Proceedings of International Joint Conference on Neural Networks, Atlanta, Georgia, USA, June 14-19, 2009

Community Self-Organizing Map and its Application
to Data Extraction
Taku Haraguchi, Haruna Matsushita and Yoshifumi Nishio

Abstract— The Self-Organizing Map (SOM) is a famousalgorithm for the unsupervised learning and visualization
introduced by Teuvo Kohonen. One of the most attractive
applications of SOM is clustering and several algorithms forvarious kinds of clustering problems have been reported and investigated. This study proposes the Community Self-Organizing
Map (CSOM) algorithm which reflects the community in thehuman society. In CSOM algorithm, the neurons create somecommunities according to their winning frequency. We apply
CSOM to various input data for clustering and data extraction,
and we investigate its behaviors. We confirm that CSOM
creates some communities and obtain efficient results for data
extraction.

Society
Supervisor
CEO

Laboratory

Chair

Company

I. I NTRODUCTIONI

N data mining, clustering is one of typical analysis
techniques and is studied for many applications, such asa statement, 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 an unsupervised neural network introduced by Kohonen
in 1982 and is a simplified model of the self-organization
process of the brain. SOM obtains statistical feature of
input data and is applied to a wide field of data classifications [2]−[8]. SOM can classify input data according tosimilarities and patterns which are obtained by the distance
between neurons and some visualization methods based on
SOM were proposed [9]-[13]. On the other hand, in the realworld, the amount and the complexity of data increase fromyear to year. Therefore, it is important to classify the data
and to exactly recognize condition of the data.
Meanwhile, in human society, human-beings belong to
sub-society, which is called community, such as company,
laboratory and circle of a hobby and so on (as Fig. 1). It isbased on definition that the human-beings are social animals
introduced by Aristotle. The social animal creates a society
and lives in the society. Furthermore, in the community,
it is also believed that the animals are centered around aleader and have the society. In other words, the community
is created as core on the leader of the community. In addition,in creating the community, the human-beings have sometendencies that human-beings easily gather around the leader,such as a CEO controlling the company, a supervisor controlling the laboratory and a chair keeping a circle together, andTaku Haraguchi, Haruna Matsushita and Yoshifumi Nishio are with
the Department of Electrical and Engineering, University of Tokushima,
Tokushima, Japan (phone: +81–88–656–7470; fax: +81–88–656–7471;
email: {taku, haruna, nishio}@ee.tokushima-u.ac.jp).

978-1-4244-3553-1/09/$25.00 ©2009 IEEE

Circle of hobby

Fig. 1. Some communities in human society. A central person is a “leader”
in each community.

so on. Besides the human-beings belong to the community,
there are also human-beings excluded from the community.
In this study, we propose a new type of SOM algorithm,
which is called Community SOM (CSOM) algorithm. The
important feature of CSOM is that neurons create someneuron-community according to their winning frequency, andthe neurons, which is not satisfied the condition, are removed
from the community including these after all leaning. We
apply CSOM for clustering and data extraction to various
input data. We confirm the efficiency of CSOM for theclustering and the data extraction.
We explain the learning algorithm of CSOM in detailin Section III. In Section IV, we apply CSOM to various
2-dimensional and 3-dimensional input data. Furthermore,
we explain the learning behaviors of CSOM in detail andconfirm the efficiency of CSOM for the clustering and thedata extraction.
II. S ELF -O RGANIZING M AP (SOM)
SOM has a two-layer structure of an input layer and acompetitive layer. 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 on the 2dimensional grid. Each neuron has a weight vectors w i =(wi1 , wi2 , · · · , wid ) (i = 1, 2, · · · , M ) with the same dimension as the input vector. The range of the input vector is1107

assumed to be between 0 and 1. The initial values of all theweight vectors are given between 0 and 1 at random.
(SOM1) Input an input vector xj to all the neurons simultaneously in parallel.
(SOM2) Find a winner c by calculating a distance between
the input vector xj and the weight vector w i of eachneuron i;c = arg min{wi − xj },i(1)where  ·  is the distance measure, in this study, we use
Euclidean distance.
(SOM3) Update the weight vectors of all the neurons as
w i (t + 1) = wi (t) + hc,i (t)(xj − w i (t)),(2)

where t is the learning step. hc,i (t) is called the neighborhood
function and is described asri − r c 2
hc,i (t) = α(t) exp −,(3)
2σ 2 (t)where r i and r c are the vectorial locations on the display
grid, α(t) is called the learning rate, and σ(t) corresponds tothe width of the neighborhood function. Both α(t) and σ(t)decrease monotonically with time, in this study, we use




t
t
α(t) = α(0) 1 −, σ(t) = σ(0) 1 −
,
T
T

(4)

