Principal Component Analysis Based on L1-Norm Maximization

In data-analysis problems with a large number of dimension, principal component analysis based on L2-norm (L2PCA) is one of the most popular methods, but L2-PCA is sensitive to outliers. Unlike L2-PCA, PCA-L1 is robust to outliers because it utilizes the L1-norm, which is less sensitive to outliers. Furthermore, the bases obtained by PCA-L1 is invariant to rotations. However, PCA-L1 needs long time to calculate bases, because PCA-L1 employs an iterative algorithm to obtain each basis, and requires to calculate an eigenvector of autocorrelation matrix as an initial vector. The autocorrelation matrix needs to be recalculated for each basis. In this paper, we propose a fast method to compute the autocorrelation matrices. In order to verify the proposed method, we apply L2-PCA, PCA-L1, and the proposed method to face recognition. Simulation results show that the proposed method provides same recognition performance as PCA-L1, and is superior to L2-PCA, while the execution time

• Type: Journal
• Year: 2008
• Where: PAMI
• Authors: Nojun Kwak
• Keywords: Autocorrelation Matrix, Outliers, PAMI 2008, Principal Component Analysis