Functional factorial K-means analysis

Michio Yamamoto, Yoshikazu Terada

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

A new procedure for simultaneously finding the optimal cluster structure of multivariate functional objects and finding the subspace to represent the cluster structure is presented. The method is based on the k-means criterion for projected functional objects on a subspace in which a cluster structure exists. An efficient alternating least-squares algorithm is described, and the proposed method is extended to a regularized method for smoothness of weight functions. To deal with the negative effect of the correlation of the coefficient matrix of the basis function expansion in the proposed algorithm, a two-step approach to the proposed method is also described. Analyses of artificial and real data demonstrate that the proposed method gives correct and interpretable results compared with existing methods, the functional principal component k-means (FPCK) method and tandem clustering approach. It is also shown that the proposed method can be considered complementary to FPCK.

Original languageEnglish
Pages (from-to)133-148
Number of pages16
JournalComputational Statistics and Data Analysis
Volume79
DOIs
Publication statusPublished - 2014
Externally publishedYes

Fingerprint

K-means
Factorial
Principal Components
Subspace
Alternating Least Squares
Least Square Algorithm
Weight Function
Basis Functions
Smoothness
Clustering
Coefficient
Demonstrate

Keywords

  • Cluster analysis
  • Dimension reduction
  • Functional data
  • K-means algorithm
  • Tandem analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

Functional factorial K-means analysis. / Yamamoto, Michio; Terada, Yoshikazu.

In: Computational Statistics and Data Analysis, Vol. 79, 2014, p. 133-148.

Research output: Contribution to journalArticle

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