Higher-order tensors are generalizations of vectors and matrices to thirdor even higher-order arrays of numbers. We consider a generalization of column and row rank of a matrix to tensors, called multilinear rank. Given a higher-order tensor, we are looking for another tensor, as close as possible to the original one and with multilinear rank bounded by prespecified numbers. In this paper, we g...

The user-based collaborative filtering (CF) algorithm is one of the most popular approaches for making recommendation. Despite its success, the traditional user-based CF algorithm suffers one serious problem that it only measures the influence between two users based on their symmetric similarities calculated by their consumption histories. It means that, for a pair of users, the influences on ...

As one of the most successful approaches to building recommender systems, collaborative filtering (CF) uses the known preferences of a group of users to make recommendations or predictions of the unknown preferences for other users. However, the open nature of collaborative filtering recommender systems allows attackers who inject biased profile data to have a significant impact on the recommen...

Recall that in Lecture 13, a randomized algorithm was described for computing a low rank approximation to the eigendecomposition of a matrix A. A drawback to this method is that the matrix A must be accessed multiple times (twice), which may not be possible in streaming models where A cannot be stored in memory [1]. For the streaming model, we require a single pass algorithm, where A is accesse...

Group technology (GT) is a useful way to increase productivity with high quality in cellular manufacturing systems (CMSs), in which cell formation (CF) is a key step in the GT philosophy. When boundaries between groups are fuzzy, fuzzy clustering has been successfully adapted to solve the CF problem; however, it may result uneven distribution of parts/machines where the problem becomes larger. ...

Group technology (GT) is a useful way to increase productivity with high quality in flexible manufacturing systems. Cell formation (CF) is a key step in GT. It is used to design a good cellular manufacturing system that uses the similarity measure between parts and machines so that it can identify part families and machine groups. Recently, fuzzy clustering has been applied in GT because the fu...