40 research outputs found
Validation of Matching
We introduce a technique to compute probably approximately correct (PAC)
bounds on precision and recall for matching algorithms. The bounds require some
verified matches, but those matches may be used to develop the algorithms. The
bounds can be applied to network reconciliation or entity resolution
algorithms, which identify nodes in different networks or values in a data set
that correspond to the same entity. For network reconciliation, the bounds do
not require knowledge of the network generation process
Multimodal Network Alignment
A multimodal network encodes relationships between the same set of nodes in
multiple settings, and network alignment is a powerful tool for transferring
information and insight between a pair of networks. We propose a method for
multimodal network alignment that computes a matrix which indicates the
alignment, but produces the result as a low-rank factorization directly. We
then propose new methods to compute approximate maximum weight matchings of
low-rank matrices to produce an alignment. We evaluate our approach by applying
it on synthetic networks and use it to de-anonymize a multimodal transportation
network.Comment: 14 pages, 6 figures, Siam Data Mining 201
Maximum Likelihood Estimation and Graph Matching in Errorfully Observed Networks
Given a pair of graphs with the same number of vertices, the inexact graph
matching problem consists in finding a correspondence between the vertices of
these graphs that minimizes the total number of induced edge disagreements. We
study this problem from a statistical framework in which one of the graphs is
an errorfully observed copy of the other. We introduce a corrupting channel
model, and show that in this model framework, the solution to the graph
matching problem is a maximum likelihood estimator. Necessary and sufficient
conditions for consistency of this MLE are presented, as well as a relaxed
notion of consistency in which a negligible fraction of the vertices need not
be matched correctly. The results are used to study matchability in several
families of random graphs, including edge independent models, random regular
graphs and small-world networks. We also use these results to introduce
measures of matching feasibility, and experimentally validate the results on
simulated and real-world networks