Generalized centered 2-D principal component analysis

Gongyu Zhou, Guangquan Xu, Jianye Hao, Shizhan Chen, Junfeng Xu, Xi Zheng

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Most existing robust principal component analysis (PCA) and 2-D PCA (2DPCA) methods involving the l₂-norm can mitigate the sensitivity to outliers in the domains of image analysis and pattern recognition. However, existing approaches neither preserve the structural information of data in the optimization objective nor have the robustness of generalized performance. To address the above problems, we propose two novel center-weight-based models, namely, centered PCA (C-PCA) and generalized centered 2DPCA with l2,p-norm minimization (GC-2DPCA), which are developed for vector- and matrix-based data, respectively. The C-PCA can preserve the structural information of data by measuring the similarity between the data points and can also retain the PCA's original desirable properties such as the rotational invariance. Furthermore, GC-2DPCA can learn efficient and robust projection matrices to suppress outliers by utilizing the variations between each row of the image matrix and employing power p of l2,1-norm. We also propose an efficient algorithm to solve the C-PCA model and an iterative optimization algorithm to solve the GC-2DPCA model, and we theoretically analyze their convergence properties. Experiments on three public databases show that our models yield significant improvements over the state-of-the-art PCA and 2DPCA approaches.
Original languageEnglish
Pages (from-to)1666-1677
Number of pages12
JournalIEEE Transactions on Cybernetics
Volume51
Issue number3
Early online date19 Aug 2019
DOIs
Publication statusPublished - Mar 2021

Keywords

  • 2-D principal component analysis (2DPCA)
  • center
  • dimensionality reduction
  • l -norm

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