22,213 research outputs found
Two asymptotic formulae on the k + 1-power free numbers
The main purpose of this paper is to study the distributive properties of k + 1-power free numbers, and give two interesting asymptotic formulae
A Faster Algorithm to Build New Users Similarity List in Neighbourhood-based Collaborative Filtering
Neighbourhood-based Collaborative Filtering (CF) has been applied in the
industry for several decades, because of the easy implementation and high
recommendation accuracy. As the core of neighbourhood-based CF, the task of
dynamically maintaining users' similarity list is challenged by cold-start
problem and scalability problem. Recently, several methods are presented on
solving the two problems. However, these methods applied an algorithm
to compute the similarity list in a special case, where the new users, with
enough recommendation data, have the same rating list. To address the problem
of large computational cost caused by the special case, we design a faster
() algorithm, TwinSearch Algorithm, to avoid computing and
sorting the similarity list for the new users repeatedly to save the
computational resources. Both theoretical and experimental results show that
the TwinSearch Algorithm achieves better running time than the traditional
method
An Accuracy-Assured Privacy-Preserving Recommender System for Internet Commerce
Recommender systems, tool for predicting users' potential preferences by
computing history data and users' interests, show an increasing importance in
various Internet applications such as online shopping. As a well-known
recommendation method, neighbourhood-based collaborative filtering has
attracted considerable attention recently. The risk of revealing users' private
information during the process of filtering has attracted noticeable research
interests. Among the current solutions, the probabilistic techniques have shown
a powerful privacy preserving effect. When facing Nearest Neighbour attack,
all the existing methods provide no data utility guarantee, for the
introduction of global randomness. In this paper, to overcome the problem of
recommendation accuracy loss, we propose a novel approach, Partitioned
Probabilistic Neighbour Selection, to ensure a required prediction accuracy
while maintaining high security against NN attack. We define the sum of
neighbours' similarity as the accuracy metric alpha, the number of user
partitions, across which we select the neighbours, as the security metric
beta. We generalise the Nearest Neighbour attack to beta k Nearest
Neighbours attack. Differing from the existing approach that selects neighbours
across the entire candidate list randomly, our method selects neighbours from
each exclusive partition of size with a decreasing probability. Theoretical
and experimental analysis show that to provide an accuracy-assured
recommendation, our Partitioned Probabilistic Neighbour Selection method yields
a better trade-off between the recommendation accuracy and system security.Comment: replacement for the previous versio
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