Fast model-based clustering of partial records

TL;DR

This paper introduces a fast, model-based clustering method for partially recorded data using a finite mixture of multivariate t distributions, which is more efficient and often more accurate than traditional imputation or case deletion methods.

Contribution

It develops a novel clustering algorithm that directly models observed data with a mixture of t distributions, avoiding imputation and full EM, and demonstrates superior performance in simulations and real data.

Findings

The method is computationally more efficient than imputation and full EM.

It achieves better cluster recovery than case deletion and imputation.

It performs comparably or better than full EM even when MAR assumptions are violated.

Abstract

Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering algorithm to the resulting altered dataset. Here, we develop clustering methodology through a model-based approach using the marginal density for the observed values, assuming a finite mixture model of multivariate $t$ distributions. We compare our approximate algorithm to the corresponding full expectation-maximization (EM) approach that considers the missing values in the incomplete data set and makes a missing at random (MAR) assumption, as well as case deletion and imputation methods. Since only the observed values are utilized, our approach is computationally more efficient than imputation or full EM. Simulation studies demonstrate that our approach has favorable recovery of the true cluster partition compared to case deletion and imputation under various missingness mechanisms, and is at least competitive with the full EM approach, even when MAR assumptions are violated. Our methodology is demonstrated on a problem of clustering gamma-ray bursts and is implemented at https://github.com/emilygoren/MixtClust.