Open AccessConstrained k ‐means on cluster proportion and distances among clusters for longitudinal data analysis
Author(s) -
Usami Satoshi
Publication year - 2014
Publication title -
japanese psychological research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.392
H-Index - 30
eISSN - 1468-5884
pISSN - 0021-5368
DOI - 10.1111/jpr.12060
Subject(s) - cluster analysis , convergence (economics) , cluster (spacecraft) , normality , similarity (geometry) , computer science , longitudinal data , data mining , mathematics , statistics , artificial intelligence , economics , image (mathematics) , programming language , economic growth
Abstract Clustering individuals by measures of similarity or dissimilarity at trajectories of changes in longitudinal data enables determination of typical patterns of development and growth. The present research proposes a new constrained k ‐means method with lower bound constraints on cluster proportions and distances among clusters at focused variables and time points to fulfill various needs in clustering longitudinal data. The method assumes a large number of clusters at the onset and iteratively deletes and combines clusters according to these constraints. An additional property of the proposed constrained k ‐means includes direct estimation of the unknown number of clusters. Simulation results clearly show the usefulness of the method for extracting clusters in plausible, real‐life analysis including non‐normality within clusters, and the proposed algorithm works well and convergence of the estimates is satisfactory. An actual example using J apanese longitudinal data regarding sleep habits and mental health is presented to verify the utility of the proposed constrained k ‐means.