Machine Learning on Network-Valued Data: The Spectral Way

Graduate Thesis Or Dissertation

Citations

Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/nk322f49w

Abstract

This dissertation considers the problem of machine learning given network-valued data, sometimes referred to as graph-valued data. Many machine learning algorithms utilize various statistics to answer a wide variety of questions in a principled manner. When data comes from Euclidean space, determination of the mean and variance is a simple algebraic operation. For graph valued data, simple statistics are non-trivial to compute; they are generalized to metric spaces and are defined by an optimization procedure over the metric space.

Chapter 1 introduces the overarching questions addressed within this dissertation and the contributions made to the field. In Chapter 2, the computation of the sample mean given a data set of graphs is explored in depth when considering a metric that compares the eigenvalues of the adjacency matrices of two graphs. The work in this chapter is novel, to the best of our knowledge, this chapter introduces the first method to compute the mean of a data set of graphs with respect to spectral information. Within Chapter 3, both the mean and the variance are used to infer the parameters of a distribution on the space of graphs with respect to spectral information. Chapter 4 considers the theoretical properties of the sample mean graph and how those properties relate to the sample data set.

Creator