D-optimality criterion for weighting variables in K-means clustering

다국어 초록 (Multilingual Abstract)

The aim of the study is how to achieve best K-means clustering structure so that k
groups uncovered reveal more meaningful within-group coherence by assigning weights
w1, ··· ,wm to m clustering variables Z1,···, Zm. We propose Wilks' lambda as a criterion
to be minimized with respect to variable weights w1,···,wm. This criterion, that is the
ratio of the determinant of the within-cluster sums of squares and cross products matrix
and that of the between clusters sums of squares and cross products matrix, is equivalent
to the D-optimality criterion in the optimal design theory and related to minimization of
the volume of the simultaneous confidence region of the cluster means. We will present
the computing algorithm for such K-means clustering and numerical examples, among
which one is simulated, two are real and the other one is the real data set augmented with
additional simulated noise variables.

참고문헌 (Reference)

1 Huh, M, "Weighting variables in K-means clustering" 36 : 67-78, 2009

2 Desarbo, W. S, "Synthesized clustering: A method foramalgamating clustering bases with differential weighting variables" 49 : 57-78, 1984

3 Steinley, D, "Selection of variables in cluster analysis: An empirical comparison of eight procedures" 73 : 125-144, 2008

4 Myers, R. H, "Response Surface Methodology" John Wiley & Sons 2002

5 Makarenkov, V, "Optimal variable weighting for ultrametric and additive trees and K-means partitioning: Methods and software" 18 : 245-271, 2001

6 Steinley, D, "K-means clustering: A half-century synthesis" 59 : 1-34, 2006

7 Modha, D. S, "Feature weighting in K-means clustering" 52 : 217-237, 2003

8 Huang, J,Z, "Automated variable weighting in K-means type clustering" 27 : 657-667, 2005

9 Steinley, D, "A new variable weighting and selection procedure for K-means cluster analysis" 43 : 77-108, 2008

10 Byrd, R. H, "A limited memory algorithm for bound constrained optimization" 16 : 1190-1208, 2005