Particles Competition and
Cooperation in Networks for
Semi

Supervised Learning
Fabricio
Breve
Department of Electrical & Computer Engineering
University of Alberta
Seminar

October 09, 2009
Contents
Introduction
◦
Semi

Supervised Learning
Model Description
◦
Initial Configuration
◦
Node and Particle Dynamics
◦
Random

Deterministic Walk
◦
Algorithm
Computer Simulations
◦
Synthetic Data Sets
◦
Real

World Data Sets
◦
Fuzzy Output and Outlier Detection
Conclusions
Introduction
Data sets under processing are becoming
larger
◦
In many situations only a small subset of items
can be effectively labeled
Labeling process is often:
Expensive
Time consuming
Requires intensive human involvement
Introduction
Supervised Learning
◦
Only labeled data items are used for training
Unsupervised Learning
◦
All data items are unlabeled
Semi

Supervised Learning
◦
Combines a few labeled data items with a
large number of unlabeled data to produce
betters classifiers
X. Zhu, “Semi

supervised
learning literature
survey,” Computer
Sciences, University of
Wisconsin

Madison,
Tech. Rep. 1530, 2005
.
Semi

Supervised Learning:
Graph

Based Methods
X. Zhu, Z.
Ghahramani
, and J. Lafferty, “Semi

supervised learning using
gaussian
fields
and harmonic functions,” in
Proceedings of the Twentieth International Conference on
Machine Learning
, 2003, pp. 912
–
919.
D. Zhou, O.
Bousquet
, T. N.
Lal
, J. Weston, and B.
Schölkopf
, “Learning with local and
global consistency,” in
Advances in Neural Information Processing Systems
, vol. 16. MIT
Press, 2004, pp. 321
–
328. [Online]. Available:
http://www.kyb.tuebingen.mpg.de/bs/people/weston/localglobal.pdf
X. Zhu and Z.
Ghahramani
, “Learning from labeled and unlabeled data with label
propagation,” Carnegie Mellon University, Pittsburgh, Tech. Rep. CMU

CALD

02

107,
2002. [Online]. Available:
http://citeseer.ist.psu.edu/581346.html
F. Wang and C. Zhang, “Label propagation through linear neighborhoods,”
IEEE
Transactions on Knowledge and Data Engineering
, vol. 20, no. 1, pp. 55
–
67, Jan. 2008.
A. Blum and S.
Chawla
, “Learning from labeled and unlabeled data using graph
mincuts
,” in
Proceedings of the Eighteenth International Conference on Machine Learning
.
San Francisco: Morgan Kaufmann, 2001, pp. 19
–
26.
M.
Belkin
, I.
Matveeva
, and P.
Niyogi
, “Regularization and
semisupervised
learning on
large graphs,” in
Conference on Learning Theory.
Springer, 2004, pp. 624
–
638.
M.
Belkin
, N. P., and V.
Sindhwani
, “On manifold regularization,” in
Proceedings of the
Tenth International Workshop on Artificial Intelligence and Statistics (AISTAT 2005).
New
Jersey: Society for Artificial Intelligence and Statistics, 2005, pp. 17
–
24.
T.
Joachims
, “
Transductive
learning via spectral graph partitioning,” in
Proceedings of
International Conference on Machine Learning
. AAAI Press, 2003, pp. 290
–
297.
Graph

Based Methods
Advantage of identifying many different
class distributions
Most of them share the regularization
framework, differing only in the particular
choice of the loss function and the
regularizer
Most of them have high order of
computational complexity (
O
(
n
3
)), making
their applicability limited to small or
middle size data sets.
X. Zhu, “Semi

supervised learning literature survey,” Computer
Sciences, University of Wisconsin

