64,340 research outputs found
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
Adversarial Directed Graph Embedding
Node representation learning for directed graphs is critically important to
facilitate many graph mining tasks. To capture the directed edges between
nodes, existing methods mostly learn two embedding vectors for each node,
source vector and target vector. However, these methods learn the source and
target vectors separately. For the node with very low indegree or outdegree,
the corresponding target vector or source vector cannot be effectively learned.
In this paper, we propose a novel Directed Graph embedding framework based on
Generative Adversarial Network, called DGGAN. The main idea is to use
adversarial mechanisms to deploy a discriminator and two generators that
jointly learn each node's source and target vectors. For a given node, the two
generators are trained to generate its fake target and source neighbor nodes
from the same underlying distribution, and the discriminator aims to
distinguish whether a neighbor node is real or fake. The two generators are
formulated into a unified framework and could mutually reinforce each other to
learn more robust source and target vectors. Extensive experiments show that
DGGAN consistently and significantly outperforms existing state-of-the-art
methods across multiple graph mining tasks on directed graphs.Comment: 8 pages, 5 figure
Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms
We consider optimal distributed computation of a given function of
distributed data. The input (data) nodes and the sink node that receives the
function form a connected network that is described by an undirected weighted
network graph. The algorithm to compute the given function is described by a
weighted directed acyclic graph and is called the computation graph. An
embedding defines the computation communication sequence that obtains the
function at the sink. Two kinds of optimal embeddings are sought, the embedding
that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes
cost of one instance of computation of function. This abstraction is motivated
by three applications---in-network computation over sensor networks, operator
placement in distributed databases, and module placement in distributed
computing.
We first show that obtaining minimum-delay and minimum-cost embeddings are
both NP-complete problems and that cost minimization is actually MAX SNP-hard.
Next, we consider specific forms of the computation graph for which polynomial
time solutions are possible. When the computation graph is a tree, a polynomial
time algorithm to obtain the minimum delay embedding is described. Next, for
the case when the function is described by a layered graph we describe an
algorithm that obtains the minimum cost embedding in polynomial time. This
algorithm can also be used to obtain an approximation for delay minimization.
We then consider bounded treewidth computation graphs and give an algorithm to
obtain the minimum cost embedding in polynomial time
Symmetrization for Embedding Directed Graphs
Recently, one has seen a surge of interest in developing such methods
including ones for learning such representations for (undirected) graphs (while
preserving important properties). However, most of the work to date on
embedding graphs has targeted undirected networks and very little has focused
on the thorny issue of embedding directed networks. In this paper, we instead
propose to solve the directed graph embedding problem via a two-stage approach:
in the first stage, the graph is symmetrized in one of several possible ways,
and in the second stage, the so-obtained symmetrized graph is embedded using
any state-of-the-art (undirected) graph embedding algorithm. Note that it is
not the objective of this paper to propose a new (undirected) graph embedding
algorithm or discuss the strengths and weaknesses of existing ones; all we are
saying is that whichever be the suitable graph embedding algorithm, it will fit
in the above proposed symmetrization framework.Comment: has been accepted to The Thirty-Third AAAI Conference on Artificial
Intelligence (AAAI 2019) Student Abstract and Poster Progra
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