The development of diagnostic tools for mixture modeling and model-based clustering
Cluster analysis performs unsupervised partition of heterogeneous data. It has applications in almost all fields of study. Model-based clustering is one of the most popular clustering methods these days due to its flexibility and interpretability. It is based on finite mixture models. However, the development of diagnostic tools and visualization tools for clustering procedures is limited. This dissertation is devoted to assessing different properties of the clustering procedure. This report has four chapters. The summary of each chapter is given below: In the first chapter we provide the practitioners with an approach to assess the certainty of a classification made in model-based clustering. The second chapter introduces a novel finite mixture model called Manly mixture model. It is capable of modeling skewness in data and performs diagnostics on the normality of variables. In the third chapter we develop an extension of the traditional K-means procedure that is capable of modeling skewness in data. The fourth chapter contributes to the ManlyMix R package, which is the developed software corresponding to our paper in Chapter 2.