Low-rank matrix approximation (LRMA) methods have achieved excellent accuracy among today's collaborative filtering (CF) methods. In existing LRMA methods, the rank of user/item feature matrices is typically fixed, i.e., the same rank is adopted to describe all users/items. However, our studies show that submatrices with different ranks could coexist in the same user-item rating matrix, so that approximations with fixed ranks cannot perfectly describe the internal structures of the rating matrix, therefore leading to inferior recommendation accuracy. In this paper, a mixture-rank matrix approximation (MRMA) method is proposed, in which user-item ratings can be characterized by a mixture of LRMA models with different ranks. Meanwhile, a learning algorithm capitalizing on iterated condition modes is proposed to tackle the non-convex optimization problem pertaining to MRMA.

Low-rank matrix approximation (LRMA) methods have achieved excellent accuracy among today's collaborative filtering (CF) methods. In existing LRMA methods, the rank of user/item feature matrices is typically fixed, i.e., the same rank is adopted to describe all users/items. However, our studies show that submatrices with different ranks could coexist in the same user-item rating matrix, so that approximations with fixed ranks cannot perfectly describe the internal structures of the rating matrix, therefore leading to inferior recommendation accuracy. In this paper, a mixture-rank matrix approximation (MRMA) method is proposed, in which user-item ratings can be characterized by a mixture of LRMA models with different ranks. Meanwhile, a learning algorithm capitalizing on iterated condition modes is proposed to tackle the non-convex optimization problem pertaining to MRMA. Experimental studies on MovieLens and Netflix datasets demonstrate that MRMA can outperform six state-of-the-art LRMA-based CF methods in terms of recommendation accuracy.

Sales pipeline win-propensity prediction is fundamental to effective sales management. In contrast to using subjective human rating, we propose a modern machine learning paradigm to estimate the win-propensity of sales leads over time. A profile-specific two-dimensional Hawkes processes model is developed to capture the influence from seller's activities on their leads to the win outcome, coupled with lead's personalized profiles. It is motivated by two observations: i) sellers tend to frequently focus their selling activities and efforts on a few leads during a relatively short time. This is evidenced and reflected by their concentrated interactions with the pipeline, including login, browsing and updating the sales leads which are logged by the system; ii) the pending opportunity is prone to reach its win outcome shortly after such temporally concentrated interactions. Our model is deployed and in continual use to a large, global, B2B multinational technology enterprize (Fortune 500) with a case study. Due to the generality and flexibility of the model, it also enjoys the potential applicability to other real-world problems.