  Analysis of matrix-variate data is becoming increasingly common in the
literature, particularly in the field of clustering and classification. It is
well-known that real data, including real matrix-variate data, often exhibit
high levels of asymmetry. To address this issue, one common approach is to
introduce a tail or skewness parameter to a symmetric distribution. In this
regard, we introduced here a new distribution called the matrix-variate skew t
distribution (MVST), which provides flexibility in terms of heavy tail and
skewness. We then conduct a thorough investigation of various characterizations
and probabilistic properties of the MVST distribution. We also explore
extensions of this distribution to a finite mixture model. To estimate the
parameters of the MVST distribution, we develop an efficient EM-type algorithm
that computes maximum likelihood (ML) estimates of the model parameters. To
validate the effectiveness and usefulness of the developed models and
associated methods, we perform empirical experiments using simulated data as
well as three real data examples. Our results demonstrate the efficacy of the
developed approach in handling asymmetric matrix-variate data.
