平成19年度電気関係学会四国支部連合大会

358

17-28

One-dimensional Looking Back SOM
for Real-Time Processing
Masato TOMITA(Tokushima University)

Haruna MATSUSHITA(Tokushima University)

1. Introduction
The Self-Organizing Map (SOM) is popular algorithm
for unsupervised learning and visualization introduced by
Teuvo Kohonen. One of the most attractive applicationsof SOM is real-time processing and several algorithms forvarious kinds of real-time prediction problems have beenreported and investigated. In this study, we propose a new
type of one-dimensional SOM algorithm, which is called
Looking Back SOM (LBSOM) algorithm. The importantfeature of LBSOM is that the neurons of LBSOM dependon the distance between each neuron. We run a simulationby using the input data depended on the order of inputting
and investigate the behavior of LBSOM. The eﬃciencies ofLBSOM are conﬁrmed by several simulation results.

2. Looking Back SOM (LBSOM)
In the LBSOM algorithm, the neurons of LBSOM depend on the distance between each neuron. In the case of
the conventional SOM, we just consider the distance between the winner neuron and each neuron. However, wealso consider the distance between the previous neuron andeach neuron in the LBSOM algorithm. Namely, the nearer
the winner neuron and the previous neuron, a neuron ismore updated. Therefore, each neurons of the proposed
SOM do not converge the same position.
(LBSOM1) The initial values of all the weight vectors aregiven between 0 and 1 at random.
(LBSOM2) An input data is inputted to all the neurons
at the same time in parallel.
(LBSOM3) We ﬁnd the winner neuron by calculating thedistance between the input data and the weight vector ofthe neuron.
(LBSOM4) We determine the update rate of all the neurons by calculating the distance between each neurons.
(LBSOM5) The weight vectors of all the neurons are updated.
(LBSOM6) The steps from (LBSOM2) to (LBSOM5) arerepeated for all the input data.

3. Simulation results
Input data is 2-dimensional input data depended on theorder of inputting of 1000 points whose distribution is nonuniform as Fig. 1(a). We consider the conventional SOM
and the proposed LBSOM with 100 neurons. And we repeat the learning for all input data once. Furthermore,
we respectively set the best value of parameters to selforganize the input data very well. From the results, wecan say that the conventional SOM tends to self-organizeout of the order of inputting. On the other hand, LBSOM
self-organizes along the order of inputting.
In order to evaluate the mapping precision of LBSOM,
we deﬁne the average quantization error eq . For example,
if the weight vector of the winner neuron is exactly thesame 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 LBSOM.
Furthermore, the improvement rate is 43 [%].

Yoshifumi NISHIO(Tokushima University)
1

0.8

0.6

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00

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00.2

1(a)
1

1

0.8

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00

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1(c)

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

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

eq

Conventional SOM
2.14

LBSOM
1.22

4. Conclusions
In this study, we have proposed the Looking Back SOM(LBSOM). We have explained the diﬀerences between
SOM and LBSOM with learning algorithm and have investigated its behavior. Furthermore, we have applied theproposed LBSOM to the input data depended on the orderof inputting and have conﬁrmed its eﬃciency.
In the future, we try to discover new applications ofLBSOM in the real-time processing.

References[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.