Many popular social web sites have emerged during the past decade and completely changed many users' everyday live. Recently, social information retrieval models, where conventional information retrieval meets the social context of search and recommendation, have become the central topic in machine learning, data mining, information retrieval and many other areas.;A particular application of social information retrieval is the recommendation. Such recommendation ranges from classic recommendation movie rating recommendation in user-item matrices, trust and reputation modeling between members in any social network. If we model such recommendation in the form of matrices, then such recommendation can be formulated as recovering missing values in the matrices. This is a classic research topics and there are numerous literature papers regarding this.;In this dissertation, we propose a few different models in terms of social recommendation. Specifically, we develop different models to predict the trust between users in the discrete domain, trust and rating prediction via aggregating heterogeneous social networks, predicting the future events of users. We will introduce these models in different chapters, provide the mathematical deviation for the objective function optimization and demonstrate the effectiveness of these methods with other benchmark methods in each category. These methods provide new perspectives for discovering un-tagged relationships and predicting future events for social networks.
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