Two-Dimensional Euler PCA for Face Recognition

Principal component analysis (PCA) projects data on the directions with maximal variances. Since PCA is quite effective in dimension reduction, it has been widely used in computer vision. However, conventional PCA suffers from following deficiencies: 1) it spends much computational costs to handle high-dimensional data, and 2) it cannot reveal the nonlinear relationship among different features of data. To overcome these deficiencies, this paper proposes an efficient two-dimensional Euler PCA (2D-

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PCA) algorithm. Particularly, 2D-

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PCA learns projection matrix on the 2D pixel matrix of each image without reshaping it into 1D long vector, and uncovers nonlinear relationships among features by mapping data onto complex representation. Since such 2D complex representation induces much smaller kernel matrix and principal subspaces, 2D-

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PCA costs much less computational overheads than Euler PCA on large-scale dataset. Experimental results on popular face datasets show that 2D-

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PCA outperforms the representative algorithms in terms of accuracy, computational overhead, and robustness.