671 research outputs found
ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers
Solving the electronic structure from a generalized or standard eigenproblem
is often the bottleneck in large scale calculations based on Kohn-Sham
density-functional theory. This problem must be addressed by essentially all
current electronic structure codes, based on similar matrix expressions, and by
high-performance computation. We here present a unified software interface,
ELSI, to access different strategies that address the Kohn-Sham eigenvalue
problem. Currently supported algorithms include the dense generalized
eigensolver library ELPA, the orbital minimization method implemented in
libOMM, and the pole expansion and selected inversion (PEXSI) approach with
lower computational complexity for semilocal density functionals. The ELSI
interface aims to simplify the implementation and optimal use of the different
strategies, by offering (a) a unified software framework designed for the
electronic structure solvers in Kohn-Sham density-functional theory; (b)
reasonable default parameters for a chosen solver; (c) automatic conversion
between input and internal working matrix formats, and in the future (d)
recommendation of the optimal solver depending on the specific problem.
Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800
basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table
Neural Graph Collaborative Filtering
Learning vector representations (aka. embeddings) of users and items lies at
the core of modern recommender systems. Ranging from early matrix factorization
to recently emerged deep learning based methods, existing efforts typically
obtain a user's (or an item's) embedding by mapping from pre-existing features
that describe the user (or the item), such as ID and attributes. We argue that
an inherent drawback of such methods is that, the collaborative signal, which
is latent in user-item interactions, is not encoded in the embedding process.
As such, the resultant embeddings may not be sufficient to capture the
collaborative filtering effect.
In this work, we propose to integrate the user-item interactions -- more
specifically the bipartite graph structure -- into the embedding process. We
develop a new recommendation framework Neural Graph Collaborative Filtering
(NGCF), which exploits the user-item graph structure by propagating embeddings
on it. This leads to the expressive modeling of high-order connectivity in
user-item graph, effectively injecting the collaborative signal into the
embedding process in an explicit manner. We conduct extensive experiments on
three public benchmarks, demonstrating significant improvements over several
state-of-the-art models like HOP-Rec and Collaborative Memory Network. Further
analysis verifies the importance of embedding propagation for learning better
user and item representations, justifying the rationality and effectiveness of
NGCF. Codes are available at
https://github.com/xiangwang1223/neural_graph_collaborative_filtering.Comment: SIGIR 2019; the latest version of NGCF paper, which is distinct from
the version published in ACM Digital Librar
NAIS: Neural Attentive Item Similarity Model for Recommendation
Item-to-item collaborative filtering (aka. item-based CF) has been long used
for building recommender systems in industrial settings, owing to its
interpretability and efficiency in real-time personalization. It builds a
user's profile as her historically interacted items, recommending new items
that are similar to the user's profile. As such, the key to an item-based CF
method is in the estimation of item similarities. Early approaches use
statistical measures such as cosine similarity and Pearson coefficient to
estimate item similarities, which are less accurate since they lack tailored
optimization for the recommendation task. In recent years, several works
attempt to learn item similarities from data, by expressing the similarity as
an underlying model and estimating model parameters by optimizing a
recommendation-aware objective function. While extensive efforts have been made
to use shallow linear models for learning item similarities, there has been
relatively less work exploring nonlinear neural network models for item-based
CF.
In this work, we propose a neural network model named Neural Attentive Item
Similarity model (NAIS) for item-based CF. The key to our design of NAIS is an
attention network, which is capable of distinguishing which historical items in
a user profile are more important for a prediction. Compared to the
state-of-the-art item-based CF method Factored Item Similarity Model (FISM),
our NAIS has stronger representation power with only a few additional
parameters brought by the attention network. Extensive experiments on two
public benchmarks demonstrate the effectiveness of NAIS. This work is the first
attempt that designs neural network models for item-based CF, opening up new
research possibilities for future developments of neural recommender systems
Fast matrix computations for pair-wise and column-wise commute times and Katz scores
We first explore methods for approximating the commute time and Katz score
between a pair of nodes. These methods are based on the approach of matrices,
moments, and quadrature developed in the numerical linear algebra community.
They rely on the Lanczos process and provide upper and lower bounds on an
estimate of the pair-wise scores. We also explore methods to approximate the
commute times and Katz scores from a node to all other nodes in the graph.
Here, our approach for the commute times is based on a variation of the
conjugate gradient algorithm, and it provides an estimate of all the diagonals
of the inverse of a matrix. Our technique for the Katz scores is based on
exploiting an empirical localization property of the Katz matrix. We adopt
algorithms used for personalized PageRank computing to these Katz scores and
theoretically show that this approach is convergent. We evaluate these methods
on 17 real world graphs ranging in size from 1000 to 1,000,000 nodes. Our
results show that our pair-wise commute time method and column-wise Katz
algorithm both have attractive theoretical properties and empirical
performance.Comment: 35 pages, journal version of
http://dx.doi.org/10.1007/978-3-642-18009-5_13 which has been submitted for
publication. Please see
http://www.cs.purdue.edu/homes/dgleich/publications/2011/codes/fast-katz/ for
supplemental code
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