Profile Analysis in Clustering with Hotelling’s T-Square Statistics

Abstract

Cluster analysis is a multivariate technique that groups objects based on their characteristics. For instance, it groups the most closely similar objects in the same cluster, thereby forming high internal homogeneity and external heterogeneity. Validation of the grouping results, carried out through profile analysis, is important to obtain the best partition that fits the basic data. Therefore, this study determined the profile analysis in clustering using Hotelling’s T square statistics on profile analysis and its application to rainfall data. Equivalent profile analysis with mixed ANOVA was used to test for hypothesis on the mean value of multiple variables (multivariate) using graph principles. In profile analysis, data plots were carried out to compare between groups of 3 patterns visually, namely, profile alignment, coincide, and alignment with the flat axis. These patterns were further validated using Hotelling's T-squared statistical test, which is a multivariate extension of the common one-sample or paired student t-test and used when the number of response variables is one or more. The result showed that the data is close to normal multivariate.