In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend the orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix pursuit iteration and find satisfactory results in a few iterations. Another advantage of our proposed algorithm is that it has only one tunable parameter, which is the rank. It is easy to understand and to use by the user. This becomes especially important in large-scale learning problems. In addition, we rigorously show that both versions achieve a linear convergence rate, which is significantly better than the previous known results. We also empirically compare the proposed algorithms with several state-of-the-art matrix completion algorithms on many real-world datasets, including the large-scale recommendation dataset Netflix as well as the MovieLens datasets. Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.

WC propose Concurrent Transaction Logic (C7X) as the language for specifying, analyzing, and scheduling of workflows. We show that both local and global properties of worktlows can be naturally represented as C7X formulas and reasoning can be done with the use of the proof theory and the semantics of this logic, We describe a transformation that leads to an eilicicnt algorithm for scheduling worldlows in the presencc of global temporal constraints, which leads to decision proccdurcs for dealing with several safety related properties such as whether every valid execution of the workflow satisfits a particular property or whether a worlcfiow execution is consistent with some given global constraints on the ordering of events in a workflow. We also provide tight complexity results on the running times of these algorithms.

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