2,124 research outputs found
Learning multifractal structure in large networks
Generating random graphs to model networks has a rich history. In this paper,
we analyze and improve upon the multifractal network generator (MFNG)
introduced by Palla et al. We provide a new result on the probability of
subgraphs existing in graphs generated with MFNG. From this result it follows
that we can quickly compute moments of an important set of graph properties,
such as the expected number of edges, stars, and cliques. Specifically, we show
how to compute these moments in time complexity independent of the size of the
graph and the number of recursive levels in the generative model. We leverage
this theory to a new method of moments algorithm for fitting large networks to
MFNG. Empirically, this new approach effectively simulates properties of
several social and information networks. In terms of matching subgraph counts,
our method outperforms similar algorithms used with the Stochastic Kronecker
Graph model. Furthermore, we present a fast approximation algorithm to generate
graph instances following the multi- fractal structure. The approximation
scheme is an improvement over previous methods, which ran in time complexity
quadratic in the number of vertices. Combined, our method of moments and fast
sampling scheme provide the first scalable framework for effectively modeling
large networks with MFNG
Multifractal analysis of perceptron learning with errors
Random input patterns induce a partition of the coupling space of a
perceptron into cells labeled by their output sequences. Learning some data
with a maximal error rate leads to clusters of neighboring cells. By analyzing
the internal structure of these clusters with the formalism of multifractals,
we can handle different storage and generalization tasks for lazy students and
absent-minded teachers within one unified approach. The results also allow some
conclusions on the spatial distribution of cells.Comment: 11 pages, RevTex, 3 eps figures, version to be published in Phys.
Rev. E 01Jan9
Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks
Random input patterns induce a partition of the coupling space of
feed-forward neural networks into different cells according to the generated
output sequence. For the perceptron this partition forms a random multifractal
for which the spectrum can be calculated analytically using the
replica trick. Phase transition in the multifractal spectrum correspond to the
crossover from percolating to non-percolating cell sizes. Instabilities of
negative moments are related to the VC-dimension.Comment: 10 pages, Latex, submitted to PR
The Methods to Improve Quality of Service by Accounting Secure Parameters
A solution to the problem of ensuring quality of service, providing a greater
number of services with higher efficiency taking into account network security
is proposed. In this paper, experiments were conducted to analyze the effect of
self-similarity and attacks on the quality of service parameters. Method of
buffering and control of channel capacity and calculating of routing cost
method in the network, which take into account the parameters of traffic
multifractality and the probability of detecting attacks in telecommunications
networks were proposed. The both proposed methods accounting the given
restrictions on the delay time and the number of lost packets for every type
quality of service traffic. During simulation the parameters of transmitted
traffic (self-similarity, intensity) and the parameters of network (current
channel load, node buffer size) were changed and the maximum allowable load of
network was determined. The results of analysis show that occurrence of
overload when transmitting traffic over a switched channel associated with
multifractal traffic characteristics and presence of attack. It was shown that
proposed methods can reduce the lost data and improve the efficiency of network
resources.Comment: 10 pages, 1 figure, 1 equation, 1 table. arXiv admin note: text
overlap with arXiv:1904.0520
Time series classification based on fractal properties
The article considers classification task of fractal time series by the meta
algorithms based on decision trees. Binomial multiplicative stochastic cascades
are used as input time series. Comparative analysis of the classification
approaches based on different features is carried out. The results indicate the
advantage of the machine learning methods over the traditional estimating the
degree of self-similarity.Comment: 4 pages, 2 figures, 3 equations, 1 tabl
Multifractality and percolation in the coupling space of perceptrons
The coupling space of perceptrons with continuous as well as with binary
weights gets partitioned into a disordered multifractal by a set of random input patterns. The multifractal spectrum can be
calculated analytically using the replica formalism. The storage capacity and
the generalization behaviour of the perceptron are shown to be related to
properties of which are correctly described within the replica
symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a
transition from percolating to non-percolating cells. The existence of empty
cells gives rise to singularities in the multifractal spectrum. The analytical
results for binary couplings are corroborated by numerical studies.Comment: 13 pages, revtex, 4 eps figures, version accepted for publication in
Phys. Rev.
Rotated multifractal network generator
The recently introduced multifractal network generator (MFNG), has been shown
to provide a simple and flexible tool for creating random graphs with very
diverse features. The MFNG is based on multifractal measures embedded in 2d,
leading also to isolated nodes, whose number is relatively low for realistic
cases, but may become dominant in the limiting case of infinitely large network
sizes. Here we discuss the relation between this effect and the information
dimension for the 1d projection of the link probability measure (LPM), and
argue that the node isolation can be avoided by a simple transformation of the
LPM based on rotation.Comment: Accepted for publication in JSTA
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