7,168 research outputs found
A Degeneracy Framework for Scalable Graph Autoencoders
In this paper, we present a general framework to scale graph autoencoders
(AE) and graph variational autoencoders (VAE). This framework leverages graph
degeneracy concepts to train models only from a dense subset of nodes instead
of using the entire graph. Together with a simple yet effective propagation
mechanism, our approach significantly improves scalability and training speed
while preserving performance. We evaluate and discuss our method on several
variants of existing graph AE and VAE, providing the first application of these
models to large graphs with up to millions of nodes and edges. We achieve
empirically competitive results w.r.t. several popular scalable node embedding
methods, which emphasizes the relevance of pursuing further research towards
more scalable graph AE and VAE.Comment: International Joint Conference on Artificial Intelligence (IJCAI
2019
Gravity-Inspired Graph Autoencoders for Directed Link Prediction
Graph autoencoders (AE) and variational autoencoders (VAE) recently emerged
as powerful node embedding methods. In particular, graph AE and VAE were
successfully leveraged to tackle the challenging link prediction problem,
aiming at figuring out whether some pairs of nodes from a graph are connected
by unobserved edges. However, these models focus on undirected graphs and
therefore ignore the potential direction of the link, which is limiting for
numerous real-life applications. In this paper, we extend the graph AE and VAE
frameworks to address link prediction in directed graphs. We present a new
gravity-inspired decoder scheme that can effectively reconstruct directed
graphs from a node embedding. We empirically evaluate our method on three
different directed link prediction tasks, for which standard graph AE and VAE
perform poorly. We achieve competitive results on three real-world graphs,
outperforming several popular baselines.Comment: ACM International Conference on Information and Knowledge Management
(CIKM 2019
Photometric Redshift Estimation Using Spectral Connectivity Analysis
The development of fast and accurate methods of photometric redshift
estimation is a vital step towards being able to fully utilize the data of
next-generation surveys within precision cosmology. In this paper we apply a
specific approach to spectral connectivity analysis (SCA; Lee & Wasserman 2009)
called diffusion map. SCA is a class of non-linear techniques for transforming
observed data (e.g., photometric colours for each galaxy, where the data lie on
a complex subset of p-dimensional space) to a simpler, more natural coordinate
system wherein we apply regression to make redshift predictions. As SCA relies
upon eigen-decomposition, our training set size is limited to ~ 10,000
galaxies; we use the Nystrom extension to quickly estimate diffusion
coordinates for objects not in the training set. We apply our method to 350,738
SDSS main sample galaxies, 29,816 SDSS luminous red galaxies, and 5,223
galaxies from DEEP2 with CFHTLS ugriz photometry. For all three datasets, we
achieve prediction accuracies on par with previous analyses, and find that use
of the Nystrom extension leads to a negligible loss of prediction accuracy
relative to that achieved with the training sets. As in some previous analyses
(e.g., Collister & Lahav 2004, Ball et al. 2008), we observe that our
predictions are generally too high (low) in the low (high) redshift regimes. We
demonstrate that this is a manifestation of attenuation bias, wherein
measurement error (i.e., uncertainty in diffusion coordinates due to
uncertainty in the measured fluxes/magnitudes) reduces the slope of the
best-fit regression line. Mitigation of this bias is necessary if we are to use
photometric redshift estimates produced by computationally efficient empirical
methods in precision cosmology.Comment: Resubmitted to MNRAS (11 pages, 8 figures
Uniqueness of diffusion on domains with rough boundaries
Let be a domain in and
a
quadratic form on with domain where the
are real symmetric -functions with
for almost all . Further assume there are such that for where is the Euclidean
distance to the boundary of .
We assume that is Ahlfors -regular and if , the Hausdorff
dimension of , is larger or equal to we also assume a mild
uniformity property for in the neighbourhood of one . Then
we establish that is Markov unique, i.e. it has a unique Dirichlet form
extension, if and only if . The result applies to forms
on Lipschitz domains or on a wide class of domains with a self-similar
fractal. In particular it applies to the interior or exterior of the von Koch
snowflake curve in or the complement of a uniformly disconnected
set in .Comment: 25 pages, 2 figure
Distance entropy cartography characterises centrality in complex networks
We introduce distance entropy as a measure of homogeneity in the distribution
of path lengths between a given node and its neighbours in a complex network.
Distance entropy defines a new centrality measure whose properties are
investigated for a variety of synthetic network models. By coupling distance
entropy information with closeness centrality, we introduce a network
cartography which allows one to reduce the degeneracy of ranking based on
closeness alone. We apply this methodology to the empirical multiplex lexical
network encoding the linguistic relationships known to English speaking
toddlers. We show that the distance entropy cartography better predicts how
children learn words compared to closeness centrality. Our results highlight
the importance of distance entropy for gaining insights from distance patterns
in complex networks.Comment: 11 page
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