Statistical Techniques for Exploratory Analysis of Structured Three-Way and Dynamic Network Data.

In this thesis, I develop different techniques for the pattern extraction and visual exploration of a collection of data matrices. Specifically, I present methods to help home in on and visualize an underlying structure and its evolution over ordered (e.g., time) or unordered (e.g., experimental conditions) index sets. The first part of the thesis introduces a biclustering technique for such three dimensional data arrays. This technique is capable of discovering potentially overlapping groups of samples and variables that evolve similarly with respect to a subset of conditions. To facilitate and enhance visual exploration, I introduce a framework that utilizes kernel smoothing to guide the estimation of bicluster responses over the array. In the second part of the thesis, I introduce two matrix factorization models. The first is a data integration model that decomposes the data into two factors: a basis common to all data matrices, and a coefficient matrix that varies for each data matrix. The second model is meant for visual clustering of nodes in dynamic network data, which often contains complex evolving structure. Hence, this approach is more flexible and additionally lets the basis evolve for each matrix in the array. Both models utilize a regularization within the framework of non-negative matrix factorization to encourage local smoothness of the basis and coefficient matrices, which improves interpretability and highlights the structural patterns underlying the data, while mitigating noise effects. I also address computational aspects of applying regularized non-negative matrix factorization models to large data arrays by presenting multiple algorithms, including an approximation algorithm based on alternating least squares.PhDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99838/1/smankad_1.pd