(CSOM1) Input an input vector xj to all the neurons
simultaneously in parallel.
(CSOM2) Find a winner c according to Eq. (1). Increase thewinning frequency of the winner c by
Wcnew = Wcold + 1.

(CSOM3) Updated the weight vectors of all the neurons
according to Eq. (2). If t ≥ Tmin is satisfied, perform(CSOM4). If not, perform (CSOM9). Tmin is fixed parameterand the minimum number of the learning in creating community.
(CSOM4) Evaluate whether the winner c satisfies the conditions of the winning 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 the threshold value and increases with learning as
t
.
(6)
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
new community Ck as c ∈ Ck (where k = nnew ). If not, cremains in its community Ck .
(CSOM6) Find a leader lk which has become the winnermost frequently among the all neurons belonging to Ck ,according to Eq. (7) as Fig. 2.
Wth (t) =lk = arg max{Wi },iwhere T is the maximum number of the learning.
(SOM4) The steps from (SOM1) to (SOM3) are repeated for
all the input data.

A. Learning Algorithm
We explain the learning algorithm of CSOM in detail. In
CSOM, M neurons are arranged as a regular 2-dimensional
grid. A winning frequency Wi is associated with each neuron
and 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.

i ∈ Ck .

(7)

Leader lk
10III. COMMUNITY S ELF -O RGANIZING M AP (CSOM)In this study, we propose a Community SOM (CSOM)
algorithm. The important feature of CSOM is that theneurons create some neuron-community according to theirwinning frequency. In other words, in CSOM algorithm,
the winner, which satisfies the condition for the winningfrequency, and its neighborhood neurons, which satisfy thesame condition, create kth community Ck . In the community
Ck , a leader lk is a neuron that has become the winner mostfrequently among the all neurons belonging to Ck . Because
in the human society, the human-beings also creates somecommunity. This phenomenon has tendency that humanbeings gather around a leader.

(5)

12

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5

Community Ck

Fig. 2. How to update leader lk in community Ck . Number in each neuron
denotes its winning frequency Wi . The neuron with Wi = 20, which is
the highest winning frequency among the neurons in the community Ck ,becomes the leader lk .

(CSOM7) Find neurons, whose winning frequency arehigher than Wth (t), in 1-neighborhoods of the winner c,then consider whether they belong to any community. If thisneighborhood neuron belongs to any community, perform(CSOM8). If not, affiliate it to the community Ck including
the winner c in Fig. 3, update the leader lk as (CSOM6), andperform (CSOM9).
(CSOM8) Compare the winning frequencies of two leaders between the community including the winner and thecommunity including winner’s neighborhood neuron. Lossof generality, assume that the winner c belongs to C1 and1108

Leader l1
Winner neuron c

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C2
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keeps on belonging to C2 .

Neighborhood neuron
absorb into C1 .

Winner’s
neighborhood neuron

(a)

(b)

Fig. 4. How to determine whether a community C1 absorb a community C2 including a neighborhood neuron. Number in each neuron denotes its winningfrequency Wi . The leader l1 and l2 are a neuron with the highest winning frequency in the community C1 and in the community C2 , respectively. (a)As the winning frequency Wl1 = 20 of the leader l1 is lower than the winning frequency Wl2 = 25 of the leader l2 , the neighborhood neuron keeps on
belonging to C2 . (b) As Wl1 = 20 is higher than Wl2 = 18, the neighborhood neuron is absorbed into C1 .

Winner neuron cand its community Ck

Winner neuron

c

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1-neighborhoodsEx.) Wth (t) = 9

This neuron does not satisfy thecondition of winning frequency.

