Combinatorial Markov Random Fields and their applications to information organization

We propose a new type of undirected graphical models called a Combinatorial Markov Random Field (Comraf) and discuss its advantages over existing graphical models. We develop an efficient inference methodology for Comrafs based on combinatorial optimization of information-theoretic objective functions; both global and local optimization schema are discussed. We apply Comrafs to multi-modal clustering tasks: standard (unsupervised) clustering, semi-supervised clustering, interactive clustering, and one-class clustering. For the one-class clustering task, we analytically show that the proposed optimization method is optimal under certain simplifying assumptions. We empirically demonstrate the power of Comraf models by comparing them to other state-of-the-art machine learning techniques, both in text clustering and image clustering domains. For unsupervised clustering, we show that Comrafs consistently and significantly outperform three previous state-of-the-art clustering techniques on six real-world textual datasets. For semi-supervised clustering, we show that the Comraf model is superior to a well-known constrained optimization method. For interactive clustering, Comraf obtains higher accuracy than a Support Vector Machine, trained on a large amount of labeled data. For one-class clustering, Comrafs demonstrate superior performance over two previously proposed methods. We summarize our thesis by giving a comprehensive recipe for machine learning modeling with Comrafs