102,250 research outputs found
Spatial preferential attachment networks: Power laws and clustering coefficients
We define a class of growing networks in which new nodes are given a spatial
position and are connected to existing nodes with a probability mechanism
favoring short distances and high degrees. The competition of preferential
attachment and spatial clustering gives this model a range of interesting
properties. Empirical degree distributions converge to a limit law, which can
be a power law with any exponent . The average clustering coefficient
of the networks converges to a positive limit. Finally, a phase transition
occurs in the global clustering coefficients and empirical distribution of edge
lengths when the power-law exponent crosses the critical value . Our
main tool in the proof of these results is a general weak law of large numbers
in the spirit of Penrose and Yukich.Comment: Published in at http://dx.doi.org/10.1214/14-AAP1006 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application
The limited penetrable horizontal visibility algorithm is a new time analysis
tool and is a further development of the horizontal visibility algorithm. We
present some exact results on the topological properties of the limited
penetrable horizontal visibility graph associated with random series. We show
that the random series maps on a limited penetrable horizontal visibility graph
with exponential degree distribution ,
independent of the probability distribution from which the series was
generated. We deduce the exact expressions of the mean degree and the
clustering coefficient and demonstrate the long distance visibility property.
Numerical simulations confirm the accuracy of our theoretical results. We then
examine several deterministic chaotic series (a logistic map, the
Hnon map, the Lorentz system, and an energy price chaotic system)
and a real crude oil price series to test our results. The empirical results
show that the limited penetrable horizontal visibility algorithm is direct, has
a low computational cost when discriminating chaos from uncorrelated
randomness, and is able to measure the global evolution characteristics of the
real time series.Comment: 23 pages, 12 figure
Toward a generic representation of random variables for machine learning
This paper presents a pre-processing and a distance which improve the
performance of machine learning algorithms working on independent and
identically distributed stochastic processes. We introduce a novel
non-parametric approach to represent random variables which splits apart
dependency and distribution without losing any information. We also propound an
associated metric leveraging this representation and its statistical estimate.
Besides experiments on synthetic datasets, the benefits of our contribution is
illustrated through the example of clustering financial time series, for
instance prices from the credit default swaps market. Results are available on
the website www.datagrapple.com and an IPython Notebook tutorial is available
at www.datagrapple.com/Tech for reproducible research.Comment: submitted to Pattern Recognition Letter
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