Modified Recursive PC Kim, Dong-Gyu; Kim, Ah-Hyoun; Kim, Hyun-Joong;
PCA(Principal Component Analysis) is a well-studied statistical technique and an important tool for handling multivariate data. Although many algorithms exist for PCA, most of them are unsuitable for real time applications or high dimensional problems. Since it is desirable to avoid extensive matrix operations in such cases, alternative solutions are required to calculate the eigenvalues and eigenvectors of the sample covariance matrix. Erdogmus et al. (2004) proposed Recursive PCA(RPCA), which is a fast adaptive on-line solution for PCA, based on the first order perturbation theory. It facilitates the real-time implementation of PCA by recursively approximating updated eigenvalues and eigenvectors. However, the performance of the RPCA method becomes questionable as the size of newly-added data increases. In this paper, we modified the RPCA method by taking advantage of the mathematical relation of eigenvalues and eigenvectors of sample covariance matrix. We compared the performance of the proposed algorithm with that of RPCA, and found that the accuracy of the proposed method remarkably improved.
Recursive PCA;Principal Component Analysis;first order perturbation theory;
Duda, R. O. and Hart, P. E. (1973). Pattern Classification and Scene Analysis, Wiley, New York.
Erdogmus, D., Rao, Y. N., Peddaneni, H., Hegde, A. and Principe, J. C. (2004). Recursive principal components analysis using eigenvector matrix perturbation, EURASIP Journal on Applied Signal Processing, 2004, 2034-2041.
Golub, G. and Loan, C. V. (1993). Matrix Computation, Johns Hopkins University Press, Baltimore, MD.
Kung, S. Y., Diamantaras, K. I. and Taur, J. S. (1994). Adaptive principal component extraction(APEX) and applications, IEEE Transaction Signal Processing, 42, 296-317.