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Nonnegative matrix factorization (NMF) is a popular technique for finding parts-based, linear representations of nonnegative data. It has been successfully applied in a wide range of applications such as pattern recognition, information retrieval, and computer vision. However, NMF is essentially an unsupervised method and cannot make use of label information. In this paper, we propose a novel semi-supervised matrix decomposition method, called Constrained Nonnegative Matrix Factorization (CNMF), which incorporates the label information as additional constraints. Specifically, we show how explicitly combining label information improves the discriminating power of the resulting matrix decomposition. We explore the proposed CNMF method with two cost function formulations and provide the corresponding update solutions for the optimization problems. Empirical experiments demonstrate the effectiveness of our novel algorithm in comparison to the state-of-the-art approaches through a set of evaluations based on real-world applications.

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With the emergence of online social networks, the social network-based recommendation approach is popularly used. The major benefit of this approach is the ability of dealing with the problems with cold-start users. In addition to social networks, user trust information also plays an important role to obtain reliable recommendations. Although matrix factorization (MF) becomes dominant in recommender systems, the recommendation largely relies on the initialization of the user and item latent feature vectors. Aiming at addressing these challenges, we develop a novel trust-based approach for recommendation in social networks. In particular, we attempt to leverage deep learning to determinate the initialization in MF for trust-aware social recommendations and to differentiate the community effect in user's trusted friendships. A two-phase recommendation process is proposed to utilize deep learning in initialization and to synthesize the users' interests and their trusted friends' interests together with the impact of community effect for recommendations. We perform extensive experiments on real-world social network data to demonstrate the accuracy and effectiveness of our proposed approach in comparison with other state-of-the-art methods.

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Bike sharing is booming globally as a green transportation mode, but the occurrence of over-demand stations that have no bikes or docks available greatly affects user experiences. Directly predicting individual over-demand stations to carry out preventive measures is difficult, since the bike usage pattern of a station is highly dynamic and context dependent. In addition, the fact that bike usage pattern is affected not only by common contextual factors (e.g., time and weather) but also by opportunistic contextual factors (e.g., social and traffic events) poses a great challenge. To address these issues, we propose a dynamic cluster-based framework for over-demand prediction. Depending on the context, we construct a weighted correlation network to model the relationship among bike stations, and dynamically group neighboring stations with similar bike usage patterns into clusters. We then adopt Monte Carlo simulation to predict the over-demand probability of each cluster. Evaluation results using real-world data from New York City and Washington, D.C. show that our framework accurately predicts over-demand clusters and outperforms the baseline methods significantly.