NOLTA 2006
11-14 september
Bologna - ITALY

Shooting SOM and its Application for Clustering
Masato Tomita† , Haruna Matsushita† and Yoshifumi Nishio†
Tokushima University
2-1 Minami-Josanjima, Tokushima, Japan
Phone:+81-88-656-7470, FAX:+81-88-656-7471
Email: {tomita, haruna, nishio}@ee.tokushima-u.ac.jp
Abstract—The Self-Organizing Map (SOM) is
popular algorithm for unsupervised learning and visualization introduced by Teuvo Kohonen. One of
the most attractive applications of SOM is clusteringand several algorithms for various kinds of clustering
problems have been reported and investigated. In thisstudy, we propose a new type of SOM algorithm, whichis called Shooting SOM (SSOM) algorithm. The important feature of SSOM is that the neurons move likeaiming at a target, namely, some neurons find near thecenter of the area where input data are concentrated
and other neurons get away from the former neurons.
Because of this feature, SSOM tends to self-organize
only in the area where input data are concentrated.
We investigate the behavior of SSOM and apply SSOM
to clustering problems.

rons move like aiming at a target, namely, some neurons find near the center of the area where input data
are concentrated and other neurons get away from theformer neurons. Because of this feature, SSOM tends
to self-organize only in the area where input data areconcentrated. We investigate the behavior of SSOM
and apply SSOM to clustering problems. The efficiencies of SSOM are confirmed by several simulation results.
In the Section II, the algorithm of the conventional
SOM is introduced. In the Section III, we explain
the learning algorithm of SSOM algorithm. In theSection IV, the behavior of SSOM is explained withsome simulation results of clustering.

1. Introduction

In this section we introduce the conventional SOM
algorithm in order to make clear new points of theproposed algorithm.
SOM has two-layer structure of the input layer andthe competitive layer. In the competitive layer, m neurons are arranged as a regular 2-dimensional grid. The
range of the elements of d-dimensional input data xj= (xj1 , xj2 , · · ·, xjd ) (j = 1, 2, · · ·, N ) are assumed.

In data mining, clustering is one of the most important issues and is also very useful for many applications, such as industrial engineering, image processing, biology and medicine. Then, the Self-Organizing
Map (SOM) attracts attentions for clustering in recent years. SOM is popular tools for clustering andvisualization of high-dimensional data [1]. SOM is unsupervised neural network introduced by Kohonen in1982 [2] and is a model simplifying self-organization
process of the brain. SOM maps multidimensional
data onto a 2-dimensional grid. SOM can classify input data according to similarities and patterns which
are obtained by the distance between neurons and isapplied to wide fields of data classifications. Althoughmany methods to extract clusters by using SOM havebeen proposed [3]-[10], it seems to be very difficult
to construct a simple method using SOM for universal input data. On the one hand, in the world, theamount and complexity of data increase from year toyear and control of large-volume data get a lot of attention. Therefore, it is important to investigate various
extraction methods of some clusters from data including some noises.
In this study, we propose a new type of SOM algorithm, which is called Shooting SOM (SSOM) algorithm. The important feature of SSOM is that the neu-

2. Self-Organizing Map (SOM)(SOM1) The initial values of all the weight vectors
wi = (wi1 , wi2 , · · · , wid ) (i = 1, 2, · · · , m) of the neurons are given between 0 and 1 in a reticular pattern.
(SOM2) An input data xj is inputted to all the neurons at the same time in parallel.
(SOM3) We find the winner neuron c by calculating
the distances between xj and wi according to;c = arg min{kwi − xj k}.
i(1)In other words, the winner neuron c is the neuron withthe weight vector nearest to the input vector xj . In
this study, Euclidean distance is used for Eq. (1).
(SOM4) The weight vectors of all the neurons are
updated as;
wi (t + 1) = wi (t) + hc,i (t)(xj − wi (t)),(2)

where t is the learning step. The function hc,i (t) iscalled the neighborhood function and it is described199

as follows;µ¶kr i − r c k2hc,i (t) = α(t) exp −,2σ 2 (t)(3)

where α(t) is the learning rate, r i and r c are the vectorial locations of the neurons on the display grid, andσ(t) corresponds to the widths of the neighborhoodfunction. α(t) and σ(t) decrease with time according
to the following equations;α(t) = α(0) (1 − t/T ) ,σ(t) = σ(0) (1 − t/T ) ,(4)where T is the maximum number of the learning.
(SOM5) The steps from (SOM2) to (SOM4) are repeated for all the input data, namely, from j = 1 to
j = N.

Figure 1: Winner neuron and 1-neighborhood neuronsof the winner neuron.

