  Classification of unlabeled data is usually achieved by supervised learning
from labeled samples. Although there exist many sophisticated supervised
machine learning methods that can predict the missing labels with a high level
of accuracy, they often lack the required transparency in situations where it
is important to provide interpretable results and meaningful measures of
confidence. Body fluid classification of forensic casework data is the case in
point. We develop a new Biclustering Dirichlet Process for Class-assignment
with Random Matrices (BDP-CaRMa), with a three-level hierarchy of clustering,
and a model-based approach to classification that adapts to block structure in
the data matrix. As the class labels of some observations are missing, the
number of rows in the data matrix for each class is unknown. BDP-CaRMa handles
this and extends existing biclustering methods by simultaneously biclustering
multiple matrices each having a randomly variable number of rows. We
demonstrate our method by applying it to the motivating problem, which is the
classification of body fluids based on mRNA profiles taken from crime scenes.
The analyses of casework-like data show that our method is interpretable and
produces well-calibrated posterior probabilities. Our model can be more
generally applied to other types of data with a similar structure to the
forensic data.
