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Two-dimensional Quaternion PCA and Sparse PCA
Xiaolin Xiao; Yicong Zhou
Source PublicationIEEE Transactions on Neural Networks and Learning Systems
Pages1 - 15

Benefited from quaternion representation that is able to encode the cross-channel correlation of color images, quaternion principle component analysis (QPCA) was proposed to extract features from color images while reducing the feature dimension. A quaternion covariance matrix (QCM) of input samples was constructed, and its eigenvectors were derived to find the solution of QPCA. However, eigen-decomposition leads to the fixed solution for the same input. This solution is susceptible to outliers and cannot be further optimized. To solve this problem, this paper proposes a novel quaternion ridge regression (QRR) model for two-dimensional QPCA (2D-QPCA). We mathematically prove that this QRR model is equivalent to the QCM model of 2D-QPCA. The QRR model is a general framework and is flexible to combine 2D-QPCA with other technologies or constraints to adapt different requirements of real-world applications. Including sparsity constraints, we then propose a quaternion sparse regression model for 2D-QSPCA to improve its robustness for classification. An alternating minimization algorithm is developed to iteratively learn the solution of 2D-QSPCA in the equivalent complex domain. In addition, 2D-QPCA and 2D-QSPCA can preserve the spatial structure of color images and have a low computation cost. Experiments on several challenging databases demonstrate that 2D-QPCA and 2D-QSPCA are effective in color face recognition, and 2D-QSPCA outperforms the state of the arts.

Keyword2d-principle Component Analysis (2d-pca) 2d-quaternion Pca (2d-qPca) 2d-quaternion Sparse Pca (2d-qsPca) Color Face Recognition Feature Extraction Partial Occlusions Qpca
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Cited Times [WOS]:15   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Corresponding AuthorYicong Zhou
Affiliationthe Department of Computer and Information Science, University of Macau, Macau 999078, China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Xiaolin Xiao,Yicong Zhou. Two-dimensional Quaternion PCA and Sparse PCA[J]. IEEE Transactions on Neural Networks and Learning Systems,2018:1 - 15.
APA Xiaolin Xiao,&Yicong Zhou.(2018).Two-dimensional Quaternion PCA and Sparse PCA.IEEE Transactions on Neural Networks and Learning Systems,1 - 15.
MLA Xiaolin Xiao,et al."Two-dimensional Quaternion PCA and Sparse PCA".IEEE Transactions on Neural Networks and Learning Systems (2018):1 - 15.
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