Regularized nonnegative matrix factorization for clustering gene expression data

Recently nonnegative Matrix Factorization (NMF) has been proven a powerful method in clustering analysis of gene expression data. There exist two popular loss functions for minimization in decomposition: one is Euclidean distance and the other generalized Kullback-Leibler divergence. Both loss functions can be derived from a linear model with additive noise, and the Euclidean distance loss corresponds to Gaussian noise while the generalized Kullback-Leibler divergence corresponds to Poisson noise. However real data is not only Gaussian or Poisson, or not both. In order to take into account complex type of noise, we combine both loss functions for NMF according to regularization method. We compared NMF based on Euclidean distance, the generalized Kullback-Leibler divergence, and our regularized version, with application in clustering gene expression data. The experimental results demonstrate the effectiveness of the proposed method.