平成18年度電気関係学会四国支部連合大会

322

Reunifying Self-Organizing Map
for Effective Clustering

17 - 26

Haruna MATSUSHITA(Tokushima University)

Yoshifumi NISHIO(Tokushima University)

1. Introduction
The Self-Organizing Map[1] (SOM) attracts attentions
for clustering in these years. However, if we apply SOM toclustering of the input data which includes some clusters
located at distant locations, there are some inactive neurons between clusters. In this study, we propose a Reunifying Self-Organizing Map which is a new SOM algorithm.
The initial state of all neurons of the proposed SOM areconnected to no neuron. However, the neurons are connected gradually to other neurons as learning progressed.
The behavior of the reunifying SOM is investigated withapplication to clustering. We can confirm that the resultof using the reunifying SOM includes no inactive neuron.

2. Reunifying Self-Organizing Map
Each neuron i has a d-dimensional weight vector wi =(wi1 , wi2 , · · · , wid ) (i = 1, 2, · · · , m). The initial state of
all neurons of the reunifying SOM are connected to noneuron, but each neurons have its own physical locationon the 2-D grid. The initial value of the weight vectors
are given at orderly position. The range of the elementsof d-dimensional input data xj = (xj1 , xj2 , · · · , xjd ) (j =1, 2, · · · , N ) are assumed to be from 0 to 1.

If kwq − wc k ≤ D(t), we perform (RSOM6). However,
if not, we except the neuron q from N c1 , and perform thesimulation again from (RSOM4).
D(t) increases monotonically with time;D(t) =(5)(RSOM6) The winner c is directly connected to a connecting neuron q, namely, nc,q becomes 1.
(RSOM7) The steps is returned to (RSOM1) and is repeated for all the input data.

3. Application to Clustering
We consider 2-dimensional input data as shown inFig. 1(a). The simulation result of the conventional SOM
is shown in Fig. 1(b). We can see that there are some inactive neurons between input data. The other side, the resultof the reunifying SOM are shown in Fig. 1(c). We confirm
that there are no inactive neurons between input data. As
we can see from these figures, the clustering ability of using
the reunifying SOM method is effective.
1(RSOM1) An input data xj is inputted to all the neurons
at the same time in parallel.
(RSOM2) The winner c is found.
(RSOM3) The weight vectors of the neurons are updated;wi (t + 1) = wi (t) + hRc,i (t)(xj − wi (t)),

Dmax
t + Dmin .
T

0.8

0.6

0.4

(1)

0.2

where hRc,i (t) is described as;µ(nc,i /m + kwi − xj k)2
hRc,i (t) = α(t) exp −2σ 2 (t)

¶00.

(2)

where where k · k is the Euclidean distance, and nc,i isthe neighborhood distance between c and each neuron i.
The neighborhood distances are defined as shortest-path
distances between connected map nodes. If a neuron i is
not connected directly or indirectly to the winner c, nc,i isequal to the number of neurons m. α(t) is the learning rate,and σ(t) corresponds to the width of the neighborhood
function. Both α(t) and σ(t) decrease monotonically withtime as follows;α(t) = α(0)(1 − t/T ), σ(t) = σ(0)(1 − t/T ),(3)(RSOM4) A set of 1-neighborhood neurons N c1 of winnerc, on the assumption that all the neurons are connected.
A set of the neurons, whose neighborhood distance isthe longest in N c1 , are denoted as Sq.
Sq = arg max{nc,i }, i ∈ N c1 .
i(4)If nc,Sq = 1, we perform (RSOM7). However, if not, weperform (RSOM5).
(RSOM5) The connecting neuron q is chosen from Sq. q
is the neuron with the weight vector closest to xj in Sq.

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1(a)
110.8

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000.2

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(b)

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1(c)

Figure 1: Clustering of 2-dimensional input data.
(a) Input data. (b) Result of the conventional SOM.
(c) Result of the reunifying SOM.

4. Conclusions
In this study, we have proposed the new SOM algorithm
which is the Reunifying SOM. We have investigated its behaviors with applications to clustering, and have confirmed
the efficiency.
Reference[1] T. Kohonen, Self-organizing Maps, Berlin, Springer,
vol. 30, 1995.