In recent years, with the development and daily update of user feedback data, the recommendation systems require algorithms able to process data accurately and fast. To tackle this data stream problem, online model updates for new data points come to be available. Another issue is how to evaluate algorithms in a streaming data environment while conventional Collaborative Filtering algorithms are proposed for stationary data. Furthermore, traditional evaluation methodologies are only useful in offline experiments. In this research, we propose a novel incremental model base on stochastic gradient decent algorithm for Matrix Factorization. In addition, we also show a prequential evaluation protocol for recommender systems, applicable for streaming data environments. Comparing with other state-of-the-art models, our algorithm has combative accuracy, while being significantly faster.

Two 3-DOF parallel mechanisms, a translational mechanism and a spherical mechanism, are analyzed. Each of two mechanisms commonly possesses three UPS serial sub-chains, and an additional passive 3-DOF PPP-type serial sub-chain and a passive 3-DOF RRR-type serial sub-chain are incorporated for the translational device and the rotational device, respectively. Such additional passive serial sub-chains act as constraints to restrict the output motion of the mechanism either in a 3-DOF translational space or in a 3-DOF spherical space. The position solutions of the proposed mechanisms and their first-order kinematic models are derived. Then their workspaces and kinematic characteristics are examined via the kinematic isotropic index

A new spherical-type 3-degree-of-freedom parallel mechanism consisting of a two degree-of-freedom parallel module and a serial module is proposed. Two alternative designs for the serial sub-chain are suggested and compared. The first design employs RU joint arrangement for the serial sub chain structure. The second design incorporates a gear chain to drive the distal revolute joint of the serial sub-chain from the base platform of the mechanism. This modification significantly improves kinematic characteristics of the mechanism within its workspace. Firstly, the closed-form solutions of both the forward and the reverse position analysis are derived. Secondly, the first-order kinematic model with respect to three inputs which are located at the base is derived. Thirdly, it is confirmed through simulation that the modified mechanism has much more improved isotropic characteristic throughout the workspace of the mechanism. Lastly, the proposed mechanism is implemented to verify the results from this analysis.