title: Subspace K-means clustering.
abstract: To achieve an insightful clustering of multivariate data, we propose subspace K-means. Its central idea is to model the centroids and cluster residuals in reduced spaces, which allows for dealing with a wide range of cluster types and yields rich interpretations of the clusters. We review the existing related clustering methods, including deterministic, stochastic, and unsupervised learning approaches. To evaluate subspace K-means, we performed a comparative simulation study, in which we manipulated the overlap of subspaces, the between-cluster variance, and the error variance. The study shows that the subspace K-means algorithm is sensitive to local minima but that the problem can be reasonably dealt with by using partitions of various cluster procedures as a starting point for the algorithm. Subspace K-means performs very well in recovering the true clustering across all conditions considered and appears to be superior to its competitor methods: K-means, reduced K-means, factorial K-means, mixtures of factor analyzers (MFA), and MCLUST. The best competitor method, MFA, showed a performance similar to that of subspace K-means in easy conditions but deteriorated in more difficult ones. Using data from a study on parental behavior, we show that subspace K-means analysis provides a rich insight into the cluster characteristics, in terms of both the relative positions of the clusters (via the centroids) and the shape of the clusters (via the within-cluster residuals).
authors.affiliation: Heymans Institute for Psychology, Psychometrics & Statistics, University of Groningen, Grote Kruisstraat 2/1, 9712TS, Groningen, The Netherlands, m.e.timmerman@rug.nl.
authors.forename: Marieke E
authors.initials: ME
authors.lastname: Timmerman
authors.forename: Eva
authors.initials: E
authors.lastname: Ceulemans
authors.forename: Kim
authors.initials: K
authors.lastname: De Roover
authors.forename: Karla
authors.initials: K
authors.lastname: Van Leeuwen
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D005163:Factor Analysis, Statistical; D008960:Models, Psychological; D015233:Models, Statistical; D015999:Multivariate Analysis