Crisp and fuzzy k-means clustering algorithms for multivariate functional data
Crisp and fuzzy k-means clustering algorithms for multivariate functional data
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DOI：
10.1007/s00180-006-0013-0
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发表时间：
2007-04
影响因子：
1.3
通讯作者：
Shuichi Tokushige;Hiroshi Yadohisa;Kōichi Inada
中科院分区：
文献类型：
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作者：
Shuichi Tokushige;Hiroshi Yadohisa;Kōichi Inada
Ramsay 提出的功能数据分析（Psychometrika 47:379–396, 1982）最近吸引了许多研究人员。最近的函数数据研究中最流行的方法是将普通数据分析的统计方法扩展到函数数据的分析（例如，Ramsay 和 Silverman 在函数数据分析 Springer，柏林海德堡纽约，1997 年，应用函数数据分析：方法和案例研究。Springer，柏林海德堡纽约，2002 年；Mizuta 在第十届日本和韩国统计联合会议论文集，第 10 页） 77–82, 2000；Shimokawa 等人，日本 J Appl Stat 29:27–39, 2000）。此外，还提出了几种对功能数据进行聚类的方法（Abraham 等人在 Scand J Stat 30:581–595, 2003 中；Gareth 和 Catherine 在 J Am Stat Assoc 98:397–408, 2003 中；Tarpey 和 kerateder 在 J Classif 20:93–114, 2003 中；Rossi 等人在 Proceedings 中）欧洲人工神经网络研讨会第 305-312 页，2004 年）。此外，Tokushige 等人。 （J Jpn Soc Comput Stat 15:319–326, 2002）针对函数数据的情况定义了函数之间的几个不同之处。在本文中，我们将现有的清晰和模糊k均值聚类算法扩展到多元函数数据的分析。特别是，我们将函数之间的差异视为函数。此外，定义为函数的聚类中心和隶属度是通过使用变分法在某个目标函数的最小值处确定的。
Functional data analysis, as proposed by Ramsay (Psychometrika 47:379–396, 1982), has recently attracted many researchers. The most popular approach taken in recent studies of functional data has been the extension of statistical methods for the analysis of usual data to that of functional data (e.g., Ramsay and Silverman in Functional data Analysis Springer, Berlin Heidelberg New York, 1997, Applied functional data analysis: methods and case studies. Springer, Berlin Heidelberg New York, 2002; Mizuta in Proceedings of the tenth Japan and Korea Joint Conference of Statistics, pp 77–82, 2000; Shimokawa et al. in Japan J Appl Stat 29:27–39, 2000). In addition, several methods for clustering functional data have been proposed (Abraham et al. in Scand J Stat 30:581–595, 2003; Gareth and Catherine in J Am Stat Assoc 98:397–408, 2003; Tarpey and kinateder in J Classif 20:93–114, 2003; Rossi et al. in Proceedings of European Symposium on Artificial Neural Networks pp 305–312, 2004). Furthermore, Tokushige et al. (J Jpn Soc Comput Stat 15:319–326, 2002) defined several dissimilarities between functions for the case of functional data. In this paper, we extend existing crisp and fuzzyk-means clustering algorithms to the analysis of multivariate functional data. In particular, we consider the dissimilarity between functions as a function. Furthermore, cluster centers and memberships, which are defined as functions, are determined at the minimum of a certain target function by using a calculus-of-variations approach.