Model-based clustering of high dimensional discrete data and compositional data

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Identification and analysis of population heterogeneity is the primary goal of cluster analysis. Clustering allows us to summarize data into homogenous groups or clusters of observations where observations within each cluster are more similar than between clusters. Model-based clustering, which utilizes mixture models, has been increasingly used in the last two decades. A finite mixture model assumes that the population consists of a finite mixture of subpopulations or components, each of which can be represented by a parametric model. Depending on the nature of the data, appropriate distributions are chosen to model various kinds of data. The long-term goal of the applicant's research program is to develop cutting edge statistical algorithms for biological datasets to gain a comprehensive understanding of biological processes. While there has been a big explosion in data generation in bioinformatics, efficiently analyzing these complex biological data sets still remains a challenge. During the tenure of the grant, the applicant's research will focus on developing novel model-based clustering algorithms for high dimensional and longitudinal discrete data and compositional data. Challenges with such analyses include the large scale nature of omics datasets, heterogeneity in the data types, and a lack of scalability of statistical models that capture the various characteristics of the underlying data generating mechanisms. The proposed research focuses on developing efficient and scalable statistical models for clustering high dimensional data and longitudinal omics data. In addition to these model developments, several open problems in model-based clustering will be explored. When the number of components in a mixture model is unknown, the EM algorithm or a variant thereof must be used in conjunction with a model-selection criterion so that every possible number of components is explored. This can be computationally expensive and using different model selection criteria on the same data can result in selection of different `best' fitting models. To date, most work on the model selection issue has focused on continuous data. Some work will focus on investigation of different model-selection criteria for discrete data and compositional data in general. Investigation of an efficient parameter framework will also be a key focus. The proposed work presents a major step forward in mixture model-based clustering of multivariate discrete data and compositional data. While the proposed research will utilize bioinformatics datasets for applications, they are applicable to discrete and compositional data encountered in many fields such as text analytics, sport analytics, etc. These algorithms will be made available publicly as open source user-friendly R packages. The impact of this work will be primarily in the computational statistics and bioinformatics communities.