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Front. Genet. | doi: 10.3389/fgene.2019.01054

Huber Loss Model Based on Sparse Graph Regularization Non-negative Matrix Factorization

 ChuanYuan Wang1, Na Yu1, Jin-Xing Liu1* and Chun-Hou Zheng1
  • 1Qufu Normal University, China

Non-negative matrix factorization (NMF) is a matrix decomposition method based on the square loss function. To exploit cancer information, cancer gene expression data often uses the NMF method to reduce dimensionality. Gene expression data usually has some noise and outliers, while the original NMF loss function is very sensitive to non-Gaussian noise. To improve the robustness and clustering performance of the algorithm, we propose a Huber Loss Model Based on Sparse Graph Regularization Non-negative Matrix Factorization (Huber-SGNMF). Huber loss is a function between L1-norm and L2-norm that can effectively handle non-Gaussian noise and outliers. Taking into account the sparsity matrix and data geometry information, sparse penalty and graph regularization terms are introduced into the model to enhance matrix sparsity and capture data manifold structure. Before the experiment, we first analyzed the robustness of Huber-SGNMF and other models. Experiments on The Cancer Genome Atlas (TCGA) data have shown that Huber-SGNMF performs better than other most advanced methods in sample clustering and differentially expressed gene selection.

Keywords: nonnegative matrix factorization, Huber loss, graph regularization, Sample clustering, robustness

Received: 20 Jul 2019; Accepted: 01 Oct 2019.

Copyright: © 2019 Wang, Yu, Liu and Zheng. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Jin-Xing Liu, Qufu Normal University, Qufu, China, sdcavell@126.com