1,961 research outputs found
Is Simple Better? Revisiting Non-linear Matrix Factorization for Learning Incomplete Ratings
Matrix factorization techniques have been widely used as a method for
collaborative filtering for recommender systems. In recent times, different
variants of deep learning algorithms have been explored in this setting to
improve the task of making a personalized recommendation with user-item
interaction data. The idea that the mapping between the latent user or item
factors and the original features is highly nonlinear suggest that classical
matrix factorization techniques are no longer sufficient. In this paper, we
propose a multilayer nonlinear semi-nonnegative matrix factorization method,
with the motivation that user-item interactions can be modeled more accurately
using a linear combination of non-linear item features. Firstly, we learn
latent factors for representations of users and items from the designed
multilayer nonlinear Semi-NMF approach using explicit ratings. Secondly, the
architecture built is compared with deep-learning algorithms like Restricted
Boltzmann Machine and state-of-the-art Deep Matrix factorization techniques. By
using both supervised rate prediction task and unsupervised clustering in
latent item space, we demonstrate that our proposed approach achieves better
generalization ability in prediction as well as comparable representation
ability as deep matrix factorization in the clustering task.Comment: version
Fast algorithms for computing the Boltzmann collision operator
The development of accurate and fast numerical schemes for the five fold
Boltzmann collision integral represents a challenging problem in scientific
computing. For a particular class of interactions, including the so-called hard
spheres model in dimension three, we are able to derive spectral methods that
can be evaluated through fast algorithms. These algorithms are based on a
suitable representation and approximation of the collision operator. Explicit
expressions for the errors in the schemes are given and spectral accuracy is
proved. Parallelization properties and adaptivity of the algorithms are also
discussed.Comment: 22 page
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