Finite multivariate density mixtures: applications and new approaches

Cluster analysis and classification of multivariate datasets are two of the most important tasks in modern statistical and data sciences. By leveraging copula-based density mixtures, this project will introduce new methods for clustering and classification of multivariate data which exhibit sophisticated dependence properties. The proposed methods will provide more reliable clustering solutions that could be in turn used, for example, for development of new therapeutic drugs and more precise quantification of gene interactions. This project will involve students, both at the undergraduate and graduate levels, to work on the computational aspects of this interdisciplinary research. The particular focus of the project will be on bolstering broader participation in statistical sciences and involvement of mentees from the underrepresented groups. Many of the students will be recruited through the National Alliance for Doctoral Studies in the Mathematical Sciences (commonly called simply “Math Alliance”) that is headquartered at Purdue University. Multivariate mixture models are widely applicable in many areas of statistics. They are particularly useful in clustering and classification of multivariate high-dimensional data. The majority of model-based clustering techniques for multivariate data are based on multivariate normal models and their direct generalizations. However, this approach is quite restrictive since, in most cases, it is difficult to model clusters of non-elliptical shapes. Even where it is possible, these models tend to be limited in their capabilities to cluster multivariate data of mixed types that include both continuous and discrete random variables. This project will develop an alternative to the existing model-based clustering methods for multivariate data. This alternative is based on using copula-based density mixtures which will allow for modeling a vast variety of dependence structures. Furthermore, the proposed solution will also allow for the principled clustering of datasets containing both continuous and discrete observations. The immediate outcome of this project will be the development of a family of computationally efficient algorithms. Such algorithms will provide reliable clustering of objects under the minimal assumptions. The proposed methodology will be widely applicable to such areas as clustering of genes and other biological entities in transcriptomics data as well as clustering of text documents, where the number of dimensions may be equal to the size of the vocabulary. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.