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Volume 2018, Article ID 2743678, 12 pages
Research Article

Graph Sparse Nonnegative Matrix Factorization Algorithm Based on the Inertial Projection Neural Network

1College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China
2College of Mobile Telecommunications, Chongqing University of Posts and Telecommunications, Chongqing 401520, China

Correspondence should be addressed to Chuandong Li; nc.ude.uws@ildc

Received 3 May 2017; Accepted 13 December 2017; Published 19 March 2018

Academic Editor: Pietro De Lellis

Copyright © 2018 Xiangguang Dai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural network, the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real-world data illustrate the effectiveness and performance of the proposed method.