66,327 research outputs found
Random graphs with a given degree sequence
Large graphs are sometimes studied through their degree sequences (power law
or regular graphs). We study graphs that are uniformly chosen with a given
degree sequence. Under mild conditions, it is shown that sequences of such
graphs have graph limits in the sense of Lov\'{a}sz and Szegedy with
identifiable limits. This allows simple determination of other features such as
the number of triangles. The argument proceeds by studying a natural
exponential model having the degree sequence as a sufficient statistic. The
maximum likelihood estimate (MLE) of the parameters is shown to be unique and
consistent with high probability. Thus parameters can be consistently
estimated based on a sample of size one. A fast, provably convergent, algorithm
for the MLE is derived. These ingredients combine to prove the graph limit
theorem. Along the way, a continuous version of the Erd\H{o}s--Gallai
characterization of degree sequences is derived.Comment: Published in at http://dx.doi.org/10.1214/10-AAP728 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Maximal entropy random networks with given degree distribution
Using a maximum entropy principle to assign a statistical weight to any
graph, we introduce a model of random graphs with arbitrary degree distribution
in the framework of standard statistical mechanics. We compute the free energy
and the distribution of connected components. We determine the size of the
percolation cluster above the percolation threshold. The conditional degree
distribution on the percolation cluster is also given. We briefly present the
analogous discussion for oriented graphs, giving for example the percolation
criterion.Comment: 22 pages, LateX, no figur
One-class classifiers based on entropic spanning graphs
One-class classifiers offer valuable tools to assess the presence of outliers
in data. In this paper, we propose a design methodology for one-class
classifiers based on entropic spanning graphs. Our approach takes into account
the possibility to process also non-numeric data by means of an embedding
procedure. The spanning graph is learned on the embedded input data and the
outcoming partition of vertices defines the classifier. The final partition is
derived by exploiting a criterion based on mutual information minimization.
Here, we compute the mutual information by using a convenient formulation
provided in terms of the -Jensen difference. Once training is
completed, in order to associate a confidence level with the classifier
decision, a graph-based fuzzy model is constructed. The fuzzification process
is based only on topological information of the vertices of the entropic
spanning graph. As such, the proposed one-class classifier is suitable also for
data characterized by complex geometric structures. We provide experiments on
well-known benchmarks containing both feature vectors and labeled graphs. In
addition, we apply the method to the protein solubility recognition problem by
considering several representations for the input samples. Experimental results
demonstrate the effectiveness and versatility of the proposed method with
respect to other state-of-the-art approaches.Comment: Extended and revised version of the paper "One-Class Classification
Through Mutual Information Minimization" presented at the 2016 IEEE IJCNN,
Vancouver, Canad
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