class distances and maximizes between-class distances in the new representation space.
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative coefficient matrix, and the coefficient matrix is used as the new representation. However, traditional NMF methods ignore the class labels of the data samples. In this paper, we proposed a supervised novel NMF algorithm to improve the discriminative ability of the new representation. Using the class labels, we separate all the data sample pairs into within-class pairs and between-class pairs. To improve the discriminate ability of the new NMF representations, we hope that the maximum distance of the within-class pairs in the new NMF space could be minimized, while the minimum distance of the between-class pairs pairs could be maximized. With this criterion, we construct an objective function and optimize it with regard to basic and coefficient matrices and slack variables alternatively, resulting in a iterative algorithm.