Competing and Accommodating Behaviorsof Peace SOM
Haruna MATSUSHITA∗ and Yoshifumi NISHIO∗∗ Department of Electrical and Electronic Engineering, Tokushima University

2–1 Minami-Josanjima, Tokushima 770–8506, Japan
Telephone: +81–88–656–7470, Fax: +81–88–656–7471, Email: {haruna, nishio}@ee.tokushima-u.ac.jp

Abstract— The Self-Organizing Map (SOM) attracts attentions
for clustering in these years. In our past study, we have proposeda method using simultaneously two kinds of SOMs whose features
are different, namely, one self-organizes the area on which input
data are concentrated, and the other self-organizes the wholeof the input space. Further, we have applied this method toclustering of data including a lot of noises and have confirmed
the efficiency. However, in order to obtain an efficient clustering
performance using this method, we must determine the appropriate number of the SOMs used in the method. In this study,
we propose the Peace SOM (PSOM) algorithm which possesses
both competing and accommodating abilities. The competing andthe accommodating behaviors of PSOM are investigated withapplications to clustering input data including a lot of noises.
We can see that PSOM successfully extracts clusters even in thecase that we do not know the number of clusters in advance.

I. I NTRODUCTION
Since we can accumulate a huge amount of data including
useless information, it is important to investigate various
extraction methods of clusters from data including a lot ofnoises. The Self-Organizing Map (SOM) attracts attentions
for clustering in these years. SOM is an unsupervised neuralnetwork introduced by Kohonen in 1982 [1] and is a model
simplifying self-organization process of the brain. SOM canobtain a statistical feature of input data and can be applied toa wide field of data classifications [2]-[5].
In our past study, we have proposed a method using
simultaneously two kinds of SOMs whose features are different (nSOM method) [6]. In the nSOM method, one selforganizes the area on which input data are concentrated, andthe other self-organizes the whole of the input space. We
have investigated competing behavior of nSOM caused by thedifference of the initial states and the neighborhood functions.
Furthermore, we have applied nSOM to clustering of data
including a lot of noises and have confirmed the efficiency.
However, in order to obtain an efficient clustering performanceusing nSOM method, we must determine the appropriate
number of the SOMs used in the method, namely, we must
know the number of clusters in advance. If we use too many
SOMs in this method, some SOMs compete with each otherin the same cluster and the one cluster is extracted as wrong
plural clusters.
In this study, we propose the Peace SOM (PSOM) algorithm
which possesses both competing and accommodating abilities.
We use this algorithm after executing the nSOM method. This

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algorithm makes the competing SOMs in the same cluster toaccommodate the cluster — hence named “peace”, while theSOMs situated far keep to compete with other SOMs.
The differences between nSOM and PSOM are as follows.
1) The number of winner neurons for one input data.
In nSOM, only one winner neuron is selected from all theneurons in the all SOMs. In PSOM, one winner neuron is
selected from every SOM. Namely, k winner neurons are
selected from k SOMs.
2) The number of updated SOMs for one input data.
In nSOM, only one SOM including the winner neuron is
updated. In PSOM, some SOMs whose winner neuron is near
the input data are updated.
In the Section II, the algorithm of the two kinds of SOMs
(nSOM) is introduced. In the Section III, we explain the learning algorithm of the proposed PSOM algorithm in detail. The
competing and the accommodating behaviors of PSOM areinvestigated in the Section IV with applications to clustering
input data including a lot of noises. For 2-dimensional input
data, extraction ability of clusters is evaluated both visuallyand quantitatively using a correct answer rate. We also apply
PSOM to 5-dimensional input data and confirm the extraction
ability for higher-dimensional data. We can see that PSOM
successfully extracts clusters even in the case that we do notknow the number of clusters in advance.
II. T WO KINDS OF SOM S (nSOM)
In our past study, we have proposed a method using simultaneously two kinds of SOMs whose features are different(nSOM method), namely, one self-organizes the area on which
input data are concentrated, and the other self-organizes thewhole of the input space. We call the former SOML and thelatter SOMG . In order to apply nSOM to clustering, we use
totally n SOMs, that is one SOMG and (n−1) SOML ; namely
SOML1 , SOML2 , · · · , SOML (n−1) . We use d-dimensional input data xj = (xj1 , xj2 , · · · , xjd ) (j = 1, 2, · · · , N ) including
a lot of noises.
The differences between SOMG and SOML are only the
initial states and the neighborhood functions. However, thesedifferences cause interesting competing behaviors of nSOM.
The difference between the initial states of SOMG and SOML
is as follows. The initial values of all the weight vectors wLlof SOMLl (l = 1, 2, · · · , n − 1) are given in the overall of
the input space at random. The initial values of all the weight

