Premium
Strong Consistency of Reduced K ‐means Clustering
Author(s) -
Terada Yoshikazu
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12074
Subject(s) - cluster analysis , mathematics , k medians clustering , correlation clustering , single linkage clustering , cure data clustering algorithm , consistency (knowledge bases) , clustering high dimensional data , fuzzy clustering , estimator , pattern recognition (psychology) , data mining , statistics , artificial intelligence , computer science , discrete mathematics
Reduced k ‐means clustering is a method for clustering objects in a low‐dimensional subspace. The advantage of this method is that both clustering of objects and low‐dimensional subspace reflecting the cluster structure are simultaneously obtained. In this paper, the relationship between conventional k ‐means clustering and reduced k ‐means clustering is discussed. Conditions ensuring almost sure convergence of the estimator of reduced k ‐means clustering as unboundedly increasing sample size have been presented. The results for a more general model considering conventional k ‐means clustering and reduced k ‐means clustering are provided in this paper. Moreover, a consistent selection of the numbers of clusters and dimensions is described.