In this age of information overload and plethora of choices, people increasingly rely on automatic recommender systems to tell them what suits their needs. A very effective approach for creating recommender systems is collaborative filtering, which is the task of predicting the preference/rating that a user would assign to an item based on preference data of that user and preference data of other users. One way to conduct collaborative filtering is through dimensionality reduction. The underlying concept of the approach lies in the belief that there are only a few features (reduced dimensions) that influence the user’s choice. In this paper we use low rank matrix factorization for dimensionality reduction. Singular Value Decomposition (SVD), which is minimizing the L2 norm is the most popular technique to perform matrix factorization. However, in most recommendation system data sets, often the users only rate a small amount of items, which creates missing data. As a result SVD fails. In recent years L1 norm has gained much importance and popularity because it is robust to outliers and missing data. In this thesis we use alternate convex optimization to perform L1 norm minimization to solve the matrix factorization problem and apply it to collaborative filtering. We also review some of the major challenges that collaborative filtering faces today and some of the other techniques used. Additionally, this thesis discusses the importance and future of collaborative filtering in medical applications that concerns the database of patient history (prescriptions/symptoms) and how it can be used as a predictive task for the future of the patient.
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