Local Learning Regularized Nonnegative Matrix Factorization

Nonnegative Matrix Factorization (NMF) has been widely used in machine learning and data mining. It aims to find two nonnegative matrices whose product can well approximate the nonnegative data matrix, which naturally lead to parts-based representation. In this paper, we present a local learning regularized nonnegative matrix factorization (LLNMF) for clustering. It imposes an additional constraint on NMF that the cluster label of each point can be predicted by the points in its neighborhood. This constraint encodes both the discriminative information and the geometric structure, and is good at clustering data on manifold. An iterative multiplicative updating algorithm is proposed to optimize the objective, and its convergence is guaranteed theoretically. Experiments on many benchmark data sets demonstrate that the proposed method outperforms NMF as well as many state of the art clustering methods.