2009 International Workshop on Nonlinear Maps and their Applications
NOMA'09, Urbino, Italy, September 10-11, 2009 (paper id: 008)

Behavior of Community Self-Organizing Map
with Camaraderie
Taku Haraguchi

Haruna Matsushita

Yoshifumi Nishio

Dept. Electrical and Electronic Eng.,
Tokushima University
Email: taku@ee.tokushima-u.ac.jp

Dept. Electrical and Electronic Eng.,
Tokushima University
Email: haruna@ee.tokushima-u.ac.jp

Dept. Electrical and Electronic Eng.
Tokushima University
Email: nishio@ee.tokushima-u.ac.jp

Abstract— In the previous study, we have proposed the Community Self-Organizing Map (CSOM) that the neurons create
some neuron-community according to their winning frequencies.
In this study, we modify the algorithm of CSOM and propose
CSOM with camaraderie. As neurons belonging to any community have the camaraderie in the community, they tend to attract
each other. Therefore, the neurons belonging to any community
self-organize only concentrated part of input data including a lotof noises. We apply modify CSOM and CSOM with camaraderie
to clustering problem for clustering and data extraction, andinvestigate its behavior and its effectiveness. The efficiencies of
COM with camaraderie are confirmed by several results.

I. I NTRODUCTION
In data mining, clustering is one of typical analysis techniques and is studied for many applications, such as astatement, a pattern recognition, an image analysis and soon. Then, the Self-Organizing Map (SOM) [1] has attracted
attention for the study on clustering in recent years. SOM is anunsupervised neural network introduced by Kohonen in 1982
and is a simplified model of the self-organization process ofthe brain. SOM obtains statistical feature of input data andis applied to a wide field of data classifications [2]-[5]. SOM
can classify input data according to similarities and patterns
which are obtained by the distance between neurons and somevisualization methods based on SOM were proposed. On theother hand, in the real world, the amount and the complexityof data increase from year to year. Therefore, it is important
to investigate various extraction method of clusters from data
including a lot of noises.
Meanwhile, it is based on definition that human-beings aresocial animals introduced by Aristotle. The human-beings aeasily gather around the leader. In other words, the community
is created as core on the leader of the community. In previous
study, we have proposed the Community Self-Organizing Map(CSOM) [6] that the neurons create some neuron-community
according to their winning frequency. We have applied CSOM
for clustering and data extraction to various input data, andconfirmed the efficiency of CSOM. However, as the simulation
result of CSOM is the same as the simulation result of theconventional SOM, it is difficult to exactly extract the clusters
from data including a lot of noises.
In this study, we modify the algorithm of CSOM andpropose CSOM with camaraderie. The features of CSOM withcamaraderie are that the neurons belonging to any community

have the camaraderie in the community. Therefore, the neurons
belonging to any community self-organize the only concentrated input data for the input data including a lot of noises.
We apply the modified CSOM and CSOM with camaraderie toclustering problem for clustering, gray scale display methodand data extraction, and investigate its behavior and the its
effectiveness.
II. M ODIFIED C OMMUNITY S ELF -O RGANIZING M AP
In our previous research, we have proposed CSOM thatthe neurons create some neuron-community according to theirwinning frequency, called community learning, and we haveconfirmed the number of communities is the same as thenumber of clusters. However, the neurons, which self-organize
the the area where the input data are concentrated, can notfrequently create the exact communities. Because there is asignificant difference in the winning frequency of the theneurons located outside between other neurons. Therefore, inmost cases, CSOM can not exactly perform the community
learning.
In this study, we modify the algorithm of CSOM as follows.
All the neurons start to accumulate the winning frequency
when the neurons start to create the community. Because,
when the neurons start to accumulate the winning frequency
after certain steps of the leaning, there is little difference in thewinning frequency of the the neurons located outside between
other neurons. As the results, the flexibility of the community
learning in the modified CSOM enhances. Furthermore, inorder to enhance the flexibility of the modify CSOM we
propose CSOM with camaraderie. The features of CSOM withcamaraderie are that the neurons belonging to any community
have the camaraderie and attract each other in the community.
A. Learning Algorithm
We explain the learning algorithm of the modified CSOM
in detail. CSOM has a two-layer structure of the input layer
and the competitive layer as the conventional SOM. In the
input layer, there are d-dimensional input vectors xj =(xj1 , xj2 , · · · , xjd ) (j = 1, 2, · · · , N ). In the competitive layer,
M neurons are arranged as a regular 2-dimensional grid.
Each neuron has a weight vectors wi = (wi1 , wi2 , · · · , wid )(i = 1, 2, · · · , M ) with the same dimension as the input vector.
A winning frequency Wi is associated with each neuron and- 95 -

