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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (3): 101-108.doi: 10.6040/j.issn.1671-9352.0.2022.059

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基于双高斯先验的低秩矩阵分解模型

韦芳,王长鹏*   

  1. 长安大学理学院, 陕西 西安 710064
  • 发布日期:2023-03-02
  • 作者简介:韦芳(1999— ),女,硕士研究生,研究方向为机器学习. E-mail:2766825663@qq.com*通信作者简介:王长鹏(1985— ),男,博士,副教授,研究方向为机器学习. E-mail:cpwang@chd.edu.cn
  • 基金资助:
    国家自然科学基金青年项目(12001057);长安大学中央高校基本科研业务费专项资金资助项目(300102122101)

Low-rank matrix factorization with double Gaussian prior model

WEI Fang, WANG Chang-peng*   

  1. School of Science, Changan University, Xian 710064, Shaanxi, China
  • Published:2023-03-02

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摘要： 为了更好地拟合复杂噪声,增强低秩矩阵分解模型的鲁棒性,将双高斯先验引入到传统的高斯混合模型中,提出了基于双高斯先验的低秩矩阵分解(low-rank matrix factorization with double Gaussian prior, DGP-LRMF)模型,通过模型分解得到的2个矩阵均服从高斯先验,从而实现对噪声的有效建模,并在贝叶斯理论框架下利用EM算法实现模型参数的推断。实验结果验证了所提模型能够有效地处理含有复杂噪声的数据,取得了更优且更具稳定性的去噪效果。

关键词: 高斯混合模型, 低秩矩阵分解, 高斯先验

Abstract: In order to fit the complex noise better and enhance the robustness of the low-rank matrix factorization model, the dual Gaussian priors are introduced into the traditional Gaussian mixture model, and the model of low-rank matrix factorization with double Gaussian prior(DGP-LRMF)is proposed, it is assumed that two matrices obtained by model decomposition obey Gaussian priori to realize the effective modeling for noise, and the EM algorithm is used to deduce the model parameters in the framework of Bayesian theory. Experimental results show that the proposed model can effectively deal with the data with complex noise and obtain better and more stable denoising performance.

Key words: Gaussian mixture model, low-rank matrix decomposition, Gaussian prior

中图分类号: 

  • TP391
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