Clustering data with values missing at random using scale mixtures of multivariate skew-normal distributions

TL;DR

This paper develops a flexible clustering method using scale mixtures of multivariate skew-normal distributions that effectively handles missing data under a missing at random mechanism, capturing skewness and heavy tails.

Contribution

It extends the FMSMSN family to incomplete data, deriving properties and an EM algorithm, enabling robust clustering with skewed, heavy-tailed data and missing values.

Findings

Demonstrates improved clustering performance with missing data

Provides closed-form expressions for missing data imputation

Shows applicability to real-world CO2 emissions data

Abstract

Handling missing data is a major challenge in model-based clustering, especially when the data exhibit skewness and heavy tails. We address this by extending the finite mixture of scale mixtures of multivariate skew-normal (FMSMSN) family to accommodate incomplete data under a missing at random (MAR) mechanism. Unlike previous work that is limited to one of the special cases of the FMSMSN family, our method offers a cluster analysis methodology for the entire family that accounts for skewness and excess kurtosis amidst data with missing values. The multivariate skew-normal distribution, as parameterised by \cite{azzalini1996} and \cite{arnoldbeaver} includes the normal distribution as a special case, which ensures that our method is flexible toward existing symmetric model-based clustering techniques under a normality assumption. We derive the distributional properties of the missing components of the data and propose an augmented EM-type algorithm tailored for incomplete observations. The modified E-step yields closed-form expressions for the conditional expectations of the missing values. The simulation experiments showcase the flexibility of the FMSMSN family in both clustering performance and parameter recovery for varying percentages of missing values, while incorporating the effects of sample size and cluster proximity. Finally, we illustrate the practical utility of the proposed method by applying special cases of the FMSMSN family to global CO2 emissions data.