Fig. 3. 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.

its neighborhood neuron belongs to C2 . The leaders of C1
and C2 are assumed as l1 and l2 , respectively. If Wl2 ≥
Wl1 , the neighborhood neuron keeps on belonging to C2 as
Fig. 4(a). If not, the neighborhood neuron belonging to C2
are absorbed into C1 as Fig. 4(b). Then, in a specific case, if
the neighborhood neuron is the leader l2 in the community
C2 , all the neurons belonging to C2 are absorbed into C1 anddecrease 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 > T /2M for each particle i. If it is not satisfied, remove
the particle i from the community including it.
IV. LEARNING RESULTS OF CSOM
A. For 2-dimensional input data (1)We consider the 2-dimensional input data generated by
the probability density function as shown in Fig. 5(a). Thisdata has four clusters, however, it is difficult to find fourclusters because the each cluster is close to each other and

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Fig. 5. Clustering for 2-dimensional input data. (a) Input data. (b) Learning
result of the conventional SOM.

the density of each cluster is different. The total number ofthe input data N is 1000. The top-left cluster has 350 data,
the top-right cluster has 200 data, left lower cluster has 150
data, right lower cluster has 300 data, and the variance of all
the clusters are the same values. The conventional SOM and
CSOM have 100 neurons (10 × 10). 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;α(0) = 0.3, σ(0) = 3.0, Tmin =T.
3

The learning result of the conventional SOM is shown in
Fig. 5(b). We can see that the conventional SOM has some
inactive neurons, which are on a part without the input data,
between clusters and the boundary line between clusters are
not clear.
1) Behavior of CSOM: Let us consider the learning
process and behaviors of CSOM in detail as Fig. 6. In
the early stage of learning as Fig. 6(b), all the neurons do
not belong to any communities, In Fig. 6(c), some neurons

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Fig. 6. Clustering by using CSOM for 2-dimensional input data. L, #, I, o, M, 1 and G denote from the largest community C1 to the seventh largest
community C7 , respectively. (a) Initial state (t = 0). (b) t = 4999. (c) t = 5200. (d) t = 5500. (e) t = 11000. (f) t = 13000. (g) Learning result before(CSOM9) (t = 15000). (h) Learning result after (CSOM9) (t = 15000).

belong to create small communities because Tmin = 5000,
however, the number of their communities are too much.
Furthermore, in Fig. 6(d), as small communities absorb
some neurons according to (CSOM7), or they merge withother small community according to (CSOM8), then theirsizes grow gradually. In the middle stage of learning as
Figs. 6(e) and (f), the size of communities grow larger
because the neurons, which are self-organizing each cluster,belong to any community on the cluster. However, somecommunities include not only the neurons self-organizing
the cluster but also the inactive neurons. In the last stageof learning as in Fig. 6(g), the number of communities
is the same as the number of clusters. Fig. 6(h) shows
the learning result after the excluding process (CSOM10)
that the neurons, whose winning frequency are not satisfied
the condition, are excluded from the community including
them. Therefore, the inactive neurons are excluded from thecommunity because whose winning frequency is low. In otherwords, the communities of CSOM are composed of only theneurons which self-organize the clusters.

where the input data are concentrated, create the communities
and the inactive neurons belong to no community.
3) Recognition of data condition: Next, in order to recognize condition of the input data, we use the gray scale display
method [9] for the conventional SOM as follows. Figure 7
shows distances between neighboring neurons and visualizes
the cluster structure of the map after learning. Black squareson this figure mean large distance between neighboring map
nodes. Clusters are typically uniform areas of white squares.
We can see that the boundary line is not clear and it isdifficult to recognize the number of clusters and the density
on its cluster.

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2) Comparison between SOM and CSOM: The learning
result of CSOM after the excluding process according to(CSOM10) is shown in Fig. 6(h). The learning result of
CSOM is completely same as the result of the conventional
SOM, however, CSOM carries out the creating of the community in parallel. From this result, we can see that the
number of communities is the same as the number of clusters.
Furthermore, only the neurons, which self-organize the area

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Fig. 7. Visualization of result of conventional SOM for 2-dimensional data.

