4,859 research outputs found
Computing Vertex Centrality Measures in Massive Real Networks with a Neural Learning Model
Vertex centrality measures are a multi-purpose analysis tool, commonly used
in many application environments to retrieve information and unveil knowledge
from the graphs and network structural properties. However, the algorithms of
such metrics are expensive in terms of computational resources when running
real-time applications or massive real world networks. Thus, approximation
techniques have been developed and used to compute the measures in such
scenarios. In this paper, we demonstrate and analyze the use of neural network
learning algorithms to tackle such task and compare their performance in terms
of solution quality and computation time with other techniques from the
literature. Our work offers several contributions. We highlight both the pros
and cons of approximating centralities though neural learning. By empirical
means and statistics, we then show that the regression model generated with a
feedforward neural networks trained by the Levenberg-Marquardt algorithm is not
only the best option considering computational resources, but also achieves the
best solution quality for relevant applications and large-scale networks.
Keywords: Vertex Centrality Measures, Neural Networks, Complex Network Models,
Machine Learning, Regression ModelComment: 8 pages, 5 tables, 2 figures, version accepted at IJCNN 2018. arXiv
admin note: text overlap with arXiv:1810.1176
Multitask Learning on Graph Neural Networks: Learning Multiple Graph Centrality Measures with a Unified Network
The application of deep learning to symbolic domains remains an active
research endeavour. Graph neural networks (GNN), consisting of trained neural
modules which can be arranged in different topologies at run time, are sound
alternatives to tackle relational problems which lend themselves to graph
representations. In this paper, we show that GNNs are capable of multitask
learning, which can be naturally enforced by training the model to refine a
single set of multidimensional embeddings and decode them
into multiple outputs by connecting MLPs at the end of the pipeline. We
demonstrate the multitask learning capability of the model in the relevant
relational problem of estimating network centrality measures, focusing
primarily on producing rankings based on these measures, i.e. is vertex
more central than vertex given centrality ?. We then show that a GNN
can be trained to develop a \emph{lingua franca} of vertex embeddings from
which all relevant information about any of the trained centrality measures can
be decoded. The proposed model achieves accuracy on a test dataset of
random instances with up to 128 vertices and is shown to generalise to larger
problem sizes. The model is also shown to obtain reasonable accuracy on a
dataset of real world instances with up to 4k vertices, vastly surpassing the
sizes of the largest instances with which the model was trained ().
Finally, we believe that our contributions attest to the potential of GNNs in
symbolic domains in general and in relational learning in particular.Comment: Published at ICANN2019. 10 pages, 3 Figure
KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation
We present KADABRA, a new algorithm to approximate betweenness centrality in
directed and undirected graphs, which significantly outperforms all previous
approaches on real-world complex networks. The efficiency of the new algorithm
relies on two new theoretical contributions, of independent interest. The first
contribution focuses on sampling shortest paths, a subroutine used by most
algorithms that approximate betweenness centrality. We show that, on realistic
random graph models, we can perform this task in time
with high probability, obtaining a significant speedup with respect to the
worst-case performance. We experimentally show that this new
technique achieves similar speedups on real-world complex networks, as well.
The second contribution is a new rigorous application of the adaptive sampling
technique. This approach decreases the total number of shortest paths that need
to be sampled to compute all betweenness centralities with a given absolute
error, and it also handles more general problems, such as computing the
most central nodes. Furthermore, our analysis is general, and it might be
extended to other settings.Comment: Some typos correcte
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