Research on the clustering algorithms in functional data analysis

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The functional data analysis is a technique proposed by Ramsay (1982)as an analytical method when the essence of the object data is not a discrete data but a function. Basic concepts of this analysis are in the expression of the data observed as a discrete data according to the function, and the effective extraction of information from this function set. These features are not in the data analysis of the past. It is a natural idea that adopts the multivariate analysis method for existing discrete data for the function data as an analytical technique when data is a function, Ramsay and Silverman (1997)enhances the regression analysis, the principal component analysis, the canonical correlation analysis, and the linear model, etc. for the functional data, Tokushige, Inada and Yadohisa (2003)gave the non-similarity between the functional data as a real number, and it is one flow of the research. We have been researching enhancing the crisp k-means method and the fuzzy k-means method that is the technique of non-hierarchical cluster analysis for the function data. the k-means method can be very useful one of the techniques used most in the cluster analysis, and to enhance this, and expect use in various fields. This study results announced with "S. Tokushige, and H. Yadohisa and K. Inada, Crisp and fuzzy k-means clustering algorithms for multivariate functional data,Computational Statistics, 22, 1, (2007),1-16."