Constrained Nonnegative Matrix Factorization Based on Label Propagation for Data Representation

Abstract

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nonnegative matrix factorization</i> (NMF) algorithms are a series of dimensional reduction techniques widely used in data preprocessing. To improve the performance of clustering and the discrimination of the low-dimensional representation in NMF, we proposed a novel semi-supervised <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constrained nonnegative matrix factorization based on label propagation</i> (LpCNMF). Specifically, the proposed LpCNMF adopts graph and label propagation as regularization terms, then makes use of a small amount of labeled data to predict the label information of the unlabeled data and finally obtains a predictive membership matrix with more label information. At the same time, we introduce an efficient alternating iterative algorithm to solve the optimization problem of the objective function in the LpCNMF. Unlike other NMF algorithms that only update the basis and coefficient matrices, the LpCNMF algorithm increases the update of the predictive membership matrix obtained by label propagation. Experimental results on various benchmark datasets demonstrate the superiority of our algorithm over existing state-of-the-art NMF algorithms. The code is publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/ycwang-libra/LpCNMF_github.git.</uri>