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 language | English |
|---|---|
| Pages (from-to) | 133-148 |
| Number of pages | 16 |
| Journal | Computational Statistics and Data Analysis |
| Volume | 79 |
| DOIs | |
| Publication status | Published - 2014 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Functional factorial K-means analysis
AU - Yamamoto, Michio
AU - Terada, Yoshikazu
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - Cluster analysis
KW - Dimension reduction
KW - Functional data
KW - K-means algorithm
KW - Tandem analysis
UR - http://www.scopus.com/inward/record.url?scp=84902256638&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84902256638&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2014.05.010
DO - 10.1016/j.csda.2014.05.010
M3 - Article
AN - SCOPUS:84902256638
VL - 79
SP - 133
EP - 148
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
ER -