JIANG Wei, MA Tingting, FENG Xiaoting, ZHAI Yun, TANG Kewei, ZHANG Jie. Robust Semi-nonnegative Matrix Factorization with Adaptive Graph Regularization for Gene Representation[J]. Chinese Journal of Electronics, 2020, 29(1): 122-131. doi: 10.1049/cje.2019.11.001
 Citation: JIANG Wei, MA Tingting, FENG Xiaoting, ZHAI Yun, TANG Kewei, ZHANG Jie. Robust Semi-nonnegative Matrix Factorization with Adaptive Graph Regularization for Gene Representation[J]. Chinese Journal of Electronics, 2020, 29(1): 122-131.

# Robust Semi-nonnegative Matrix Factorization with Adaptive Graph Regularization for Gene Representation

##### doi: 10.1049/cje.2019.11.001
Funds:  This work is supported by the National Natural Science Foundation of China (No.61771229, No.61672178, No.61702243, No.61702245).
• Corresponding author: ZHANG Jie (corresponding author) received the Ph.D. degree in 2015 from the Dalian University of Technology, China. She is currently a lecturer with the School of Mathematics, Liaoning Normal University, China. Her current research interests include geometric processing and machine learning. (Email:jzhang@lnnu.edu.cn)
• Rev Recd Date: 2019-08-03
• Publish Date: 2020-01-10
• Various data representation algorithms have been proposed for gene expression. There are some shortcomings in traditional gene expression methods, such as learning the ideal affinity matrix to effectively capture the geometric structure of genetic data space, and reducing noises and outliers influences of data input. We propose a novel matrix factorization algorithm called Robust semi-nonnegative matrix factorization (RSNMF) with adaptive graph regularization, which simultaneously performs matrix robust factorization with learning affinity matrix in a unified optimization framework. RSNMF also uses a loss function based on l2,1-norm to improve the robustness of the model against noises and outliers. A novel Augmented Lagrange multiplier (ALM) is designed to obtain the optimal solution of RSNMF. The results of extensive experiments that were performed on gene expression datasets demonstrate that RSNMF outperforms the other algorithms, which validates the effectiveness and robustness of RSNMF.
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