A personalized recommendation algorithm based on approximating the singular value decomposition (ApproSVD)

Personalized recommendation is, according to the user's interest characteristics and purchasing behavior, to recommend information and goods to users in which they may be interested. With the rapid development of Internet technology, we have entered the era of information explosion, where huge amounts of information are presented at the same time. On one hand, it is difficult for the user to discover information in which he is most interested, on the other hand, general users experience difficult in obtaining information which very few people browse. In order to extract information in which the user is interested from a massive amount of data, we propose a personalized recommendation algorithm based on approximating the singular value decomposition (SVD) in this paper. SVD is a powerful technique for dimensionality reduction. However, due to its expensive computational requirements and weak performance for large sparse matrices, it has been considered inappropriate for practical applications involving massive data. Finally, we present an empirical study to compare the prediction accuracy of our proposed algorithm with that of Drineas's LINEARTIMESVD algorithm and the standard SVD algorithm on the Movie Lens dataset, and show that our method has the best prediction quality. © 2012 IEEE.

Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities

In this paper, we consider a class of time-delay singular systems with Lipschitz non-linearities. A method of designing full-order observers for the systems is presented which can handle non-linearities with large-Lipschitz constants. The Lipschitz conditions are reformulated into linear parameter varying systems, then the Lyapunov–Krasovskii approach and the convexity principle are applied to study stability of the new systems. Furthermore, the observers design does not require the assumption of regularity for singular systems. In case the systems are non-singular, a reduced-order observers design is proposed instead. In both cases, synthesis conditions for the observers designs are derived in terms of linear matrix inequalities which can be solved efficiently by numerical methods. The efficiency of the obtained results is illustrated by two numerical examples.