平成21年度電気関係学会四国支部連合大会

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Behavior of Community Self-Organizing Map
Taku HARAGUCHI(Tokushima University)

Haruna MATSUSHITA(Tokushima University)

1. Introduction
The Self-Organizing Map (SOM) has attracted attention
for the study on clustering in recent years. Meanwhile, inhuman society, there is a fascinating story that humanbeings belong to sub-society, which is called community,
and are called social animals. Furthermore, the community is created around the leader of the community. In
this study, we propose Community Self-Organizing Map(CSOM) which is a new SOM algorithm. In CSOM algorithm, the neurons create some communities according totheir winning frequency. We apply CSOM to various input
data for clustering.

2. Community Self-Organizing Map
In CSOM algorithm, the neurons create some communities according to their winning frequency. Furthermore,
the community is created around the leader of the community. M neurons are arranged as a regular 2-dimensionalgrid. A winning frequency Wi (i = 1, 2, · · · , M ) is associated with each neuron i and is initially set to zero: Wi = 0.
The number of members in each community Ck and thenumber of communities n are zero. Before learning, the all
neurons do not belong to any community, however, they
gradually belong to a community with learning.
(CSOM1) An input is given to all the neurons at the sametime in parallel.
(CSOM2) Find a winner c by calculating a distance between the input vector xj (j = 1, 2, · · · , N ) and the weightvector wi of each neuron i. The winner neuron c is theneuron with the weight vector nearest to the input vector
xj . Update the weight vectors of all the neurons. If halftime of the learning is over, increase the winning frequencyof the winner c by
Wcnew = Wcold + 1,Yoshifumi NISHIO(Tokushima University)

including the winner c, update the leader lk as (CSOM5)
and perform (CSOM8).
(CSOM7) Compare the winning frequencies of two leaders between the community including the winner andthe community including winner’s neighborhood neuron.
Without loss of generality, assume that the winner c belongs to C1 and its neighborhood neuron belongs to C2 .
The leaders of C1 and C2 are assumed as l1 and l2 , respectively. If Wl2 ≥ Wl1 , the neighborhood neuron keeps on
belonging to C2 . If not, the neighborhood neuron belonging to C2 is absorbed into C1 . Then, in a speciﬁc case, if
the neighborhood neuron is the leader l2 in the community
C2 , all the neurons belonging to C2 are absorbed into C1
and decrease the number of communities as nnew = nold −1.
(CSOM8) Repeat the steps from (CSOM1) to (CSOM7)
for all the input data.
(CSOM9) After all learning are ﬁnished, check whether
Wi > 0.8 × T /M for each particle i. If this is not satisﬁed,
remove the particle i from the community including it.

3. Application to Clustering
We consider 2-dimensional input data shown inFig. 1(a). The simulation results of the conventional SOM
and CSOM are shown in Figs. 1(b) and (c), respectively.
In Fig. 1(c), we can see that the number of communities is
the same as the number of clusters. Furthermore, only theneurons, which self-organize the area where the input data
are concentrated, create the communities. Therefore, wecan see the number of clusters by investigating the numberof communities.
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and perform (CSOM3). If not, perform (CSOM8).
(CSOM3) Evaluate whether the winner c satisﬁes thecondition of the winning frequency to update the community information. If Wc > Wth (t) is satisﬁed, perform(CSOM4). If not, perform (CSOM8) without updating thecommunity information. Wth (t) is the threshold value andincreases with learning ast
Wth (t) =.
(2)
2M(CSOM4) Find a community Ck including the winner c.
If winner c does not belong to any community, create a
new community, nnew = nold + 1, and aﬃliate the winner cto new community Ck as c ∈ Ck (where k = nnew ). If not,c remains in its community Ck .
(CSOM5) Find a leader lk which has become the winnermost frequently among the all neurons belonging to Ck ,according to Eq. (3).
lk = arg max{Wi },ii ∈ Ck .

(3)

(CSOM6) Find the neurons, whose winning frequencies
are higher than Wth (t), in 1-neighborhood of the winner c,then consider whether they belong to any community. If
this neighborhood neuron belongs to any community, perform (CSOM7). If not, aﬃliate it to the community Ck

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Figure 1: Simulation results for 2-dimensional input data.
(a) Input Data. (b) Conventional SOM. (c) CSOM. ▲, ★
and ■ denote neurons belonging to the largest community C1 , the second community C2 and the third largest
community C3 , respectively.

4. Conclusions
In this study, we have proposed CSOM. We have investigated its behavior and have conﬁrmed that the numberof communities is the same as the number of clusters.