859 research outputs found
Matched Filters for Noisy Induced Subgraph Detection
The problem of finding the vertex correspondence between two noisy graphs
with different number of vertices where the smaller graph is still large has
many applications in social networks, neuroscience, and computer vision. We
propose a solution to this problem via a graph matching matched filter:
centering and padding the smaller adjacency matrix and applying graph matching
methods to align it to the larger network. The centering and padding schemes
can be incorporated into any algorithm that matches using adjacency matrices.
Under a statistical model for correlated pairs of graphs, which yields a noisy
copy of the small graph within the larger graph, the resulting optimization
problem can be guaranteed to recover the true vertex correspondence between the
networks.
However, there are currently no efficient algorithms for solving this
problem. To illustrate the possibilities and challenges of such problems, we
use an algorithm that can exploit a partially known correspondence and show via
varied simulations and applications to {\it Drosophila} and human connectomes
that this approach can achieve good performance.Comment: 41 pages, 7 figure
Matched filters for noisy induced subgraph detection
First author draftWe consider the problem of finding the vertex correspondence between two graphs with different number of vertices where the smaller graph is still potentially large. We propose a solution to this problem via a graph matching matched filter: padding the smaller graph in different ways and then using graph matching methods to align it to the larger network. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks, though there are currently no efficient algorithms for solving this problem. We consider an approach that exploits a partially known correspondence and show via varied simulations and applications to the Drosophila connectome that in practice this approach can achieve good performance.https://arxiv.org/abs/1803.02423https://arxiv.org/abs/1803.0242
The Ubiquity of Large Graphs and Surprising Challenges of Graph Processing: Extended Survey
Graph processing is becoming increasingly prevalent across many application
domains. In spite of this prevalence, there is little research about how graphs
are actually used in practice. We performed an extensive study that consisted
of an online survey of 89 users, a review of the mailing lists, source
repositories, and whitepapers of a large suite of graph software products, and
in-person interviews with 6 users and 2 developers of these products. Our
online survey aimed at understanding: (i) the types of graphs users have; (ii)
the graph computations users run; (iii) the types of graph software users use;
and (iv) the major challenges users face when processing their graphs. We
describe the participants' responses to our questions highlighting common
patterns and challenges. Based on our interviews and survey of the rest of our
sources, we were able to answer some new questions that were raised by
participants' responses to our online survey and understand the specific
applications that use graph data and software. Our study revealed surprising
facts about graph processing in practice. In particular, real-world graphs
represent a very diverse range of entities and are often very large,
scalability and visualization are undeniably the most pressing challenges faced
by participants, and data integration, recommendations, and fraud detection are
very popular applications supported by existing graph software. We hope these
findings can guide future research
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