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Fig. 8. Extraction results of cluster. (a) Clusters extracted by the conventional SOM. (b)−(e) Cluster extracted by from the largest community C1 , which
the number of neurons belonging to is the largest, to the fourth community C4 , which the number of neurons belonging to is the smallest, by using CSOM,
respectively.

On the other hand, Table I shows the community situationof CSOM after learning. The number of communities is thesame as the number of clusters, we can understand the roughnumber of clusters by using simple method, which is torecognize the number of communities and the number ofneurons belonging to the community. In this table, the number of members denotes the number of neurons belonging toeach community, and we express the number of members as
community size. In other words, each community C1 , C2 , C3
and C4 contains to 26, 22, 13 and 9 neurons, respectively.
The community size depends on the number of the input
data in the cluster. In other words, the size of the community,
which is composed of the neurons self-organizing the cluster
containing a lot of the input data, is large.
TABLE IC OMMUNITY SITUATION OF CSOM FOR 2- DIMENSIONAL INPUT DATA .
Number of community n = 4
Community Ck
Number of members
C1
26
C2
22
C3
13
C4
9

4) Application to Data Extraction: The concept using
CSOM is to recognize condition of the input data. We carryout the cluster extraction of cluster from the results of twoalgorithms as Fig. 5(b) and Fig. 6(h). The extraction method
is a 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 CSOM, after learning, the input data, which is within aradius of R from all neurons belonging to each community
on the map, are classified into the cluster.
The extraction result of the conventional SOM is shown in
Fig. 8(a) and the extraction results of respective communities
in CSOM are shown in Figs. 8(b)−(e), respectively (R =0.05). In the conventional SOM, we can see that the result
obtains almost same as the input data, in other words, theconventional SOM can not exact the cluster relationship. In
CSOM, as all the neurons belonging to the each community
self-organize the each cluster, the results as Figs. 8(b)−(e)obtain four clusters. Besides, the community size depends
on the number of the input data in the cluster. Therefore,
we can obtain the cluster containing the most input data inall the clusters by extracting the largest community C1 , asFig. 8(b).
B. For 2-dimensional input data (2)Next, we consider another 2-dimensional input data shownin Fig. 9(a). The input data is generated artificially as follows.
The total number of the input data N is 1000, and the input
data contain two clusters. 200 data are distributed within
range from 0.4 to 0.6 horizontally and from 0.4 to 0.6
vertically. The remaining 800 data are distributed around thecentral data. We repeat the learning 15 times for all the input
data, namely T = 15000. The learning conditions are thesame as those used in Subsection IV-A.

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Fig. 9. Clustering for 2-dimensional input data. L and # denote the largest community C1 and the second largest community C2 , respectively. (a) Input
data. (b) Learning result of the conventional SOM. (c) Learning result of CSOM.

The learning results of the conventional SOM and CSOM
are shown in Figs. 9(b) and (c), respectively. We can see that
CSOM can classify outside cluster into only one community.
Furthermore, some neurons, which self-organize the central
area where the input data are concentrated, create one community. Therefore, the number of communities is the sameas the number of clusters.
Furthermore, Table II shows the community situation of
CSOM for 2-dimensional input data. Each community C1and C2 contains 39 and 16 neurons. The neurons belonging
to C1 self-organize the outside cluster, and the neurons
belonging to C2 self-organize the central cluster. The neurons
gather on the cluster containing a lot of the input data,
therefore, the community size becomes large depending onit.
TABLE II

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Fig. 10. Extraction results of cluster by using CSOM. (a) Cluster extracted
by the largest community C1 . (b) Cluster extracted by the second community
C2 .

1) Application to Data Extraction: We carry out thecluster extraction of clusters by using the learning resultof CSOM as Fig. 9(c). The extraction results of respective
communities in CSOM are shown in Figs. 10(a) and (b)(R = 0.05). Because the inactive neurons belong to nocommunity, only the neurons self-organizing the clusters
belong to the communities. Therefore, the extraction resultsof CSOM obtain exactly two clusters, which are the center
cluster and the out-side cluster.

