A pairwise likelihood approach to simultaneous clustering and dimensional reduction of ordinal data

TL;DR

This paper introduces a novel pairwise likelihood method for simultaneous clustering and dimensionality reduction of ordinal data, effectively identifying relevant features while discarding noise variables.

Contribution

It proposes a new model based on latent variables and an EM-like algorithm to handle the complexity of multidimensional integrals in clustering ordinal data.

Findings

Effective in detecting discriminative dimensions

Successfully discards noise variables

Demonstrated on real and simulated datasets

Abstract

The literature on clustering for continuous data is rich and wide; differently, that one developed for categorical data is still limited. In some cases, the problem is made more difficult by the presence of noise variables/dimensions that do not contain information about the clustering structure and could mask it. The aim of this paper is to propose a model for simultaneous clustering and dimensionality reduction of ordered categorical data able to detect the discriminative dimensions discarding the noise ones. Following the underlying response variable approach, the observed variables are considered as a discretization of underlying first-order latent continuous variables distributed as a Gaussian mixture. To recognize discriminative and noise dimensions, these variables are considered to be linear combinations of two independent sets of second-order latent variables where only one contains the information about the cluster structure while the other contains noise dimensions. The model specification involves multidimensional integrals that make the maximum likelihood estimation cumbersome and in some cases infeasible. To overcome this issue the parameter estimation is carried out through an EM-like algorithm maximizing a pairwise log-likelihood. Examples of application of the model on real and simulated data are performed to show the effectiveness of the proposal.