1,517 research outputs found
Estimating parameters of a multipartite loglinear graph model via the EM algorithm
We will amalgamate the Rash model (for rectangular binary tables) and the
newly introduced - models (for random undirected graphs) in the
framework of a semiparametric probabilistic graph model. Our purpose is to give
a partition of the vertices of an observed graph so that the generated
subgraphs and bipartite graphs obey these models, where their strongly
connected parameters give multiscale evaluation of the vertices at the same
time. In this way, a heterogeneous version of the stochastic block model is
built via mixtures of loglinear models and the parameters are estimated with a
special EM iteration. In the context of social networks, the clusters can be
identified with social groups and the parameters with attitudes of people of
one group towards people of the other, which attitudes depend on the cluster
memberships. The algorithm is applied to randomly generated and real-word data
A Coherent Ising Machine Based On Degenerate Optical Parametric Oscillators
A degenerate optical parametric oscillator network is proposed to solve the
NP-hard problem of finding a ground state of the Ising model. The underlying
operating mechanism originates from the bistable output phase of each
oscillator and the inherent preference of the network in selecting oscillation
modes with the minimum photon decay rate. Computational experiments are
performed on all instances reducible to the NP-hard MAX-CUT problems on cubic
graphs of order up to 20. The numerical results reasonably suggest the
effectiveness of the proposed network.Comment: 18 pages, 6 figure
Clustering and Community Detection with Imbalanced Clusters
Spectral clustering methods which are frequently used in clustering and
community detection applications are sensitive to the specific graph
constructions particularly when imbalanced clusters are present. We show that
ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to
imbalanced cluster sizes since they tend to emphasize cut sizes over cut
values. We propose a graph partitioning problem that seeks minimum cut
partitions under minimum size constraints on partitions to deal with imbalanced
cluster sizes. Our approach parameterizes a family of graphs by adaptively
modulating node degrees on a fixed node set, yielding a set of parameter
dependent cuts reflecting varying levels of imbalance. The solution to our
problem is then obtained by optimizing over these parameters. We present
rigorous limit cut analysis results to justify our approach and demonstrate the
superiority of our method through experiments on synthetic and real datasets
for data clustering, semi-supervised learning and community detection.Comment: Extended version of arXiv:1309.2303 with new applications. Accepted
to IEEE TSIP
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