Madison, Tech. Rep. 1530, 2005.
Particle
Competition
M. G.
Quiles
, L. Zhao, R. L. Alonso, and R. A. F.
Romero, “Particle competition for complex
network community detection,” Chaos, vol.
18, no. 3, p. 033107, 2008. [Online]. Available:
http://link.aip.org/link/?CHAOEH/18/033107/
1
◦
Particles walk in the network and compete with
each other in such a way that each of them tries
to possess as many nodes as possible.
◦
Each particle prevents other particles to invade
its territory.
◦
Finally, each particle is confined inside a network
community.
Illustration of the
community detection
process by competitive
particle walking. The
total number if nodes is
N=128, the number of
communities is
M=4. The
proportion of out links is
z
out
/ k=0.2, and the
average node degree is
k=16. (a) Initial
configuration. Four
particles, represented
by yellow the lightest
gray, cyan the second
lightest gray, orange the
third lightest gray, and
blue the second darkest
gray, are randomly put
in the network. Red the
darkest gray represents
free nodes. (b) A
snapshot at iteration
250. (c) A snapshot at
iteration 3500. (d) A
snapshot at iteration
7000.
Proposed Method
Particles competition and cooperation in
networks
◦
Competition for possession of nodes of the
network
◦
Cooperation among particles from the same
team (label)
Each team of particles tries to dominate as many
nodes as possible in a cooperative way and at the
same time prevent intrusion of particles of other
teams.
◦
Random

deterministic walk
Initial
Configuration
A particle is generated for each labeled node of
the network
◦
Particle’s
home node
Particles with same label play for the same team
Nodes have an ownership vector
◦
Labeled nodes have ownership set to their respective
teams.
Ex: [ 1 0 0 0 ] (4 classes, node labeled as class A)
◦
Unlabeled nodes have levels set equally for each team
Ex: [ 0.25 0.25 0.25 0.25 ] (4 classes, unlabeled node)
Particles initial position is set to their respective
home nodes.
0
1
0
1
Node and Particle Dynamics
Node Dynamics
◦
When a particle selects a neighbor to visit:
It decreases the domination level of the other
teams in this same node
It increases the domination level of its team in the
target node
Exception:
Labeled nodes domination levels are fixed
0
1
0
1
t
t+1
Node and Particle Dynamics
Particle Dynamics
◦
A particle will get:
stronger when it is targeting a node being
dominated by its team
weaker when it is targeting a node dominated by
other teams
0.8
0.2
0.2
0.8
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
4
2
Node and Particle Dynamics
Distance table
◦
Keep the particle aware of
how far it is from its home
node
Prevents the particle from losing
all its strength when walking into
enemies neighborhoods
Keep them around to protect
their own neighborhood.
◦
Updated dynamically with local
information
Does not require any prior
calculation
0
1
1
2
3
3
4
4
?
Particles Walk
Shocks
◦
A particle really visits a target
node only if the domination
level of its team is higher
than others;
◦
otherwise, a shock happens
and the particle stays at the
current node until next
iteration.
How a particle chooses a
neighbor node to target?
◦
Random walk
◦
Deterministic walk
0.6
0.4
0.3
0.7
Random

deterministic walk
Random walk
The particle randomly
chooses any neighbor
to visit with no
concern about
domination levels or
distance
Deterministic walk
The particle will prefer
visiting nodes that its
team already
dominates and nodes
that are closer to their
home nodes
The particles must exhibit both movements in order to achieve
an equilibrium between exploratory and defensive behavior
0.8
0.2
0.6
0.4
0.3
0.7
Deterministic Moving Probabilities
Random Moving Probabilities
35%
18%
47%
33%
33%
33%
v
1
v
2
v
3
v
4
v
2
v
3
v
4
v
2
v
3
v
4
Algorithm
1)
Build the adjacency matrix,
2)
Set nodes domination levels,
3)
Set initial positions of particles at their corresponding
home nodes. Set particle strength and distance,
4)
Repeat steps 5 to 9 until convergence or until a predefined
number of steps has been achieved,
5)
For each particle, complete steps 6 to 9,
6)
Select the target node by using the combined random

