Multi-Sample Cluster Analysis as an Alternative to Multiple Comparison Procedures

摘要

This paper studies multi-sample cluster analysis, the problem of grouping samples, as an alternative to multiple comparison procedures through the development and the introduction of model-selection criteria such as those: Akaike's Information criterion (AIC) and Schwarz's Criterion (SC), as new procedures for comparing means, groups, or samples, and so forth, in identifying and selecting the homogeneous groups or samples from the heterogeneous ones in multi-sample data analysis problems. An enumerative clustering technique is presented to generate all possible choices of clustering alternatives of groups, or samples on the computer using efficient combinatorial algorithms without forcing an arbitrary choice among the clustering alternatives, and to find all sufficiently simple groups or samples consistent with the data and identify the best clustering among the alternative clusterings. Numerical examples are carried out and presented on a real data set on grouping the samples into fewer than K groups. Through a Monte Carlo study, an application of multi-sample cluster analysis is shown in designing optimal decision tree classifiers in reducing the dimensionality of remotely sensed heterogenous data sets to achieve a parsimonious grouping of samples. The results obtained demonstrate the utility and versatility of model-selection criteria which avoid the notorious choice of levels of significance and which are free from the ambiguities inherent in the application of conventional hypothesis testing procedures.