Multi-Domain Collaborative Recommendation with Feature Selection

Collaborative f iltering, as one of the most popular techniques, plays an important role in recommendation systems. However,when the user-item rating matrix is sparse,its performance will be degenerate. Recently,domain-specific recommendation approaches have been developed to address this problem.The basic idea is to partition the users and items into overlapping domains, and then perform recommendation in each domain independently. Here, a domain means a group of users having similar preference to a group of products. However, these domain-specific methods consisting of two sequential steps ignore the mutual benefi t of domain segmentation and recommendation. Hence, a unified framework is presented to simultaneously realize recommendation and make use of the domain information underlying the rating matrix in this paper. Based on matrix factorization,the proposed model learns both user preferences of multiple domains and preference selection vectors to select relevant features for each group of products. Besides, local context information is utilized from the user-item rating matrix to enhance the new framework.Experimental results on two widely used datasets, e.g., Ciao and Epinions, demonstrate the effectiveness of our proposed model.

Unknown constrained mechanisms operation based on dynamic interactive control

In order to operate various constrained mechanisms with assistive robot manipulators, an interactive control algorithm is proposed in this paper. This method decouples motion and force control in the constrained frame, and modifies the motion velocity online. Firstly, the constrained frame is determined online according to previous motion direction; then the selection matrix is adjusted dynamically, the constrained motion direction is chosen as the driving-axis. Consequently, the driving-axis and non-driving-axis are decoupled; finally, velocity control and impedance control are implied on above axes respectively. The selecting threshold for driving-axis is also varying dynamically to fit different constrained mechanism. Door-opening experiments are conducted to verify the performance of the proposed method.

Degrees of freedom in low rank matrix estimation

The objective of this paper is to quantify the complexity of rank and nuclear norm constrained methods for low rank matrix estimation problems. Specifically, we derive analytic forms of the degrees of freedom for these types of estimators in several common settings. These results provide efficient ways of comparing different estimators and eliciting tuning parameters. Moreover, our analyses reveal new insights on the behavior of these low rank matrix estimators. These observations are of great theoretical and practical importance. In particular, they suggest that, contrary to conventional wisdom, for rank constrained estimators the total number of free parameters underestimates the degrees of freedom, whereas for nuclear norm penalization, it overestimates the degrees of freedom. In addition, when using most model selection criteria to choose the tuning parameter for nuclear norm penalization, it oftentimes suffices to entertain a finite number of candidates as opposed to a continuum of choices. Numerical examples are also presented to illustrate the practical implications of our results.