Parameter-less Auto-weighted multiple graph regularized Nonnegative Matrix Factorization for data representation

TLDR: In GNMF, an affinity graph is constructed to encode the geometrical information and a matrix factorization is sought, which respects the graph structure, and the empirical study shows encouraging results of the proposed algorithm in comparison to the state-of-the-art algorithms on real-world problems.

Abstract: Recently, multiple graph regularizer based methods have shown promising performances in data representation However, the parameter choice of the regularizer is crucial to the performance of clustering and its optimal value changes for different real datasets To deal with this problem, we propose a novel method called Parameter-less Auto-weighted Multiple Graph regularized Nonnegative Matrix Factorization (PAMGNMF) in this paper PAMGNMF employs the linear combination of multiple simple graphs to approximate the manifold structure of data as previous methods do Moreover, the proposed method can automatically learn an optimal weight for each graph without introducing an additive parameter Therefore, the proposed PAMGNMF method is easily applied to practical problems Extensive experimental results on different real-world datasets have demonstrated that the proposed method achieves better performance than the state-of-the-art approaches