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vectors wG of SOMG are given around the center of the input
space at random. The second difference is the neighborhood
function of each SOM. The learning rate of SOML is given
as decreasing rapidly, on the other side, the learning rate of
SOMG decreases monotonically with time. In addition, thewidth of the neighborhood function of SOMG is given as
decreasing slowly, however the width of the neighborhood
function of SOML decreases monotonically with time.
The important feature in the learning process of nSOM isthat only one neuron of all the neurons in the all SOMs canbe a winner for one input data, therefore, n SOMs competewith each other. In addition, by the two differences between
SOMG and SOML , SOML tends to self-organize the area
where the input data are dense, and SOMG tends to selforganize the whole input space except the area occupied by
SOML . Namely, SOML can find the clusters by themselves.
We have applied nSOM to clustering. After learning of
nSOM, in order to extract only clusters from the input data
including a lot of noises, we calculate the distance between
the input data xj and the weight vectors in SOMLl . If thecalculated distance is smaller than a threshold value R, theinput data xj is classified into the cluster corresponding to
SOMLl . However, in order to extract clusters using nSOM,
we need to know the exact number of clusters in advance.
III. P EACE SOM (PSOM)In this study, we propose the Peace SOM (PSOM) algorithm
which possesses both competing and accommodating abilities.
We use this algorithm after executing the nSOM method.
A. Learning Algorithm
We explain the learning algorithm of PSOM. In the PSOM
algorithm, we use only SOML after executing the nSOM.
(PSOM1) An input data xj is inputted to all the neurons of
SOMLl at the same time in parallel.
(PSOM2) We find winner neurons cl in every SOMLl by
calculating the distance between xj and the weight vector
wLl i of the neuron i of SOMLl , according to;
cl = arg min{wL li − xj }.
i(1)

In other words, all SOMs of PSOM have one winner neuron.
In this study, Euclidean distance is used for (1).
(PSOM3) The weight vectors of all the neurons of all SOMLl
are updated according to the following equation;
wLl i (t + 1) = wLl i (t) + hLl cl ,i (t)(xj − wLl i (t)).

(2)

The function hLl cl ,i (t) is called the neighborhood function
and is one of the best used function in the learning algorithmsof SOM. This is described as follows;r i − r cl 2
hLl cl ,i (t) = pcl (t) exp −,(3)
2σ 2 (t)where pcl (t) is the learning function, r i and r cl are thevectorial locations on the display grid, and σ(t) corresponds
to the widths of the neighborhood function. σ(t) is generally

given as decreasing with time according, in this study, it isaccording to the following equation;
σ(t) = σ(0)(1 − t/T ),(4)

