平成20年度電気関係学会四国支部連合大会

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Clustering of Lazy Self-Organizing Map
Considering Lazy-Neuron Rate
Taku HARAGUCHI(Tokushima University)

Haruna MATSUSHITA(Tokushima University)

1. Introduction

Yoshifumi NISHIO(Tokushima University)

monotonically decreases with the learning step;

The Self-Organizing Map (SOM)[1] has attracted attention for the study on clustering in recent years. Meanwhile,
there is a fascinating report that about 20% of worker ants
are “lazy”[2], however, there is no evidence to prove definite reason and assuredness of the report at the presentstage. In this study, we propose Lazy Self-Organizing Map
which is a new SOM algorithm. The important feature ofthe LSOM is three kinds of neurons exist. Furthermore, thelearning rate of the LSOM depends on each neuron’s character and lazy-neuron rate, and monotonically decreases
with the learning step. We apply the LSOM consideringlazy-neuron rate to various input data set and conﬁrm its
eﬀectiveness.

2. Lazy Self-Organizing Map
In the LSOM algorithm, the feature of the LSOM
is that three kinds of neurons exist; worker neurons,
lazy neurons, which do not work, and indecisiveneurons which are the neighborhoods of the lazy neurons. M neurons have d-dimensional weight vector wi =(wi1 , wi2 , · · · , wid ) (i = 1, 2, · · · , M ) respectively. (p × M )neurons are classiﬁed into a set of the lazy neurons Slazy
at random. i.e., p denotes lazy-neuron rate.
(LSOM1) An input xj = (xj1 , xj2 , · · · , xjd ) (j =1, 2, · · · , N ) is given to all the neurons at the same timein parallel.
(LSOM2) We ﬁnd a winner neuron c by calculating thedistances between the input vector xj and the weight vector wi of the neuron i. If c ∈ Slazy , we perform (LSOM3).
If not, we perform (LSOM4).
(LSOM3) The lazy neuron, which is the winner c, is excluded from the set of the lazy neuron Slazy , and a neuron
f is selected to become a member of Slazy . f is farthestfrom the input data xj and is not in Slazy ;f = arg max{kwi − xj k},

i 6∈ Slazy .

i(1)In other words, the lazy neuron becomes worker if it becomes the winner c, and another neuron f becomes lazy.
(LSOM4) We ﬁnd the indecisive neurons. A set of the indecisive neurons Nlazy are the neighborhoods of each lazyneuron l in Slazy .
Nlazy = {i |kr i − r l k2 ≤ D(t),(2)i 6= c, i 6∈ Slazy , l ∈ Slazy },where ||r i − r l || is the neighborhood distance between map
nodes i and l on the map grid, and D(t) corresponds tothe neighborhood size. D(t) increases with learning step
according to the following equation;[]t,(3)T
where [ · ] denotes the Gauss’ notation and Dmax is a ﬁxed
parameter deciding the max value of D(t), t is the learning
step, T is the maximum number of the learning.
(LSOM5) The weight vectors of all the neurons are updated. The learning rate of the LSOM α(t) depends oneach neuron’s character and the lazy-neuron rate p, andD(t) = Dmax

α(t) =)(t αlazy( 1 − pT , )if i = l, l ∈ Slazy
if i ∈ Nlazyotherwise,αN (1 − (1 − p) Tt ) ,αw 1 − (1 − p) Tt ,(4)

where αw is the learning rate of the worker neurons, αlazy is
the learning rate of the lazy neurons and αN is the learning
rate of the indecisive neurons, namely αlazy < αN < αw .
(LSOM6) The steps from (LSOM1) to (LSOM5) are repeated for all the input data.

3. Application to Clustering
We consider 2-dimensional input data: Target data set
shown in Fig. 1(a). The simulation result of the conventional SOM is shown in Fig. 1(b). We can see that the conventional SOM does not self-organize up to all the outliersof the input data. Meanwhile, the result of the LSOM are
shown in Fig. 1(c). We can see that the LSOM can selforganize up to all the corner data than the conventional
SOM. From these ﬁgures, we can conﬁrm the eﬀectivenessof the LSOM for input data having density diﬀerence.
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Figure 1: Simulation results for Target data. (a) Input
Data. (b) Conventional SOM. (c) LSOM.

4. Conclusions
In this study, we have proposed the LSOM. We haveinvestigated its behaviors and have conﬁrmed the eﬀectiveness of the LSOM containing the lazy neurons, whichis from 10% to 20% of the total.
Reference[1] T. Kohonen, Self-organizing Maps, Berlin, Springer,
vol. 30, 1995.
[2] H. Hasegawa, “Optimization of GROUP Behavior,”
Japan Ethological Society Newsletter, no. 43, pp. 22–23,
2004.