The learning results of the conventional SOM and CSOM
are shown in Figs. 11(b) and (c), respectively. CSOM canclassify the neurons on seven clusters into respective sevencommunities. Furthermore, Table III shows the community
situation of CSOM for Hepta data. Each community fromC1 to C7 contains from 7 to 4 neurons. There is no
significant difference in the number of members between
respective communities. This is because that the number ofthe input data in each cluster is almost the same, however, thedensity distribution of central cluster and other six clusters
is different. Therefore, the each community size is almost
the same when both the number of the input data and thedensity distribution in each cluster are almost the same. In
other words, we can consider that the subtle difference ofthe community size is the influence of the initial state andorder of the input data.

C. For Hepta data

D. For 3-dimensional data

Next, we consider a 3-dimensional input data called Hepta
data set [14] shown in Fig. 11(a) which has a clustering
problem of different densities in clusters. The total numberof the input data N is 212, and the input data has sevenclusters. We repeated the learning 70 times for all the input
data, namely T = 14840. The learning conditions are thesame as those used in Subsection IV-A.

Finally, we consider another 3-dimensional input data
shown in Fig. 12(a). The input data is generated artificiallyas follows. The total number of the input data N is 1000,
and the input data contain two clusters. Centrally-located 200
data are distributed within cube 0.2 on a side. The remaining
800 data are distributed around centrally-located data. We
repeat the learning 15 times for all the input data, namely

COMMUNITY SITUATION OF CSOM FOR 2- DIMENSIONAL INPUT DATA .

Number of community n = 2
Community Ck
Number of members
C1
39
C2
16

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Fig. 11. Clustering for Hepta data. L, #, I, o, M, 1 and G denote from the largest community C1 to the seventh largest community C7 , respectively.
(a) Input data. (b) Learning result of the conventional SOM. (c) Learning result of CSOM.

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Fig. 12. Clustering for 3-dimensional input data. L and # denote the largest community C1 and the second largest community C2 , respectively. (a) Input
data. (b) Learning result of the conventional SOM. (c) Learning result of CSOM.

TABLE IIITABLE IVCOMMUNITY SITUATION OF CSOM FOR H EPTA DATA .

COMMUNITY SITUATION OF CSOM FOR 3- DIMENSIONAL INPUT DATA .

Number of community n = 7
Community Ck
Number of members
C1
7
C2
7
C3
7
C4
7
C5
6
C6
6
C7
4

Number of community n = 2
Community Ck
Number of members
C1
41
C2
17

T = 15000. The learning conditions are the same as thoseused in Subsection IV-A.
The learning results of the conventional SOM and CSOM
are shown in Figs. 12(b) and (c), respectively. CSOM canclassify the input data in the outside cluster having a complicated shape into only one community. Furthermore, someneurons, which self-organize the central area where the input
data are concentrated, create one community, and a lot of theinactive neurons belong to no community. In other words, thenumber of communities is the same as the number of clusters.
Therefore, from Table IV, we can know that the number ofclusters is two by the number of communities.

1) Application to Data Extraction: We carry out thecluster extraction of cluster by using the learning result of
CSOM as Fig. 12(c). The extraction results of respective
communities in CSOM are shown in Figs. 13(a) and (b)(R = 0.05). Because the inactive neurons belong to nocommunity, only the neurons self-organizing the clusters
belong to the communities. Therefore, the extraction resultsof CSOM obtain exactly two clusters, which are the center
cluster and the out-side cluster.
V. C ONCLUSION
In this study, we proposed a new SOM algorithm which iscalled Community Self-Organizing Map (CSOM). The important feature of CSOM is that neurons create some neuron
communities according to their winning frequency We haveapplied CSOM to the clustering and the data extraction forvarious input data for the clustering and the data extraction.

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Fig. 13. Extraction results of cluster by using CSOM. (a) Cluster extracted
by the largest community C1 . (b) Cluster extracted by the second largest
community C2 .

We have confirmed that the number of communities createdby CSOM is the same as the number of clusters, and the each
community size depends on the number of the input data inthe cluster and the shape of the cluster. We have confirmed
the effectiveness of CSOM in the application to the cluster
extraction.
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