deterministic rule,
7)
Update target node domination levels,
8)
Update particle strength,
9)
Update particle distance table,
10)
Label each unlabeled data item by the team of maximum
level of domination.
SYNTHETIC DATA SETS
Computer Simulations
Fig. 1. Classification of the
banana

shaped patterns. (a)
toy data set with 2; 000
samples divided in two classes,
20 samples are pre

labeled
(red circles and blue squares).
(b) classification achieved by
the proposed algorithm.
Fig. 3. Time series for different
values of
p
det
: (a) correct
detection rate (b) nodes’
maximum domination level (c)
average particle strength. Each
point is the average of 200
realizations using a banana

shaped toy data set
REAL

WORLD DATA
SETS
Computer Simulations
Fuzzy Output and Outlier
Detection
There are common cases where some
nodes in a network can belong to more
than one community
◦
Example: In a social network of friendship,
individuals often belong to several
communities: their families, their colleagues,
their classmates, etc
◦
These are called
overlap nodes
◦
Most known community detection algorithms
do not have a mechanism to detect them
Fuzzy Output and Outlier
Detection
Particle’s standard algorithm
◦
Final ownership levels define nodes labels
Very volatile under certain conditions
In overlap nodes the dominating team changes frequently
Levels do not correspond to overlap measures
Particle’s modified algorithm
◦
New variable: temporal averaged domination level
for each team at each node
Weighted by particle strength
Considers only the random movements
Now the champion is not the team who have won the last
games, but rather the team who have won more games in
the whole championship
Fig. 9. Fuzzy classification of two banana

shaped classes generated with different
variance parameters: (a)
s
= 0.6 (b)
s
= 0.8 (c)
s
= 1.0. Nodes size and colors
represent their respective overlap index detected by the proposed
method
.
Fig. 9. Fuzzy classification of two banana

shaped classes generated with different
variance parameters: (a)
s
= 0.6 (b)
s
= 0.8 (c)
s
= 1.0. Nodes size and colors
represent their respective overlap index detected by the proposed
method
.
Fig. 9. Fuzzy classification of two banana

shaped classes generated with different
variance parameters: (a)
s
= 0.6 (b)
s
= 0.8 (c)
s
= 1.0. Nodes size and colors
represent their respective overlap index detected by the proposed
method
.
Fig. 10. Classification of normally distributed classes (Gaussian distribution). (a) toy
data set with 1,000 samples divided in four classes, 20 samples are labeled,
5 from each class (red squares, blue triangles, green lozenges and purple stars). (b)
nodes size and colors represent their respective overlap index detected by the
proposed method.
Fig. 10. Classification of normally distributed classes (Gaussian distribution). (a) toy
data set with 1,000 samples divided in four classes, 20 samples are labeled,
5 from each class (red squares, blue triangles, green lozenges and purple stars). (b)
nodes size and colors represent their respective overlap index detected by the
proposed method.
Fig. 11. Comparative between the standard and the modified models: (a)
artificial data set with some wrongly labeled nodes (b) classification by the
standard particles method (c) classification by the modified particles method
Fig. 11. Comparative between the standard and the modified models: (a)
artificial data set with some wrongly labeled nodes (b) classification by the
standard particles method (c) classification by the modified particles method
Fig. 11. Comparative between the standard and the modified models: (a)
artificial data set with some wrongly labeled nodes (b) classification by the
standard particles method (c) classification by the modified particles method
Fig. 12. The karate club network. Nodes size and colors represent their
respective overlap index detected by the
proposed
method
.
Conclusions
The main contributions of the proposed model can
be outlined in the following way:
◦
unlike most other graph

based models, it does not rely on
loss functions or
regularizers
;
◦
it can classify data with many different distribution,
including linearly non

separable data;
◦
it has a lower order of complexity than other graph

based
models, thus it can be used to classify large data sets;
◦
it can achieve better classification rate than other classical
graph

based methods;
◦
it can detect overlap nodes and provide a fuzzy output for
each of them;
◦
it can be used to detect outliers and, consequently, to stop
error propagation.
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