Maximal Interaction Two-Mode Clustering

Abstract

Most classical approaches for two-mode clustering of a data matrix are designed to attain homogeneous row by column clusters (blocks, biclusters), that is, biclusters with a small variation of data values within the blocks. In contrast, this article deals with methods that look for a biclustering with a large interaction between row and column clusters. Thereby an aggregated, condensed representation of the existing interaction structure is obtained, together with corresponding row and column clusters, which both allow a parsimonious visualization and interpretation. In this paper we provide a statistical justification, in terms of a probabilistic model, for a two-mode interaction clustering criterion that has been proposed by Bock (1980). Furthermore, we show that maximization of this criterion is equivalent to minimizing the classical least-squares two-mode partitioning criterion for the double-centered version of the data matrix. The latter implies that the interaction clustering criterion can be optimized by applying classical two-mode partitioning algorithms. We illustrate the usefulness of our approach for the case of an empirical data set from personality psychology and we compare this method with other biclustering approaches where interactions play a role.

Model-based co-clustering for ordinal data

“…Natural competitors of our BOS model for ordinal data are either continuous two-mode clustering methods or categorical two-mode clustering methods. For the former case, double k-means (Vichi, 2001) or two-mode Gaussian mixture analysis (Govaert and Nadif, 2013) could be used, as illustrated in Schepers et al (2017). However, since double k-means seems to be not publicly available, we decide to restrict our attention to the latter which is available in the BlockCluster package (Bathia BOS whereas the categorical model has 31 continuous parameters.…”

REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction

“…For instance, arguments in favor of the need for personalized medicine (Hamburg and Collins 2010;Collins and Varmus 2015) are based on the assumption that patient by treatment interaction (i.e., treatment effect heterogeneity) exists (Rothwell 1995) and should be taken into account in the assignment of patients to treatments. Additional examples of research problems pertaining to the study of interaction in two-mode data are discussed in Schepers et al (2017).…”

“…These methods have in common that a specific type of structure is imposed on the row by column interaction (Alin and Kurt 2006). Another approach recently proposed is maximal interaction two-mode clustering (Schepers et al 2017), which belongs to the more general class of two-mode clustering or biclustering methods (Van Mechelen et al 2004;Madeira and Oliveira 2004).…”

A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

“…Clustering in combination with modeling the relationships between the categorical response variables is a widely employed procedure in data analysis. In general, most classical two-mode clustering methods are designed to attain homogeneous row-by-column clusters, while other methods are designed to find partitions based on the optimization of within-block interactions for a single quantitative dependent variable (Schepers, Bock, & Van Mechelen, 2017). For contingency tables, various procedures have been proposed to combine categories in terms of a particular homogeneity criterion (Goodman, 1981;Govaert & Nadif, 2014;Kateri & Iliopoulos, 2003), or seeking to maximize a measure of dependence (Bock, 2003;Govaert, 1995).…”

“…Latent block clustering methods have been proposed using a Poisson model, for example in information retrieval (Li & Zha, 2006), or for sequencing data (Witten, 2011), among others. With the aim of reducing the number of parameters and at the same time to facilitate the interpretation, clustering and representation methods have been proposed in different areas for different data sets (see, e.g., Kim, Choi, & Hwang, 2017;Vera, Mac ıas, & Heiser, 2009a, Vera, Mac ıas, & Heiser, 2009bVera, Mac ıas, & Heiser, 2013).…”