Leader lk

is set to zero initially: Wi = 0. The number of members
in each community Ck and the number of community nare zero. Before learning, the all neurons do not belong
to any community, however, they gradually belong to somecommunity with learning.
(CSOM1) Input an input vector xj to all the neurons simultaneously in parallel.
(CSOM2) Find a winner c by calculating a distance between
the input vector xj and the weight vector wi of each neuron i;c = arg min{kwi − xj k},i(1)where k · k is the distance measure, in this study, we use
Euclidean distance.
(CSOM3) Updated the weight vectors of all the neurons as
wCi (t + 1) = wCi (t) + hCc,i (t)(xj − wi (t)),(2)

where t is the learning step. hCc,i (t) is called the neighborhood function and is described as()
2 β(t) exp − kr i −2r c k , if i ∈ Ck
2σ
(t)
)
(
hCc,i (t) =(3)2
 α(t) exp − kr i −2r c k , otherwise,
2σ (t)

10
12

Wcnew = Wcold + 1.

Community Ck

Fig. 1. How to update leader lk in community Ck . Number in each neuron
denotes its winning frequency Wi . The neuron with Wi = 20, which is thehighest winning frequency among the neurons in the community Ck , becomesthe leader lk .

(CSOM7) Find neurons, whose winning frequency are higher
than Wth (t), in 1-neighborhoods of the winner c, then consider
whether they belong to any community. If this neighborhood
neuron belongs to any community, perform (CSOM8). If
not, affiliate it to the community Ck including the winnerc in Fig. 2, update the leader lk as (CSOM6), and perform(CSOM9).
Winner neuron cand its community Ck

Tmin t) .
(6)
T M(CSOM5) Find the community Ck including the winner c.
If winner c does not belong to any community, create a newcommunity, nnew = nold + 1, and affiliate the winner c to newcommunity Ck as c ∈ Ck (where k = nnew ). If not, c remains
in its community Ck .
(CSOM6) Find a leader lk which has become the winner mostfrequently among the all neurons belonging to Ck , according
to Eq. (7) as Fig. 1.
Wth (t) = (1 −ii ∈ Ck .

Winner neuroncCommunity Ck

10
12

20

15

5

1-neighborhoodsEx.) Wth (t) = 9

This neuron does not satisfy thecondition of winning frequency.

Fig. 2. How to update community Ck . Number in each neuron denotes
its winning frequency Wi . The winner’s 1-neighborhood neurons with higher
winning frequency than Wth (t) belong to community Ck . The neuron with
Wi = 5, which is lower winning frequency than Wth (t), belongs to nocommunity.

