Mixtures of Skewed Matrix Variate Bilinear Factor Analyzers
This work addresses the need for dimension reduction and clustering techniques for three-way data, which is incremental as it extends existing models to incorporate skewness.
The authors tackled the problem of clustering high-dimensional matrix variate data by proposing mixtures of bilinear factor analyzers using four skewed matrix variate distributions, as existing methods assume normality and may not handle skewness or kurtosis effectively.
In recent years, data have become increasingly higher dimensional and, therefore, an increased need has arisen for dimension reduction techniques for clustering. Although such techniques are firmly established in the literature for multivariate data, there is a relative paucity in the area of matrix variate, or three-way, data. Furthermore, the few methods that are available all assume matrix variate normality, which is not always sensible if cluster skewness or excess kurtosis is present. Mixtures of bilinear factor analyzers using skewed matrix variate distributions are proposed. In all, four such mixture models are presented, based on matrix variate skew-t, generalized hyperbolic, variance-gamma, and normal inverse Gaussian distributions, respectively.