平成19年度電気関係学会四国支部連合大会

357

17-27

Self-Organizing Map Considering
Winning Frequency
Taku HARAGUCHI(Tokushima University)

Masato TOMITA
Haruna MATSUSHITA
Yoshifumi NISHIO(Tokushima University) (Tokushima University)(Tokushima University)

1. Introduction
The Self-Organizing Map (SOM) [1][2] is an unsupervised neural network introduced by Teuvo Kohonen. SOM
has attracted attention in studies of clustering in recentyears. In this study, we propose a new type of SOM algorithm, which is called SOM considering Winning Frequency(WF-SOM) algorithm. The most important feature of WFSOM is that each neuron has individuality by considering
winning frequency. Namely, if the winning frequency of aneuron is smaller and the neuron is nearer to the winner
neuron, the neuron is updated more greatly. We investigate
the behavior of WF-SOM and apply WF-SOM to clustering problems. The eﬃciencies of WF-SOM are conﬁrmed
by several simulation results.

if the weight vector of the winner neuron is exactly thesame as input data, the value of eq is 0.
The calculated results are summarized in Table 1. We
can evaluate the eﬀectiveness of the method using WFSOM. Furthermore, the improvement rate is 17.8 [%].
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2. WF-SOM
In the WF-SOM algorithm, if the winning frequency ofa neuron is smaller and the neuron is nearer to the winner
neuron, the neuron is updated more greatly. Namely, even
if it is seldom a winner, though it is near the winner neuron, it is updated greatly. Slick neurons always exist. Thisis similar to an unreasonable situation at human society.
(WF-SOM1) The initial values of all the weight vectors
wi = (wi1 , wi2 , · · · , wid ) (i = 1, 2, · · · , M ) are given between 0 and 1 at random.
(WF-SOM2) An input data xj = (xj1 , xj2 , · · · , xjd ) (j =1, 2, · · · , N ) is inputted to all the neurons at the same timein parallel.
(WF-SOM3) We ﬁnd the winner neuron c by calculating
the distance between xj and wi .
(WF-SOM4) We accumulate the number becoming thewinner for each neuron for every learning.
(WF-SOM5) The weight vectors of all the neuron areupdated by considering winning frequency. If the winningfrequency of a neuron is smaller and the neuron is nearer
to the winner neuron, a neuron is more updated.
(WF-SOM6) The steps from (WF-SOM2) to (WFSOM5) are repeated for all the input data.

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000.60.81(c)Figure 1: Learning results. (a) Input data. (b) The conventional SOM. (c) WF-SOM.

Table 1: Average quantization error [%] for 2dimensional input data.

eq

Conventional SOM
1.57

WF-SOM
1.33

4. Simulation results

5. Conclusions

Input data is 2-dimensional random data of 1000 points
whose distribution is non-uniform as Fig. 1(a). The number of learning of SOM and WF-SOM is 3 times. We consider the conventional SOM and the proposed WF-SOM
with 100 neurons (10 × 10). From the results, we cansay that in the case of the small number of learning theconventional SOM does not tend to self-organize up to
all the corners of the input. On the other hand, in thecase of the small number of learning WF-SOM can tend toself-organize up to all the corners of the input. Although
WF-SOM can self-organize more exactly and quickly thanSOM, it tends to produce twists between the neurons.
In order to evaluate the mapping precision of WF-SOM,
we deﬁne the average quantization error eq . For example,

In this study, we have proposed WF-SOM. We have explained the diﬀerences between SOM and WF-SOM withlearning algorithm and have investigated its behavior. Furthermore, we have applied the proposed WF-SOM to clustering problems in the case of the small number of learningand have conﬁrmed its exact and quick self-organization.
In the future, we try to reduce the twists between neurons.
Reference[1] T. Kohonen, “The Self-Organizing Maps,” Neurocomputing, vol. 21, pp. 1-6, 1998.
[2] T. Kohonen, Self-Organizing Maps, Berlin, Springer,
vol. 30, 1995.