(25) Hamparsum Bozdogan and Stanley L. Sclove. Multi-sample cluster analysis using Akaike's information criterion. Annals of the Institute of Statistical Mathematics 36 (1984), 163-180.
Multi-sample cluster analysis, the problem of grouping samples, is studied from an information-theoretic viewpoint via Akaike's Information Criterion (AIC). This criterion combines the maximum value of the likelihood with the number of parameters used in achieving that value. The multi-sample cluster problem is defined, and AIC is developed for this problem. The form of AIC is derived in both the multivariate analysis of variance (MANOVA) model and in the multivariate model with varying mean vectors and variance-covariance matrices. Numerical examples are presented for AIC and another criterion called w-square. The results demonstrate the utility of AIC in identifying the best clustering alternatives.