11,402 research outputs found
Deep Learning based Recommender System: A Survey and New Perspectives
With the ever-growing volume of online information, recommender systems have
been an effective strategy to overcome such information overload. The utility
of recommender systems cannot be overstated, given its widespread adoption in
many web applications, along with its potential impact to ameliorate many
problems related to over-choice. In recent years, deep learning has garnered
considerable interest in many research fields such as computer vision and
natural language processing, owing not only to stellar performance but also the
attractive property of learning feature representations from scratch. The
influence of deep learning is also pervasive, recently demonstrating its
effectiveness when applied to information retrieval and recommender systems
research. Evidently, the field of deep learning in recommender system is
flourishing. This article aims to provide a comprehensive review of recent
research efforts on deep learning based recommender systems. More concretely,
we provide and devise a taxonomy of deep learning based recommendation models,
along with providing a comprehensive summary of the state-of-the-art. Finally,
we expand on current trends and provide new perspectives pertaining to this new
exciting development of the field.Comment: The paper has been accepted by ACM Computing Surveys.
https://doi.acm.org/10.1145/328502
Positive contraction mappings for classical and quantum Schrodinger systems
The classical Schrodinger bridge seeks the most likely probability law for a
diffusion process, in path space, that matches marginals at two end points in
time; the likelihood is quantified by the relative entropy between the sought
law and a prior, and the law dictates a controlled path that abides by the
specified marginals. Schrodinger proved that the optimal steering of the
density between the two end points is effected by a multiplicative functional
transformation of the prior; this transformation represents an automorphism on
the space of probability measures and has since been studied by Fortet,
Beurling and others. A similar question can be raised for processes evolving in
a discrete time and space as well as for processes defined over non-commutative
probability spaces. The present paper builds on earlier work by Pavon and
Ticozzi and begins with the problem of steering a Markov chain between given
marginals. Our approach is based on the Hilbert metric and leads to an
alternative proof which, however, is constructive. More specifically, we show
that the solution to the Schrodinger bridge is provided by the fixed point of a
contractive map. We approach in a similar manner the steering of a quantum
system across a quantum channel. We are able to establish existence of quantum
transitions that are multiplicative functional transformations of a given Kraus
map, but only for the case of uniform marginals. As in the Markov chain case,
and for uniform density matrices, the solution of the quantum bridge can be
constructed from the fixed point of a certain contractive map. For arbitrary
marginal densities, extensive numerical simulations indicate that iteration of
a similar map leads to fixed points from which we can construct a quantum
bridge. For this general case, however, a proof of convergence remains elusive.Comment: 27 page
Some General Aspects of Coset Models and Topological Kazama-Suzuki Models
We study global aspects of N=2 Kazama-Suzuki coset models by investigating
topological G/H Kazama-Suzuki models in a Lagrangian framework based on gauged
Wess-Zumino-Witten models. We first generalize Witten's analysis of the
holomorphic factorization of bosonic G/H models to models with N=1 and N=2
supersymmetry. We also find some new anomaly-free and supersymmetric models
based on non-diagonal embeddings of the gauge group. We then explain the basic
properties (action, symmetries, metric independence, ...) of the topologically
twisted G/H Kazama-Suzuki models. We explain how all of the above generalizes
to non-trivial gauge bundles.
We employ the path integral methods of localization and abelianization (shown
to be valid also for non-trivial bundles) to establish that the twisted G/H
models can be localized to bosonic H/H models (with certain quantum
corrections), and can hence be reduced to an Abelian bosonic T/T model, T a
maximal torus of H. We also present the action and the symmetries of the
coupling of these models to topological gravity. We determine the bosonic
observables for all the models based on classical flag manifolds and the
bosonic observables and their fermionic descendants for models based on complex
Grassmannians.Comment: expanded version to appear in NPB: construction of wave functions,
proof of holomorphic factorization and localization extended to non-trivial
gauge bundles; 73 pages, LaTeX fil
Detecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approach
The increasing availability of temporal network data is calling for more
research on extracting and characterizing mesoscopic structures in temporal
networks and on relating such structure to specific functions or properties of
the system. An outstanding challenge is the extension of the results achieved
for static networks to time-varying networks, where the topological structure
of the system and the temporal activity patterns of its components are
intertwined. Here we investigate the use of a latent factor decomposition
technique, non-negative tensor factorization, to extract the community-activity
structure of temporal networks. The method is intrinsically temporal and allows
to simultaneously identify communities and to track their activity over time.
We represent the time-varying adjacency matrix of a temporal network as a
three-way tensor and approximate this tensor as a sum of terms that can be
interpreted as communities of nodes with an associated activity time series. We
summarize known computational techniques for tensor decomposition and discuss
some quality metrics that can be used to tune the complexity of the factorized
representation. We subsequently apply tensor factorization to a temporal
network for which a ground truth is available for both the community structure
and the temporal activity patterns. The data we use describe the social
interactions of students in a school, the associations between students and
school classes, and the spatio-temporal trajectories of students over time. We
show that non-negative tensor factorization is capable of recovering the class
structure with high accuracy. In particular, the extracted tensor components
can be validated either as known school classes, or in terms of correlated
activity patterns, i.e., of spatial and temporal coincidences that are
determined by the known school activity schedule
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