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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2020, Vol. 35 Issue (2): 127-140    DOI:
    
Study on functional clustering analysis methods
SUN Li-rong, ZHUO Wei-jie, WANG Kai-li, MA Jia-hui
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018
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Abstract  For functional clustering, similarity measure is one of the major approaches. However,
most researches measure the similarity of functional data from a single perspective, using either a
numerical distance approach or a curve shape approach. This paper proposes a new similarity measure
based on extreme point bias compensation. This new measure gives consideration to the numerical
distance and curve shape simultaneously. And the empirical results show the validity of the new
measure. Further, a multifunction clustering analysis method, the function entropy weight method, is
developed, which enriches the functional clustering analysis methods.

Key words： functional clustering      bias compensation      extreme point      similarity measure      functional entropy weight method     
Published: 07 July 2020
CLC:     
  O212.1  
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SUN Li-rong
ZHUO Wei-jie
WANG Kai-li
MA Jia-hui
Cite this article:

SUN Li-rong, ZHUO Wei-jie, WANG Kai-li, MA Jia-hui. Study on functional clustering analysis methods. Applied Mathematics A Journal of Chinese Universities, 2020, 35(2): 127-140.

URL:

http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2020/V35/I2/127


函数型聚类分析方法研究

基于距离度量的函数型数据聚类是目前函数型聚类分析方法的主要研究方向
之一, 而该方法主要是基于数值距离或曲线形态的单一角度来衡量函数型数据的相似
性. 为了解决这种单一性, 提出一种同时兼顾函数型数据的数值距离和曲线形态的相
似性度量方法—基于极值点偏差补偿的相似性度量, 并给出实证分析, 结果显示该方
法比较有效. 进一步提出一种多元函数型聚类分析方法—函数型熵权法, 丰富了函数
型聚类分析方法.

关键词： 函数型聚类分析,  B样条基,  欧式距离,  极值点,  函数型熵值法 
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