where T is the maximum number of the learning. The learning
function pcl (t) is a key function deciding the behavior of
PSOM and is explained in the next subsection.
(PSOM4) The steps from (PSOM1) to (PSOM3) are repeated
for all the input data, namely from j = 1 to j = N .
B. Learning function
We propose the learning function for PSOM. The learning
function plays an important role in the algorithm and produces
the competing behavior and the accommodating behavior of
PSOM. The value of the learning function is determined by the
distance between the input vector xj and the winner neuron
cl of SOMLl , according to;wL lcl − xj 2
pcl (t) = α(t) exp −
,
(5)
2σP2
where wL lcl is the weight vector of the winner neuron cl of
SOMLl , σP corresponds to the width of the learning function,and α(t) corresponds to the maximum value of the learning
function. α(t) decrease with time according to the following
equation;α(t) = α(0)(1 − t/T ).
(6)
It is desirable to choose σP as a small value such as lessthan 0.1, because this is a key point to decide their competing
behavior and accommodating behavior. Namely, some SOMs
whose winner neuron is near the input data are significantly
updated and this means that these SOMs tend to accommodate
the input data each other. Conversely, some SOMs whose
winner neuron is far apart from the input data are updated
very little and this means that these SOMs keep to competewith other SOMs.
IV. A PPLICATION TO C LUSTERING
A. 2-dimensional input data
First, we consider 2-dimensional input data as shown in
Fig. 1(a). The input data is generated artificially as follows.
Total number of the input data N is 1600. 25% of the input
data are distributed within a range from 0.2 to 0.3 horizontallyand from 0.7 to 0.8 vertically, and these data are called thecluster C1 . 50% of the input data are distributed in anothercluster C2 , whose horizontal-values follow the normal distribution N (0.7, 0.04), and the vertical-values N (0.2, 0.0016).
The remaining 25% of the input data are distributed between
0 and 1 at random.
Because the input data include 2 clusters, we use one
SOMG and two SOML (n = 3). Each SOM has 100 neurons(10×10), namely 3 SOMs have totally 300 neurons, and theseneurons are arranged on a 2-dimensional hexagon. We repeat
the learning four times for all input data.
The simulation result is shown in Fig. 1(b). We can see that
two SOML stay around the two clusters by the competing

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Clustering of 2-dimensional input data. (a) Input data. (b) Simulated result of nSOM (n = 3). (c) Clusters extracted by SOML .

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Fig. 2. Extraction of clusters using inappropriate number of SOML . (a) 3 SOML for 2 clusters. (b) Cluster extracted by SOML1 . (c) Cluster extracted by
SOML2 . (d) Cluster extracted by SOML3 .
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Input data extracted by PSOM. (a) Learning result of PSOM (n = 4). (b) SOML1 . (c) SOML2 . (d) SOML3 .

behavior of nSOM method. Figure 1(c) shows the two SOML
and the input data classified into the clusters corresponding
to them using algorithm in the Section II (R = 0.05). As we
can see from the figures, SOML can successfully extract theclusters, and the noises are removed by SOMG . This is theresult of the nSOM when we know the number of the clusters
in advance.
On the other hand, Fig. 2(a) shows the result for the same
input data using three SOML , namely the number of SOML
is more than the number of clusters. In this case two SOML
compete with each other in the same cluster located at thelower part of the input space and the extraction of the clusters
does not succeed as shown in Figs. 2(b) and (c).
Now, we apply the PSOM algorithm after Fig. 2(a). We
repeat the PSOM algorithm four times for all the input data.
The parameters of the learning are chosen as follows;α(0) = 0.4, σ(0) = 1.5, σP = 1/16.
The result is shown in Fig. 3(a). We can see that the two
SOML , which competed with each other in Fig. 2(a), areaccommodating in one cluster. This is because all SOMs havea winner neuron for one input data and the SOMs whose
winner neurons are close to the input data are significantly
updated. On the other hand, the SOML situated on the othercluster located close to the left-top corner keeps the position
without accommodating. This is because the SOMs whose
winner neurons are far apart from the input data are updated
very little.
We carry out the extraction of clusters from Fig. 3(a). Figures 3(b), (c) and (d) show that the input data are classified into
the clusters corresponding to SOML 1 , SOML 2 and SOML 3 ,respectively (R = 0.05).
In order to investigate the ability of the PSOM algorithm,

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TABLE II
5- DIMENSIONAL G AUSSIAN DATA .
N o.
C1
C2
C3
C4

Mean value
Variance
Mean value
Variance
Mean value
Variance
Mean value
Variancex1
0.8
0.00640.35
0.01440.6
0.00160.2
0.0064x2
0.3
0.03240.8
0.00160.9
0.00640.1
0.04

Coordinate axes
x3
x4
0.7
0.2
0.01440.00360.3
0.7
0.04
0.03240.1
0.1
0.00360.01
0.8
0.4
0.00160.09

we carry out the simulations with excessive number of SOMs.
Figure 4 shows the result using six SOMs for the same input
data, namely, 5 SOML just for 2 clusters. As we can see fromthe figures, 5 SOML can not extract the clusters correctly.
However, PSOM can extract 2 clusters as if they know thenumber of the clusters.
1

