Research on the clustering algorithms in functional data analysis

函数型数据分析是Ramsay（1982）提出的一种分析方法，其对象数据的本质不是离散数据而是函数。这种分析的基本概念是将观测到的数据按照函数表示为离散数据，并从这个函数集合中有效地提取信息。这些特征在以往的数据分析中是没有的。当数据是函数时，对函数数据采用针对现有离散数据的多变量分析方法作为分析技术是自然的想法，Ramsay和Silverman（1997）增强了针对函数数据的回归分析、主成分分析、典型相关分析和线性模型等，Tokushige，Inada和Yadohisa（2003）将函数数据之间的非相似性定义为一个真实的数，这是本文的研究流程之一。我们一直在研究增强清晰的k-means方法和模糊k-means方法，这是一种功能数据的非层次聚类分析技术。k-means方法可以是聚类分析中最常用的技术之一，并且为了增强这一点，期望在各个领域中使用。本研究结果以“S。Tokushige和H. Yadohisa和K. Inada，Crisp和fuzzy k-means聚类算法在多元函数数据中的应用，Computational Statistics，22，1，（2007），1 -16. "

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."