IEICE TRANS. FUNDAMENTALS, VOL.E90–A, NO.10 OCTOBER 2007

2085

PAPER

Special Section on Nonlinear Theory and its Applications

Tentacled Self-Organizing Map for Eﬀective Data Extraction
Haruna MATSUSHITA†a) , Student Member and Yoshifumi NISHIO†b) , Member

SUMMARY
Since we can accumulate a large amount of data including
useless information in recent years, it is important to investigate various
extraction method of clusters from data including much noises. The SelfOrganizing Map (SOM) has attracted attention for clustering nowadays.
In this study, we propose a method of using plural SOMs (TSOM: Tentacled SOM) for eﬀective data extraction. TSOM consists of two kinds
of SOM whose features are diﬀerent, namely, one self-organizes the area
where input data are concentrated, and the other self-organizes the wholeof the input space. Each SOM of TSOM can catch the information of other
SOMs existing in its neighborhood and self-organizes with the competing
and accommodating behaviors. We apply TSOM to data extraction from
input data including much noise, and can confirm that TSOM successfully
extracts only clusters even in the case that we do not know the number ofclusters in advance.
key words: self-organizing maps, clustering, data extraction, data segmentation

1.

Introduction

Since we can accumulate a large amount of data including
useless information nowadays, it is important to investigate
various extraction methods of clusters from data includingmuch noise. Then, the Self-Organizing Map (SOM) has attracted attention in recent years. SOM is an unsupervisedneural network introduced by Kohonen in 1982 [1] and isa model simplifying self-organization process of the brain.
SOM can obtain a statistical feature of input data and canbe applied to a wide field of data classifications [2]–[7]. Although many methods to extract clusters by using SOM havebeen proposed, it seems to be very diﬃcult to construct a
simple method of using SOM for universal input data.
In our past study, we have proposed a method of simultaneously using two kinds of SOM whose features are
diﬀerent (nSOM method) [8]. In the nSOM method, one
self-organizes the area where input data are concentrated,
and the other self-organizes the whole of the input space.
We call the former SOML and the latter SOMG . We haveinvestigated competing behavior of nSOM caused by thediﬀerence of the initial states and the neighborhood functions. Furthermore, we have applied nSOM to clustering ofdata including much noise and have confirmed its eﬃciency.
However, nSOM method has two disadvantages in order toManuscript received December 4, 2006.
Final manuscript received May 22, 2007.
†
The authors are with the Department of Electrical and Electronic Engineering, Tokushima University, Tokushima-shi, 770–
8506 Japan.
a) E-mail: haruna@ee.tokushima-u.ac.jpb) E-mail: nishio@ee.tokushima-u.ac.jp
DOI: 10.1093/ietfec/e90–a.10.2085

obtain an eﬃcient clustering performance.
1) We must set the initial state of SOMG avoiding clusters.
2) We must determine the appropriate number of SOMs,
namely, we must know the number of clusters in advance.
Regarding the case 1), it is diﬃcult to set the initial state
properly in higher-dimensional space. Regarding the case2), if we use too many SOMs in nSOM method, some SOMs
compete with each other in the same cluster and the one
cluster is extracted as wrong plural clusters.
We have also proposed the Peace SOM algorithm [9]which remedies the above problem 2). PSOM possesses
both competing and accommodating abilities and is used
after executing the nSOM method. This algorithm makes
the competing SOMs in the same cluster to accommodate
the cluster, while the SOMs situated far keeping to competewith other SOMs. We have investigated the competing andthe accommodating behaviors of PSOM with applications
to clustering input data including much noise. However,the learning process is a little bit complicated, because thePSOM algorithm must be used after executing the nSOM
method, namely it is the two-tiered learning.
In this study, we propose a method of using plural
SOMs (TSOM: Tentacled SOM) for eﬀective data extraction. TSOM method possesses both abilities of nSOM and
PSOM, namely, TSOM has context sensitive behaviors ofcompeting and accommodating. The plural SOMs of TSOM
consist of the two kinds of SOM, SOML and SOMG . SOML
self-organizes the area where input data are concentrated,while SOMG self-organizes the whole of the input space,in the same way as nSOM method. In the TSOM algorithm, one SOMG and plural SOML are used. Each SOM
of TSOM can catch the information of other SOMs existing
in its neighborhood — hence the name “tentacled.” TSOM
has the following three key rules.
1. Winner SOM: All SOMs of TSOM have one winner neuron, respectively. However, neurons of all SOMs are NOT
updated. One or more winner SOMs are decided for one input data, and the weight vectors of only the winner SOM are
updated.
2. The update direction yG i of SOMG : the update directionof SOMG is decided by the positional relation with SOML .
3. Learning function: SOML are updated according to thelearning function which is the same function used in PSOM
algorithm.
These key roles make the behavior of TSOM interesting.
Namely, SOML and SOML which are located close to eachc 2007 The Institute of Electronics, Information and Communication Engineers
Copyright IEICE TRANS. FUNDAMENTALS, VOL.E90–A, NO.10 OCTOBER 2007

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other accommodate each other, contrary, SOMG and SOML
which are located close to each other compete against witheach other. SOML and SOML , which are located far apart,also compete against with each other.
In Sect. 2, we explain the key points and the learningalgorithm of the proposed TSOM algorithm in detail. The
competing and the accommodating behaviors of TSOM areinvestigated in the Sect. 3 with applications to data extraction from input data including much noise. For 2 and 3dimensional input data, extraction ability of clusters is evaluated both visually and quantitatively using a correct answer
rate. We also apply TSOM to 5-dimensional input data andconfirm the extraction ability for higher-dimensional data.
We can see that TSOM successfully extracts clusters evenin the case that we do not know the number of clusters inadvance.
2.

