Title: Approximation of upper percentile points for the second largest latent root in principal component analysis

Authors: Takakazu Sugiyama; Toru Ogura; Yuichi Takeda; Hiroki Hashiguchi

Addresses: Soka University, 1-236, Tangi-Cho, Hachioji-Shi, Tokyo 192-8577, Japan ' Chuo University, 1-13-27, Kasuga, Bunkyo-Ku, Tokyo 112-8551, Japan ' Kanagawa Institute of Technology, 1030, Shimo-ogino, Atsugi, Kanagawa 243-0292, Japan ' Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Abstract: The approximate distribution of the largest latent root was proposed by Sugiyama (1972b). We extend his idea and propose an approximate distribution of the upper percentile points for the second largest latent root of the Wishart matrix. The proposed approximate distribution is adjusted by the expectation of each latent root. The simulation results show the validity of our adjustment for the expectation of each latent root, and the proposed approximate distribution is effective also in various cases, even when the dimension and sample size are both large.

Keywords: approximate distribution; principal component analysis; PCA; second largest latent root; upper percentile point; Wishart matrix.

DOI: 10.1504/IJKESDP.2013.058126

International Journal of Knowledge Engineering and Soft Data Paradigms, 2013 Vol.4 No.2, pp.107 - 117

Available online: 08 Dec 2013 *

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