Research on the clustering algorithms in functional data analysis

功能数据分析是Ramsay(1982)提出的一种分析方法，当对象数据的本质不是离散数据而是函数时，函数数据分析是一种分析方法。这种分析的基本概念是根据函数将观察到的数据表示为离散数据，并从该函数集中有效地提取信息。这些特征没有出现在过去的数据分析中。将已有离散数据的多元分析方法作为函数数据的分析方法是自然而然的想法，Ramsay和Silverman(1997)加强了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)给出了函数数据之间的不相似性作为实数，这是研究的一个流派。我们一直在研究改进的精确k-均值方法和模糊k-均值方法，即函数数据的非层次聚类分析技术。K-均值方法是在聚类分析中使用最多的技术之一，可以非常有用，以加强这一点，并有望在各种领域中使用。这项研究结果与“S.Tokushige，以及H.Yadohisa和K.Inada，Crisp and Fuzzyk-Means算法用于多变量函数数据，计算统计，22，1，(2007)，1-16”一起公布。

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."