Nonnegative matrix factorization with adaptive neighbors

TL;DR: Nonnegative Matrix factorization is presented with Adaptive Neighbors (NMFAN) for clustering and an efficient iterative updating algorithm is proposed and its convergence is also guaranteed theoretically.

Abstract: Nonnegative Matrix factorization (NMF) and its graph regularized extensions have been playing an outstanding role in machine learning and data mining. Recent studies of graph regularized NMF have focused on the application for clustering algorithms. The clustering results of these methods highly depend on the data similarity learning since the data group is utilized based on the input data similarity matrix. Previous graph regularized NMF usually construct the data graph by considering the K-Nearest Neighbors (KNN) which may mislead the factorization since the nearest neighbors may belong to different clusters. That is, it is not a good similarity measurement to construct the data graph by considering the KNN. In this paper, we present NMF with Adaptive Neighbors (NMFAN) for clustering. NMFAN learns the data similarity matrix by assigning the adaptive and optimal neighbors for each data point by exploring the local connectivity of data. It is based on the assumption that the data points with a smaller distance should have a larger probability to be neighbors. Furthermore, in order to achieve the ideal neighbors assignment, we constrain the data similarity matrix such that the neighbors assignment becomes an adaptive process, thus an ideal neighbors assignment can be expected. In order to solve the optimization problem of our method, an efficient iterative updating algorithm is proposed and its convergence is also guaranteed theoretically. Experiments on benchmark data sets demonstrate the effectiveness of the proposed method.