27,560 research outputs found
Statistical mechanics of voting
Decision procedures aggregating the preferences of multiple agents can
produce cycles and hence outcomes which have been described heuristically as
`chaotic'. We make this description precise by constructing an explicit
dynamical system from the agents' preferences and a voting rule. The dynamics
form a one dimensional statistical mechanics model; this suggests the use of
the topological entropy to quantify the complexity of the system. We formulate
natural political/social questions about the expected complexity of a voting
rule and degree of cohesion/diversity among agents in terms of random matrix
models---ensembles of statistical mechanics models---and compute quantitative
answers in some representative cases.Comment: 9 pages, plain TeX, 2 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages
Riemannian-geometric entropy for measuring network complexity
A central issue of the science of complex systems is the quantitative
characterization of complexity. In the present work we address this issue by
resorting to information geometry. Actually we propose a constructive way to
associate to a - in principle any - network a differentiable object (a
Riemannian manifold) whose volume is used to define an entropy. The
effectiveness of the latter to measure networks complexity is successfully
proved through its capability of detecting a classical phase transition
occurring in both random graphs and scale--free networks, as well as of
characterizing small Exponential random graphs, Configuration Models and real
networks.Comment: 15 pages, 3 figure
Functional Complexity Measure for Networks
We propose a complexity measure which addresses the functional flexibility of
networks. It is conjectured that the functional flexibility is reflected in the
topological diversity of the assigned graphs, resulting from a resolution of
their vertices and a rewiring of their edges under certain constraints. The
application will be a classification of networks in artificial or biological
systems, where functionality plays a central role.Comment: 11 pages, LaTeX2e, 5 PostScript figure
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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