A novel incremental principal component analysis and its application for face recognition

Principal component analysis (PCA) has been proven to be an efficient method in pattern recognition and image analysis. Recently, PCA has been extensively employed for face-recognition algorithms, such as eigenface and fisherface. The encouraging results have been reported and discussed in the literature. Many PCA-based face-recognition systems have also been developed in the last decade. However, existing PCA-based face-recognition systems are hard to scale up because of the computational cost and memory-requirement burden. To overcome this limitation, an incremental approach is usually adopted. Incremental PCA (IPCA) methods have been studied for many years in the machine-learning community. The major limitation of existing IPCA methods is that there is no guarantee on the approximation error. In view of this limitation, this paper proposes a new IPCA method based on the idea of a singular value decomposition (SVD) updating algorithm, namely an SVD updating-based IPCA (SVDU-IPCA) algorithm. In the proposed SVDU-IPCA algorithm, we have mathematically proved that the approximation error is bounded. A complexity analysis on the proposed method is also presented. Another characteristic of the proposed SVDU-IPCA algorithm is that it can be easily extended to a kernel version. The proposed method has been evaluated using available public databases, namely FERET, AR, and Yale B, and applied to existing face-recognition algorithms. Experimental results show that the difference of the average recognition accuracy between the proposed incremental method and the batch-mode method is less than 1%. This implies that the proposed SVDU-IPCA method gives a close approximation to the batch-mode PCA method.