Sensitivity Analysis for Multiple Similarity Method and Its Application
Kuniyoshi Hayashi, Yutaka Tanaka
Graduate School of Information Sciences and Technology, Hokkaido University, Sapporo, Hokkaido, Japan; Institute of Statistical Mathematics, Tachikawa, Tokyo, Japan

Multiple similarity method which was proposed by Iijima et al. (1973) in pattern recognition is one of discriminant methods and it can save calculation time and memory size in multi-class classification. Multiple similarity method (MSM) is so similar to CLAFIC (CLAss Featuring Information Compression) which is also discriminant method and a member of linear subspace method, but it was proposed from a different background. In statistics, a method of diagnostics based on influence functions has been developed for a lot of statistical methods. For example, influence functions for classical discriminant analysis were already derived and evaluating the influence of training observations for the classifier has also been performed (Campbell, 1978; Huang et al., 2007).

Hayashi et al. (2010) defined a discriminant score for CLAFIC and derived the influence func-tions. Using these derived influence functions, we also developed sensitivity analysis for CLAFIC focusing on multiple-case diagnostics and applied our method to a classification with a simulation dataset. With this method, we could detect influential observations for the classifier.

In this paper, we define a discriminate score for MSM and derive the empirical influence func-tion and the sample influence function. In addition, we propose sensitivity analysis for it and apply this analysis for MSM to a classification. We show the effectiveness by detecting influential observations for the classifier.


Campbell, N. A. (1978). The influence function as an aid in outlier detection in discriminant analysis, Applied Statistics, 27, 3, 251-258.

Hayashi, K., Minami, H. and Mizuta, M. (2010). On Multiple-Case Diagnostics in Linear Subspace Method, Proceedings in Computational Statistics 2010, Springer-Verlag Berlin Heidelberg 2010, 493-500.

Huang, Y., Kao, T. L. and Wang, T. H. (2007). Influence functions and local influence in linear discriminant analysis. Computational Statistics and Data Analysis 51, 3844-3861.

Iijima, T., Genchi, H. and Mori, K. (1973). A theory of character recognition by pattern matching method, Proceedings of the 1st International Joint Conference on Pattern Recognition, 50-56.

Keywords: Discriminant analysis; Perturbation; Influence function

Biography: Kuniyoshi Hayashi is a postgraduate student of Graduate School of Information Sciences and Technology, Hokkaido University. He is a research fellow of the Japan Society for the Promotion of Science (#22-9127).