A multi-scale framework for graph based machine learning problems
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Graph data have become essential in representing and modeling relationships between entities and complex network structures in various domains such as social networks and recommender systems. As a main contributor of the recent Big Data trend, the massive scale of graphs in modern machine learning problems easily overwhelms existing methods and thus sophisticated scalable algorithms are needed for real-world applications. In this thesis, we develop a novel multi-scale framework based on the divide-and-conquer principle as an effective and scalable approach for machine learning tasks involving large sparse graphs. We first demonstrate how our multi-scale framework can be applied to the problem of computing the spectral decomposition of massive graphs, which is one of the most fundamental low-rank matrix approximations used in numerous machine learning tasks. While popular solvers suffer from slow convergence, especially when the desired rank is large, our method exploits the clustering structure of the graph and achieves superior performance compared to existing algorithms in terms of both accuracy and scalability. While the main goal of the divide-and-conquer approach is to efficiently compute solutions for the original problem, the proposed multi-scale framework further admits an attractive but less obvious feature that machine learning problems can benefit from. Particularly, we consider partial solutions of the subproblems computed in the process as localized models of the entire problem. By doing so, we can combine models at multiple scales from local to global and generate a holistic view of the underlying problem to achieve better performance than a single global view. We adapt such multi-scale view for the problems of link prediction in social networks and collaborative filtering in recommender systems with additional side information to obtain a model that can make accurate and robust predictions in a scalable manner.