(5)

Evaluate whether the winner c satisfies the conditions of thewinning frequency to update the community informations. If
Wc > Wth (t) is satisfied, perform (CSOM5). If not, perform(CSOM9) without updating the community. Wth (t) is thethreshold value and increases with learning as

lk = arg max{Wi },15

5where r i and r c are the vectorial locations on the display
grid, α(t) is called the learning rate, and σ(t) corresponds
to the width of the neighborhood function. σ(t) decrease
monotonically with time;
(
)
(
)
t
t
α(t) = α(0) 1 −, σ(t) = σ(0) 1 −
, (4)
T
T
where T is the maximum number of the learning. The learning
function β(t) is explained in the next subfunction.
If t ≥ Tmin is satisfied, perform (CSOM4). If not, perform(CSOM9). Tmin is fixed parameter and the minimum numberof the learning in creating community.
(CSOM4) Increase the winning frequency of the winner c by

20

(7)

(CSOM8) Compare the winning frequencies of two leaders between the community including the winner and thecommunity including winner’s neighborhood neuron. Loss ofgenerality, assume that the winner c belongs to C1 and its
neighborhood neuron belongs to C2 . The leaders of C1 andC2 are assumed as l1 and l2 , respectively. If Wl2 ≥ Wl1 ,the neighborhood neuron keeps on belonging to C2 . If not,the neighborhood neuron belonging to C2 are absorbed into
C1 . Then, in a specific case, if the neighborhood neuron is theleader l2 in the community C2 , all the neurons belonging to C2
are absorbed into C1 and decrease the number of communities
as nnew = nold − 1.
(CSOM9) Repeat the steps from (CSOM1) to (CSOM8) for
all the input data.
(CSOM10) After all learning are finished, check whether
Wi > 3T /4M for each particle i. If it is not satisfied, remove
the particle i from the community including it.

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B. Learning function
We propose new learning function based on the learning
function proposed in our past study [5]. The value of thelearning function is determined by the distance between the
input vector xj and the weight vector wCi of the neuron
i belonging to the any community according to fellowing
equation;()
kxi − r i k2β(t) = α(t) exp −
,
(8)
2 (t)
2σC
where σC is a fixed parameter and is called a camaraderie
parameter. The camaraderie parameter controls the camaraderie of the neurons belonging to the any community. If
the parameter σC is more small value, the movement of theneurons, which are away from the input data, belonging to
the any community weakens. In this case, we can say that thecamaraderie in the community enhances.
III. E XPERIMENT R ESULTS

to the any community do not spread out of the area where
the input data are concentrated. In other words, the neurons
belonging any community have camaraderie and attract eachother in the community. From these reasons, we can confirm
that CSOM with camaraderie obtains the most effective result.
B. Visualization Method
Next, we confirm the recognition of the input data. As thesimulation result of the modified CSOM is the same as thesimulation result of the conventional SOM, we use the grayscale display method [8] for the conventional SOM and CSOM
with camaraderie as Figs. 4(a) and (b), respectively. Fromthese results, we can see that the boundary lines of CSOM
with camaraderie are clearer than the conventional SOM.
This means that the total number of neurons self-organizing
the respective clusters in CSOM with camaraderie is morethan it in the conventional SOM. Therefore, we can say that
CSOM with camaraderie obtains more exact map reflecting
the distribution state of the input data.

A. Comparison with three algorithms
We consider the 2-dimensional input data containing sevenclusters and a lot of noises as shown in Fig. 3(a). The total
number of the input data N is 1000 and 200 data are randomly
distributed within a range from 0 to 1. The respective clusters
have 800 data, and the number of each cluster and the varianceof all the clusters are about the same values. The conventional
SOM, the modified CSOM and CSOM with camaraderie have
144 neurons (12 × 12), respectively. We repeat the learning
15 times for all the input data, namely T = 15000. The
parameters for the learning for two algorithm are chosen as
follows;
T
1, σC =.
2
15
Figures 3(b), (c) and (d) show the learning results of theconventional SOM, the modified CSOM and CSOM withcamaraderie, respectively. In Figs. 3(b) and (c), we can seethat the conventional SOM is easily affected to the noises.
In addition, the simulation result of the modified CSOM isthe same as the simulation result of the conventional SOM.
Therefore, the modified CSOM is also affected to the noises
and the neurons, which self-organize the unnecessary data, also
belong to any community. On the other hand, in Fig. 3(d), we
can see that CSOM with camaraderie is not affected to thenoises and the number of communities are the same as thenumber of clusters. This means that the neurons belonging
to any community self-organize only concentrated part of the
input data. Let us consider this obtained result. In CSOM
with camaraderie, the neurons belonging to the any community
move to fit the area where the input data are concentrated. The
behavior can be explained by the learning function Eq. 8. Thislearning function enhances the movement of the neurons if theneurons belonging to the any community are close to the input
data. Meanwhile, this learning function weaken the movementof the neurons if the neurons belonging to the any community
are away from the input data. Hence, the neurons belonging

