## "Exploring Clustering Structure in Ranking Data"

**Abstract:** Cluster analysis is concerned with finding homogeneous groups in a population. Model-based clustering methods provide a framework for developing clustering methods through the use of statistical models. This approach allows for uncertainty to be quantified using probability and for the properties of a clustering method to be understood on the basis of a well defined statistical model. Mixture models provide a basis for many model-based clustering methods. Ranking data arise when judges rank some or all of a set of objects. Examples of ranking data include voting data from elections that use preferential voting systems (eg. PR-STV) and customer preferences for products in marketing applications. A mixture of experts model is a mixture model in which the model parameters are functions of covariates. We explore the use of mixture of experts models in cluster analysis, so that clustering can be better understood. The choice of how and where covariates enter the mixture of experts model has implications for the clustering performance and the interpretation of the results. The use of covariates in clustering is demonstrated on examples from studying voting blocs in elections and examining customer segments marketing. This work was completed in collaboration with Claire Gormley.

**Bio:** Brendan Murphy is Associate Professor of Statistics in the School of Mathematical Sciences & the Complex and Adaptive Systems Laboratory at University College Dublin, Ireland. His research focuses on statistical model-based approaches to clustering, classification and network modeling. He is interested in applications of statistical methods in social science, food science and bioinformatics. He completed his PhD in Statistics at Yale University since then has held positions in Trinity College Dublin and the University of Washington. He currently serves as associate editor for the Annals of Applied Statistics and Statistics and Computing and review editor for Statistical Analysis & Data Mining.

## Comments