Missing Values and Directional Outlier Detection in Model-Based Clustering

Model-based clustering tackles the task of uncovering heterogeneity in a data set to extract valuable insights. Given the common presence of outliers in practice, robust methods for model-based clustering have been proposed. However, the use of many methods in this area becomes severely limited in applications where partially observed records are common since their existing frameworks often assume complete data only. Here, a mixture of multiple scaled contaminated normal (MSCN) distributions is extended using the expectation-conditional maximization (ECM) algorithm to accommodate data sets with values missing at random. The newly proposed extension preserves the mixture's capability in yielding robust parameter estimates and performing automatic outlier detection separately for each principal component. In this fitting framework, the MSCN marginal density is approximated using the inversion formula for the characteristic function. Extensive simulation studies involving incomplete data sets with outliers are conducted to evaluate parameter estimates and to compare clustering performance and outlier detection of our model to other mixtures.