The massive number of online choices, e-commerce items, and related data available on the web makes it profoundly challenging for users to extract insightful information that can help them decide on what to select among a vast multitude of choices. In recent years, recommender systems have played an important role in reducing the overwhelming impact of such information overload. In particular, a specific form of recommender system, which is known as collaborative filtering, is the most popular approach to building these systems, and it has been successfully employed in many applications. More importantly, the matrix completion paradigm provides an appealing solution to the collaborative filtering problem in recommendation systems. However, collaborative filtering based approaches perform poorly for sparse data and specifically for the so-called cold start users.Recently, there has been an upsurge interest in utilizing other rich sources of side infor- mation about items/users to compensate for the insufficiency of rating information. Such information is of more importance to be aggregated when a single view of the data is sparse or even incomplete. Due to the advent and popularity of online social networks and e-commerce websites, many different types of side information are available that can be taken into account in addition to traditional rating matrices in order to improve the recommendation.The overarching goal of this thesis is to propose a novel and general algorithmic framework based on matrix factorization that simultaneously exploits the similarity information among users and items to alleviate the data sparsity issue and specifically the cold-start problem. Weextend matrix factorization and propose a model that takes into account the side information as well as the rating matrix. Therefore, by modeling different types of side information, such as social or trust/distrust relationships between users and meta-data about items, as a constraint similarity/dissimilarity graph, we propose an effective recommendation framework that is able to boost the recommendation accuracy and overcome the challenges in existing recommendation systems such as cold-start users/items and data sparsity problems. The proposed modeling framework is capable of performing both rating and link prediction.Based on the proposed framework, a key objective of this thesis is to develop novel algo- rithms and derive theoretical guarantees for their performance. The algorithms we developed so far have been experimentally evaluated and compared against existing state-of-the-art methods on real life datasets (such as MovieLens, NIPS, Epinions and etc.). Our experi- mental results show that our proposed modeling framework and related algorithms achieve substantial quality gains when compared to with existing methods. Our experimental results also illustrate how our framework and algorithms can overcome the shortcomings of other state-of-the-art recommendation techniques.
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