A mixture model for the classification of three-way proximity data

Large data sets organized into a three-way proximity array are generally difficult to comprehend and specific techniques are necessary to extract relevant information.The existing classification methodologies for dissimilarities between objects collected in different occasions assume a unique common underlying classification structure. However, since the objects’ clustering structure often changes along the occasions, the use of a single classification to reconstruct the taxonomic information frequently appears quite unrealistic.The methodology proposed here models the dissimilarities in a likelihood framework. The goal is to identify a (secondary) partition of the occasions in homogeneous classes and, simultaneously, a (primary) consensus partition of the objects within each of such classes. Furthermore, a class-specific dimensionality reduction operator is also included which allows to identify classes of occasions such that the within-class variability is minimized.The model is formalized as a finite mixture of multivariate normal distributions and solved by a numerical method based on ECM strategy.