0.25
0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05

(a)

(b)

Fig. 4. Visualization of results of 2-dimensional data. (a) Conventional SOM.
(b) CSOM with camaraderie.

α(0) = 0.3, σ(0) = 3.5, Tmin =C. Application of data extraction
Next, we carry out the extraction of cluster from the resultsof three algorithm as Figs. 3(b), (c) and (d). The extraction
method is relatively simple as follows. In the conventional
SOM, after learning, the input data, which is within a radius of
R from all neurons on the map, are classified into the cluster.
In the modified CSOM and CSOM with camaraderie, after
learning, the input data, which is within a radius of R fromall neurons belonging to each community on the map, areclassified into the cluster.
The extraction result of the conventional SOM is shown in
Fig. 5(a), and the extraction results of respective communities
in the modified CSOM and CSOM with camaraderie areshown in Figs. 5(b) and (c), respectively (R = 0.05). In
the conventional SOM, we can see that the cluster obtainedby the conventional SOM includes a lot of noises. In otherwords, the conventional SOM obtains the unnecessary data.
In the modified CSOM and CSOM with camaraderie, as all
the neurons belonging to the each community self-organize
the each cluster, the results as Figs. 5(b) and (c) obtain sevenclusters and doesn’t include a lot of noises. Besides, as all
the neurons belonging to the each community self-organize- 97 -

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Simulation results for 2-dimensional data. (a) Input data. (b) Conventional SOM. (c) Conventional CSOM. (d) CSOM with camaraderie.

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Fig. 5. Extraction results of clusters. (a) Clusters extracted by the conventional SOM. (b) Clusters extracted by the modify CSOM. (c) Clusters extracted by
CSOM with camaraderie. (d) Clusters extracted by the largest community C1 by using CSOM with camaraderie.

the each cluster, we can obtain one cluster by extracting one
community, as Fig. 5(d).
Furthermore, in order to investigate the ability of threealgorithms quantitatively, we define the correct answer rate
RCI as follows [5];RCI =NrI − NeI,
NCI

(i = 1, 2, · · ·),(9)where NCI is the true number of the input data within thecluster CI , NrI is the obtained number of the desired input
data within CI , and NeI is the obtained number of undesired
input data out of CI .
TABLE IC ORRECT ANSWER RATE [%] FOR 2- DIMENSIONAL INPUT DATA .
MethodConventional SOM
CSOM
CSOM with camaraderie

NeI
115
49
38

NrI
915
847
827

Correct answer rate [%]
85.6
93.6
94.3

Table I shows the correct answer rate of the conventional
SOM, the modified CSOM and CSOM with camaraderie forthe 2-dimensional data, respectively. From this table, we cansee that the correct answer rate of CSOM with camaraderie
is the best value and NeI is smallest in three algorithms.
Therefore, we can confirm that CSOM obtains the most exact
clusters and the most effective result in three algorithms.

IV. C ONCLUSION
In this study, we have modified the algorithm of COM andproposed CSOM with camaraderie. The features of CSOM
with camaraderie are that the neurons belonging to any community have the camaraderie in the community. We haveapplied the modify COM and CSOM with camaraderie toclustering problem, and investigated the efficiency of new
algorithm and the camaraderie in the community by using
various method. In consequence, we can say that CSOM withcamaraderie obtains the most result in three algorithms.
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