关键词: 函数型数据分析, 自适应权重；迭代更新；聚类分析

Abstract: Traditional clustering methods fail to analyze functional data with sparse property and infinite dimensional structure. To solve the problem, this paper presents an algorithm of adaptive iterative updating clustering analysis after defining the concept and connotation of functional data. First, construct a finite-dimensional functional multivariate space from infinite-dimensional one by using the parameter information of original data; On this basis, build an adaptive weighted clustering statistics as the criteria for giving initial clusters according to the difference of the information content implied in variables; Further, under the given threshold limit, gather the convergence optimal result to define the final categories by updating the ascription of initial clusters with adaptive iterative process. Stochastic simulation and empirical test shows the correct classification rate of our method is significantly higher than other clustering methods, reflecting the superiority and the effectiveness of our method in practical application.

Key words: functional data analysis, adaptive weighting, iterative update, clustering analysis