(SSOM5) The weight vectors of all the neurons are
updated as;

3. Shooting SOM (SSOM)wi (t + 1) = wi (t) + Ai × hc,i (t)(xj − wi (t)),

In this section we introduce SSOM algorithm in order to make clear new points of the proposed algorithm.

where t is the learning step and α(t) is the learning
rate. α(t) decrease with time according to the following equations;α(t) = α(0) (1 − t/T ) ,3.1. Learning Algorithm
We explain the learning algorithm of SSOM. In
SSOM, m neurons are arranged as a regular 2dimensional grid. The range of the elements of ddimensional input data xj = (xj1 , xj2 , · · · , xjd ) (j =1, 2, · · · , N ) are assumed.
(SSOM1) The initial values of all the weight vectors
wi = (wi1 , wi2 , · · · , wid ) (i = 1, 2, · · · , m) of the neurons are given between 0 and 1 in a reticular pattern.
(SSOM2) An input data xj is inputted to all the neurons at the same time in parallel.
(SSOM3) We find the winner neuron c by calculating
the distances between xj and wi according to;c = arg min{kwi − xj k}.
i(7)

(8)

where T is the maximum number of the learning.
(SSOM6) The steps from (SSOM2) to (SSOM5) arerepeated for all the input data, namely, from j = 1 toj = N.
4. Simulation Results
4.1. Behavior of SSOM
We consider the 2-dimensional input data of 480
points whose distribution is as Fig. 2. Each 10 clustersdistribute 40 points at random.
The remaining 80 points are uniformly distributed
1(5)

0.8

In other words, the winner neuron c is the neuron withthe weight vector nearest to the input vector xj . In
this study, Euclidean distance is used for Eq. (5).
(SSOM4) We measure whether the winner neuron or
1-neighborhood of the winner neuron or otherwise andshow in Fig. 1.
Furthermore, we determine the update rate Ai foreach cases as follows.;
if i = c
 1,−0.04, if i is 1-neighborhood of c
Ai =0,otherwise.

(6)

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Figure 2: 2-dimensional input data.
between 0 and 1 at random. We consider the conventional SOM and the proposed SSOM with 25 neurons200

(5 × 5). The parameters for the learning of the conventional SOM and SSOM are chosen as follows;α(0) = 0.4, σ(0) = 1/16,(9)We execute the learning for all input data once.
The simulation results of SSOM is shown in Fig. 3(c).
SSOM self-organizes near the center of the area wherethe input data are concentrated.
Let us examine the behavior of SSOM in more detail. As we can see from Fig. 3(b) and Fig. 3(c), theconventional SOM self-organizes input data including
some noises with all neurons. However, we can seethat SSOM moves like aiming at a target from learning process. Certain neuron moves toward the cluster
to hit a center of the area where input data are concentrated, and other neurons moves toward other cluster
and go away. Therefore, only one neuron by the one
cluster self-organizes its cluster and SSOM can effectively self-organize many clusters. In doing so, SSOM
can self-organize as well as the conventional SOM withminimum neurons because SSOM does not use extra
neurons.
4.2. Data Extraction
The concept using SSOM can be exploited to extract
the data only in clusters of the input data including
some noises, because SSOM can find near the centerof such areas by itself. We carry out the extractionof cluster after Fig. 3(d). The extraction method is arelatively simple as follows. After learning, the input
data which is within a radius of R from all neurons on
the map are classified into the cluster and extract only
the cluster.
The simulation results of SSOM are shown inFigs. 4(a) and (b), respectively (R = 0.06). As we
can see from these figures, SSOM can successfully findnear the center of the cluster and can extract as wellas the conventional SOM with less neurons.
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4.3. Simulation Results for Large Input Data
We consider the 2-dimensional input data of 1240
points whose distribution is as Fig. 5. Each 31 clusters
distribute 40 points at random.
We consider SSOM with 64 neurons (8 × 8). The2
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2Figure 5: 2-dimensional input data.
parameters for the learning of SSOM are chosen as
follows;α(0) = 0.3, σ(0) = 1/16.
(10)
We execute the learning for all input data once. The
simulation results of SSOM is shown in Fig. 6(a).
SSOM self-organizes near the center of the area where
the input data are concentrated. Furthermore, we
carry out the extraction of cluster after Fig. 6(a). Theextraction results of SSOM are shown in Figs. 6(b),(R = 0.06). As we can see from these figures, SSOM
can successfully find the cluster.
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Figure 6: Learning results. (a) Learning result ofSSOM. (b) Clusters extracted by SSOM.

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5. Conclusions

1(b)Figure 4: Extraction of cluster. (a) Clusters extracted
by the conventional SOM. (b) Clusters extracted bySSOM

In this study, we have proposed the Shooting SOM(SSOM). We have explained the differences between
the conventional SOM and SSOM have investigatedits behavior. Furthermore, we have applied SSOM toextract all near the center of clusters and have confirmed its efficiency.

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1(c)Figure 3: Learning results. (a) Initial state. (b) Learning result of the conventional SOM. (c) Learning resultof SSOM.

In the future, we try to discover new applications ofSSOM in diverse fields such as sound data processing.

[10] H. Matsushita and Y. Nishio, “Competing andAccommodating Behaviors of Peace SOM,” Proc.
of ISCAS’06, 2006 (to appear).

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