Post on 24-Feb-2016
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Particle competition for complex network
community detection Author: Marcos G. Quiles, Liang Zhao,
Ronaldo L. Alonso, and Roseli A.RomeroAn Interdisciplinary Journal of Nonlinear Science
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The concept-Randomness and Determinism-Competition The method The experiments
Outline
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Human decision making is a tradoff between randomness and determinism.
When one has complete knowledge about a
specific subject, a deterministic choice can be made, on the other hand, a random decision is made when one knows nothing about it.
Randomness and Determinism
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Competition is a natural process widely observed in living sharing limited resources.
Competition
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In the proposed model, particles walk in the network and compete with each other that each of them tries to possess as many nodes as possible.
The process continues until a dynamical equilibrium(when each community has only one particle) state is reached.
The method
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Each particle has two variables )(,)( tt jvj
j
0)(if,))(()(
0)(if,))(()(
0)(if,)(
)1(
)1(
],[)(
particleofnexploratioofabilitythe
orncompetitiooflevelthezingcharacteripotentialparticletheis:)(
timeatparticlebyvisitedbeingnodethe:)(
min
max
maxmin
jijj
jijj
ij
j
ivj
j
j
j
jivj
tvtt
tvtt
tvt
t
vt
t
t
tvt
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Each node has three variables iv
momentat this
notor particle aby visitedis node a whether means, iablebinary var a is:
at time node of potential the:)(
state free aat is node if 0or
particle aby occpied if value theit takes
.timeat node theof particleowner theregistersfirst the:)(
ii
ii
jj
ii
vv
tvtv
tvtv
iii vtvtv ,)(,)(
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jiij
jiivi
ii
i
iij
iii
tvvt
tvvtv
vtv
tv
tvv
vtvtv
)(and1if,)1(
)(and1if,})(,max{
0if,)(
)1(
)(and1if,
0if,)()1(
min
min
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Each particle has probability pdet to take deterministic moving and 1- pdet to take random moving
Random moving: randomly selects a neighbor to visit(immediately return to the node visited at last iteration is not allowed ,unless the node’s degree is 1).
Deterministic moving: allows the particle always to visit a node that is already owned by it.
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2 3
5 4
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A particle encounters one of the following three situation s for each visit
1.If a node being visited by a particle has no owner yet.
2.If a node being visited by a particle belong to the particle itself.
3. If a node being visited by a particle belong to another particle.
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At beginning, K particles are put at K randomly chosen vertices of a network.
Each particle has initial potential
Each node has initial potential
Still at this moment, all vertices are free
j min)0( j
iv min)0( iv
0)0( iv
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T=0
13
1
2 3
5 4
67
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0)0(2 v
0)0(7 v
21 )0( vv
72 )0( vv
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The Experiments
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