Exponential Graph Regularized Non-Negative Low-Rank Factorization for Robust Latent Representation

Guowei Yang, Lin Zhang and Minghua Wan ()
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Guowei Yang: School of Computer Science (School of Intelligent Auditing), Nanjing Audit University, Nanjing 211815, China
Lin Zhang: School of Computer Science (School of Intelligent Auditing), Nanjing Audit University, Nanjing 211815, China
Minghua Wan: School of Computer Science (School of Intelligent Auditing), Nanjing Audit University, Nanjing 211815, China

Mathematics, 2022, vol. 10, issue 22, 1-20

Abstract: Non-negative matrix factorization (NMF) is a fundamental theory that has received much attention and is widely used in image engineering, pattern recognition and other fields. However, the classical NMF has limitations such as only focusing on local information, sensitivity to noise and small sample size (SSS) problems. Therefore, how to develop the NMF to improve the performance and robustness of the algorithm is a worthy challenge. Based on the bottlenecks above, we propose an exponential graph regularization non-negative low-rank factorization algorithm (EGNLRF) combining sparseness, low rank and matrix exponential. Firstly, based on the assumption that the data is corroded, we decompose a given raw data item with a data error fitting noise matrix, applying a low-rank constraint to the denoising data. Then, we perform a non-negative factorization on the resulting low-rank matrix, from which we derive the low-dimensional representation of the original matrix. Finally, we use the low-dimensional representation for graph embedding to maintain the geometry between samples. The graph embedding terms are matrix exponentiated to cope with SSS problems and nearest neighbor sensitivity. The above three steps will be incorporated into a joint framework to validate and optimize each other; therefore, we can learn latent data representations that are undisturbed by noise and preserve the local structure of known samples. We conducted simulation experiments on different datasets and verified the effectiveness of the algorithm by comparing the proposed with the lasting ones related to NMF, low rank and graph embedding.

Keywords: non-negative matrix factorization; low rank; matrix exponential; graph embedding; image representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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