New exploratory clustering tool

Abstract

This paper describes a clustering method on three-way arrays making use of an exploratory visualization approach. The aim of this study is to cluster samples in the object mode of a three-way array, which is done using the scores (sample loadings) of a three-way factor model, for example, a Tucker3 or a PARAFAC model. Further, tools are developed to explore and identify reasons for particular clusters by visually mining the data using the clustering results as guidance. We introduce a three-way clustering tool and demonstrate our results on a metabolite profiling dataset. We explore how high performance liquid chromatography (HPLC) measurements of commercial extracts of St. John's wort (natural remedies for the treatment of mild to moderate depression) differ and which chemical compounds account for those differences. Using common distance measures, for example, Euclidean or Mahalanobis, on the scores of a three-way model, we verify that we can capture the underlying clustering structure in the data. Beside this, by making use of the visualization approach, we are able to identify the variables playing a significant role in the extracted cluster structure. The suggested approach generalizes straightforwardly to higher-order data and also to two-way data. Copyright © 2007 John Wiley & Sons, Ltd.