A Kullback-Leibler divergence approach to blind image restoration

Entropy Analysis of Soccer Dynamics

This paper adopts the information and fractional calculus tools for studying the dynamics of a national soccer league. A soccer league season is treated as a complex system (CS) with a state observable at discrete time instants, that is, at the time of rounds. The CS state, consisting of the goals scored by the teams, is processed by means of different tools, namely entropy, mutual information and Jensen–Shannon divergence. The CS behavior is visualized in 3-D maps generated by multidimensional scaling. The points on the maps represent rounds and their relative positioning allows for a direct interpretation of the results.

Ranking-Oriented Collaborative Filtering

Collaborative filtering (CF) is one of the most effective techniques in recommender systems, which can be either rating oriented or ranking oriented. Ranking-oriented CF algorithms demonstrated significant performance gains in terms of ranking accuracy, being able to estimate a precise preference ranking of items for each user rather than the absolute ratings (as rating-oriented CF algorithms do). Conventional memory-based ranking-oriented CF can be referred to as pairwise algorithms. They represent each user as a set of preferences on each pair of items for similarity calculations and predictions. In this study, we propose ListCF, a novel listwise CF paradigm that seeks improvement in both accuracy and efficiency in comparison with pairwise CF. In ListCF, each user is represented as a probability distribution of the permutations over rated items based on the Plackett-Luce model, and the similarity between users is measured based on the Kullback--Leibler divergence between their probability distributions over the set of commonly rated items. Given a target user and the most similar users, ListCF directly predicts a total order of items for each user based on similar users’ probability distributions over permutations of the items. Besides, we also reveal insightful connections among pointwise, pairwise, and listwise CF algorithms from the perspective of the matrix representations. In addition, to make our algorithm more scalable and adaptive, we present an incremental algorithm for ListCF, which allows incrementally updating the similarities between users when certain user submits a new rating or updates an existing rating. Extensive experiments on benchmark datasets in comparison with the state-of-the-art approaches demonstrate the promise of our approach.