Clustering Three-Way Data with Outliers

Matrix-variate normal mixture models are a powerful statistical tool used to represent complex data structures that involve matrices, such as multivariate time series, spatial data, and image data. Detecting outliers in matrix-variate normal mixture models is crucial for identifying anomalous observations that deviate significantly from the underlying distribution. Outliers can provide valuable insights into data quality issues, anomalies, or unexpected patterns. Outliers, and their treatment, is a long-studied topic in the field of applied statistics. The problem of handling outliers in multivariate clustering has been studied in several contexts including work by García-Escudero et al. (2008), Punzo and McNicholas (2016), Punzo et al. (2020), and Clark and McNicholas (2023).