Covariance Clustering on Skewed Data

A specific type of few-shot learning deals with a large number of classes with few observations per class and data living in a high-dimensional space. It is often assumed that each class follows a multivariate normal distribution. To estimate the parameters of the classes, information is often pooled across classes via a pooled covariance estimate. This is a strong assumption to make, especially as the number of classes increases, and thus, a method has recently been proposed to cluster covariance matrices, which allows for a more flexible way of pooling information across classes. This method relies on the assumption of normality, which is easily violated in real-world datasets. We propose extending the method of clustering covariance matrices to skewed data by assuming each class follows a multivariate normal after some transformation is applied such as the Manly transform. This method is applied to a forensic glass dataset that has this few-shot learning structure. Research funded by a joint National Science Foundation and National Geospatial-Intelligence Agency project titled “ATD: Development of Statistical Methods for Detection and Characterization of Latent Subpopulations of Classes” under award No. 2428037. The findings are solely those of the authors.