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n
3
4
6

Method
nSOM
PSOM
nSOM
PSOM
nSOM
PSOM

1
86.78
87.66
60.71
88.79
89.55
95.27

2
85.07
90.55
32.49
88.92
47.98
88.41

SOMLl
3
4
87.31
93.03
66.92
7.81
94.53 88.29

5
41.94
88.54

15
20

TABLE IIIn5
7

Method
nSOM
PSOM
nSOM
PSOM

1
95.59
98.24
87.14
84.23

2
82.65
81.07
80.46
87.09

SOMLl
3
4
82.99 90.07
81.33 90.40
46.48 31.23
98.24 61.83

5
71.61
75.08

6
29.14
65.23

(7)

where NC I is the true number of the input data within thecluster CI , Nr I is the obtained number of the desired input
data within CI , and NeI is the obtained number of undesired
input data out of CI .
The calculated results are summarized in Table I. When thenumber of SOML is equal to the number of the clusters (n=3),
RC I is similar without adding PSOM algorithm. However, forthe case of larger n, the effect of the PSOM is obvious.
TABLE IC ORRECT ANSWER RATE [%] FOR 2- DIMENSIONAL INPUT DATA .

20

C ORRECT ANSWER RATE [%] FOR 5- DIMENSIONAL INPUT DATA .

In order to evaluate the clustering ability of PSOM quantitatively, we define the correct answer rate RC I as follows;(I = 1, 2, · · ·),15

Furthermore, we perform the simulation for 5-dimensional
input data of 1600 points. This data include four clusters anda lot noises, and the four clusters are generated by random
Gaussian data as shown in Table II.
We carry out simulations for the cases of n = 5 and n = 7.
The parameters of the learning for n = 5 and n = 7 arechosen as follows;n = 5 ⇒ α(0) = 0.7, σ(0) = 1.3, σP = 1/16,
n = 7 ⇒ α(0) = 0.85, σ(0) = 1.7, σP = 1/16.
The results of the calculated correct answer rates are summarized in Table III. We can say that the PSOM algorithm
is effective in the case that we do not know the number ofthe clusters in advance, and is useful to clustering for higherdimensional input data.

(b)

Nr I − N e I,
NC I

Probability [%]B. 5-dimensional input data

Fig. 4. Cluster extraction using excessive number of SOMs. (a) Learning
result of nSOM (n = 6). (b) Learning result of PSOM.

RC I =

x5
0.7
0.00640.2
0.01440.9
0.00360.3
0.01

V. C ONCLUSIONSIn this study, we have proposed the Peace SOM (PSOM) algorithm which possesses both competing and accommodating
abilities. We have investigated its competing and accommodating behaviors. Furthermore, we have applied PSOM to extract
clusters in the case that we do not know the number of theclusters in advance, and have confirmed the efficiency.
R EFERENCES[1] T. Kohonen, Self-organizing Maps, Berlin, Springer, vol. 30, 1995.
[2] Y. Cheng, “Clustering with Competing Self-Organizing Maps,” Proc. of
IJCNN’92, vol. IV, pp.785-790, 1992.
[3] W. Wan and D. Fraser, “M2dSOMAP:Clustering and Classification of Remotely Sensed Imagery by Combining Multiple Kohonen Self-Organizing
Maps and Associative Memory,” Proc. IJCNN, vol.3, pp.2464-2467, 1993.
[4] J. Vesanto and E. Alhoniemi, “Clustering of the Self-Organizing Map,”
IEEE Transactions on Neural Networks, vol. 11, no. 3, pp.586-600, 2000.
[5] I. Lapidot, H. Guterman and A. Cohen, “Unsupervised Speaker Recognition Based on Competition Between Self-Organizing Maps,” IEEE
Transactions on Neural Networks, vol. 13, no. 4, pp.877-887, 2002.
[6] H. Matsushita and Y. Nishio, “Competing Behavior of Two Kinds of
SOMs and its Application to Clustering,” Proc. WSOM, pp.355-362, 2005.

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