平成19年度電気関係学会四国支部連合大会

359

17-29

SOM with False Neighbor Degree
between Neurons
Haruna MATSUSHITA(Tokushima University)

Yoshifumi NISHIO(Tokushima University)

1. Introduction
In the real world, it is not always true that the nextdoor
house is close to my house, in other words, “neighbors”
are not always “true neighbors”. In this study, we propose
a new Self-Organizing Map (SOM) algorithm, SOM withFalse Neighbor degree between neurons (called FN-SOM).
The behavior of FN-SOM is investigated with learning forthe input data which includes some clusters located at distant locations. We conﬁrm that FN-SOM can obtain more
eﬀective map reﬂecting the distribution state of input data
than the conventional SOM [1].

2. SOM with False Neighbor Degreeneighbor f , Rr or Ck , is increased. If q and f are in ther-th row and in the k-th or (k + 1)-th column, the falseneighbor degree Ck between the cokumns k and k + 1 isincreased according to{Cknew= Ckold+(kwf − wq k4
1 − exp −2σF 2)},(4)

where σF is a constant parameter.
(FN10) γi of all the neurons are reset to zero.
(FN11) The steps from (FN1) to (FN10) are repeated for
all the input data.

3. Application to Clustering

We explain FN-SOM algorithm. Input data xj =(xj1 , xj2 , · · · , xjd ) (j = 1, 2, · · · , N ) is d-dimensional. Eachneuron i has a weight vector wi = (wi1 , wi2 , · · · , wid )(i = 1, 2, · · · , n × m). False-neighbor degrees of rows Rr(1 ≤ r ≤ n − 1) are allocated between adjacent rows of FNSOM with the size of n × m grid. Likewise, false-neighbor
degrees of columns Ck (1 ≤ k ≤ m − 1) are allocated between adjacent columns of FN-SOM. The initial values ofall of the false-neighbor degrees are set to zero, and theinitial values of all the weight vectors are given over theinput space at random. Moreover, a winning frequency γi
is associated with each neuron and is set to zero initially.

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. On the other side, theresult of FN-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
FN-SOM method is eﬀective.
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(FN1) An input vector xj is inputted to all the neurons.
(FN2) A winner c is found.
(FN3) Increment the winning frequency of the winner cby γc new = γc old + 1.
(FN4) The neighboring distances between the winner cand the other neurons are calculated. For instance, for
two neurons s1 and s2 , the neighboring distance is deﬁned
as the following measure;

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where rs1 < rs2 , ks1 < ks2 .
(FN5) The weight vectors of the neurons are updated as

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wi (t + 1) = wi (t) + hF c,i (t)(xj − wi (t)),

0.1df (s1 , s2 ) =(|rs1 − rs2 | +∑rs2 −1+(|ks1 − ks2 | +r=rs12Rr )∑ks2 −12(1)k=ks1 Ck ) ,(2)where hF c,i (t) is the neighborhood function of FN-SOM:(df (c, i)
hF c,i (t) = α(t) exp − 22σ (t))

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Figure 1: Clustering of 2-dimensional input data. (a) Input.

(3)∑nm(FN6) Ifγ ≥ λ is satisﬁed, we ﬁnd the falsei=1 ineighbors and increase the false-neighboring degree, according to the steps from (FN7) to (FN10). If not, weperform step (FN11).
(FN7) We ﬁnd the neuron q which has become the winnerleast frequently.
(FN8) A false-neighbor f of q is chosen from the set of
direct topological neighbors of q denoted as Nq 1 . f is theneuron whose weight vector is most distant from q.
(FN9) A false-neighbor degree between q and its false

data. (b) Result of the conventional SOM. (c) Result of FNSOM.

4. Conclusions
In this study, we have proposed the new SOM algorithm,
SOM with False Neighbor degree between neurons. We
have investigated its behaviors with an application to clustering, and have conﬁrmed the eﬃciency.
Reference[1] T. Kohonen, Self-organizing Maps, Berlin, Springer,
vol. 30, 1995.