2006 IEEE Workshop on Nonlinear Circuit Networks (NCN'06)
Tokushima University, Tokushima, Japan, Dec. 9, 2006

Gray Scale Display Reflecting Each Slice ofLearning Results Using Shooting SOM
Masato Tomita, Haruna Matsushita, Yoshifumi Nishio
Department Electrical and Electronic Engineering, Tokushima University
Email: {tomita, haruna, nishio}@ee.tokushima-u.ac.jp

Abstract— The Self-Organizing Map (SOM) is popular algorithm for unsupervised learning introduced by Teuvo Kohonen.
One of the most attractive applications of SOM is data visualization. In the previous study, we have proposed a new type of SOMalgorithm, which is called Shooting SOM (SSOM) algorithm. The
important feature of SSOM is that only some neurons near thecluster move toward the cluster to hit the area where input data
are concentrated. Because of this feature, SSOM tends to selforganize each cluster along the figure of each cluster. We apply
SSOM to data visualization problems.
(a)(b)
Fig. 1.

Gray scale display method

1zI. S HOOTING SOM (SSOM)
In this section, we introduce SSOM algorithm.
(SSOM1) The initial values of all the weight vectors of theneurons are given between 0 and 1 in a reticular pattern.
(SSOM2) An input data is inputted to all the neurons at thesame time in parallel.
(SSOM3) We find the winner neuron by calculating thedistances between the input data and the weight vector of theneuron.
(SSOM4) We measure whether the winner neuron or 1neighborhood of the winner neuron or otherwise. Furthermore,
we determine the update rate for each cases.
(SSOM5) The weight vectors of all the neurons are updated.
(SSOM6) The steps from (SSOM2) to (SSOM5) are repeated
for all the input data.
II. G RAY SCALE DISPLAY
A. Display method
In this study, we propose a display method using SSOM.
The proposed display method is that the shading is reflected by
the number of becoming the winner as shown in Fig. 1(a). For
example, because the neuron 5 becomes a winner 5 times, theshading of the circle color is the deepest. In contrast, because
neurons 7 and 8 have never been a winner, the shading of thesecircles is the lightest. Namely, the more number of becoming
the winner is deeper color. And the proposed display methodreflects each slice of learning results as shown in Fig. 1(b).
Therefore, we can see the positional relationship of input dataand rough density.
B. Application of simulaiton results
We apply the gray scale display method to the learningresults. The results are shown in Fig. 2. As we can see fromFig. 2(b), the conventional display method using the conventional SOM can not discriminate clusters well. However, wecan see that the proposed gray scale method using SSOM
visualizes the positional relationship of input data and roughdensity from Fig. 2(c).

0.50110.5
y0.50 0x(a)

(b)

(c)

Fig. 2.
Simulation results. (a) 3-dimensional input data of the Lorenz
attractor. (b) The conventional SOM. (c) SSOM.

III. C ONCLUSIONSIn this study, we have applied Shooting SOM (SSOM) tovisualize the relationship of input data and have confirmed its
efficiency by combining the best properties of SSOM and theproposed display method.
R EFERENCES[1] M. Tomita, H. Matsushita and Y. Nishio, “Shooting SOM and its
Application for Clustering,” Proc. of NOLTA’06, pp. 199-202, 2006.

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