Semi-supervised Model-Based Clustering for Ordinal Data

This paper introduces a semi-supervised learning technique for model-based clustering. Our research focus is on applying it to matrices of ordered categorical response data, such as those obtained from the surveys with Likert scale responses. We use the proportional odds model, which is popular and widely used for analyzing such data, as the model structure. Our proposed technique is designed for analyzing datasets that contain both labeled and unlabeled observations from multiple clusters. The model fitting is performed using the expectation-maximization (EM) algorithm, incorporating the labeled cluster memberships, to cluster the unlabeled observations. To evaluate the performance of our proposed model, we conducted a simulation study in which we tested the model from eight different scenarios, each with varying combinations and proportions of known and unknown cluster memberships. The fitted models accurately estimate the parameters in most of the designed scenarios, indicating that our technique is effective in clustering partially-labeled data with ordered categorical response variables.