25,649 research outputs found
Spectral Detection on Sparse Hypergraphs
We consider the problem of the assignment of nodes into communities from a
set of hyperedges, where every hyperedge is a noisy observation of the
community assignment of the adjacent nodes. We focus in particular on the
sparse regime where the number of edges is of the same order as the number of
vertices. We propose a spectral method based on a generalization of the
non-backtracking Hashimoto matrix into hypergraphs. We analyze its performance
on a planted generative model and compare it with other spectral methods and
with Bayesian belief propagation (which was conjectured to be asymptotically
optimal for this model). We conclude that the proposed spectral method detects
communities whenever belief propagation does, while having the important
advantages to be simpler, entirely nonparametric, and to be able to learn the
rule according to which the hyperedges were generated without prior
information.Comment: 8 pages, 5 figure
Collaborative Deep Learning for Recommender Systems
Collaborative filtering (CF) is a successful approach commonly used by many
recommender systems. Conventional CF-based methods use the ratings given to
items by users as the sole source of information for learning to make
recommendation. However, the ratings are often very sparse in many
applications, causing CF-based methods to degrade significantly in their
recommendation performance. To address this sparsity problem, auxiliary
information such as item content information may be utilized. Collaborative
topic regression (CTR) is an appealing recent method taking this approach which
tightly couples the two components that learn from two different sources of
information. Nevertheless, the latent representation learned by CTR may not be
very effective when the auxiliary information is very sparse. To address this
problem, we generalize recent advances in deep learning from i.i.d. input to
non-i.i.d. (CF-based) input and propose in this paper a hierarchical Bayesian
model called collaborative deep learning (CDL), which jointly performs deep
representation learning for the content information and collaborative filtering
for the ratings (feedback) matrix. Extensive experiments on three real-world
datasets from different domains show that CDL can significantly advance the
state of the art
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