Tentacled Self-Organizing Map (TSOM)In this study, we propose a method of using plural SOMs
(TSOM: Tentacled SOM) for eﬀective data extraction. The
plural SOMs of TSOM contains the two kinds of SOM,
namely SOMG and SOML . Each SOM of TSOM exchanges
their own position information each other and self-organizes
with the competing and accommodating behaviors.
In the TSOM algorithm, we use totally n SOMs,
that is one SOMG and (n − 1) SOML ; namely
SOML1 , SOML2 , · · · , SOML(n−1) . Each SOM consists ofm neurons located at regular 2-dimensional grid. The lattice of the grid is either hexagonal or rectangle. Eachneuron i of SOMG has a d-dimensional weight vector
wGi = (wGi 1 , wGi 2 , · · · , wGi d ), and each neuron i of SOMLl(l = 1, 2, · · · , n − 1) also has the weight vector wLl i =(wLl i1 , wLl i2 , · · · , wLl id ). The input data is denoted by x j =(x j 1 , x j 2 , · · · , x j d ) ( j = 1, 2, · · · , N).
TSOM has three key rules, namely, “Winner SOM,”“The update direction of SOMG ” and “Learning function.”
We explain these key points with the learning algorithm inthis section.

2.1 Winner SOM Deciding Rule
We use plural SOMs for TSOM algorithm and find winner neurons in every SOM for one input data by calculating
the distance between x j and all the weight vector. In otherwords, each winner neuron is the neuron with the weightvector closest to x j in each SOM, namely, all SOMs of
TSOM have one winner neuron, respectively. The winner
neuron of SOMG is denoted by cG , and the winner neuron of
SOMLl is denoted by cLl . However, neurons of all SOMs are
NOT updated, the weight vectors updated are that of only
the winner SOM.
We explain the method for deciding the winner SOM.
This plays a very important role in the TSOM algorithm andproduces the competing behavior and the accommodating
behavior of TSOM. The winner SOM is determined by the
position of each winner neuron of each SOM.
[For SOML ](1) The winner SOM is SOMLl if the winner neuron cLl of
SOMLl has the weight vector closest to x j in all the winner
neurons (as Fig. 1(a)).
(2) Plural SOML can be the winner SOMs if the distances
between x j and winner neurons of plural SOML are less thanRL (t), namely wLl cLl − x j  ≤ RL (t) (as Fig. 1(b)).
[For SOMG ](3) The winner SOM is SOMG if the winner neuron cG of
SOMG has the weight vector closest to x j in all the winner
neurons, and all winner neurons of SOML are more thanRL (t) away from x j (as Fig. 1(c)).
(4) SOMG can not be the winner if distances between x j andwinner neurons of SOML are not more than RL (t) although
the winner neuron cG of SOMG has the weight vector closest
to x j in all the winner neurons (as Fig. 1(d)).
In the case (4), the weight vectors wG of SOMG are updated to minus direction. The value of deciding the update
direction of SOMG for the input data x j can be written as;⎧⎪1,
if case (3)
⎪
⎪
⎨
−1,
if case (4)yG j = ⎪
(1)
⎪
⎪
⎩ 0,
otherwise
In other words, SOMG and SOML , which are located close

(a)

(b)

(c)

Fig. 1 Example of winner SOM and the location of winner neurons. (a) Winner SOM is SOML1 .
(b) Winner SOMs are SOML1 and SOML2 . (c) Winner SOM is SOMG . (d) Winner SOM is SOML1 .

(d)

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to each other, compete against each other.
RL (t) plays an tentacle of each SOM and increases withtime according to;⎧
t/T ⎫

⎪
⎪
⎪
⎪
0.005
⎨
⎬
RL (t) = RLm ⎪
1−
,
(2)
⎪
⎪
⎪
⎩
⎭
RLm
where RLm is a maximum value of RL (t), and T is the maximum number of the learning.
2.2 Learning Algorithm
The range of the elements of the input data x j are assumed
to be from 0 to 1. The initial values of all the weight vector
of SOMG and SOML are given between 0 and 1 at random.
(TSOM1) An input data x j is inputted to all the neurons of
SOMG and SOML simultaneously in parallel.
(TSOM2) Distances between x j and all the weight vectorsof all SOM are calculated. The winner neuron of each SOM
is the neuron with the weight vector closest to x j in each
SOM;
cG = arg min{wGi − x j },icLl = arg min{wLl i − x j },i(3)where  ·  is the distance measure, in this study, Euclidian
distance.
(TSOM3) One or more winner SOMs are determined by
the distance between x j and the winner neurons, according
to II. A.
(TSOM4) The weight vectors of neurons of SOMG and
SOML are updated.
The weight vectors of neurons in SOMG are updated
according to the following equation;wGi (t + 1) = wGi (t) + yG j · hGcG ,i (t)(x j − wG i (t)),(4)

where yG j is the value of deciding the update direction of
SOMG for x j determined by Eq. (1), and hGcG ,i (t) is theneighborhood function of SOMG described as follows;ri − rcG 2
hGcG ,i (t) = α(t) exp −,(5)
2σ2 (t)where ri is the vectorial locations on the display grid of neuron i, α(t) is the learning rate, and σ(t) corresponds to thewidths of the neighborhood function. Both α(t) and σ(t) decrease monotonically with time according to the following
equation;α(t) = α(0)(1 − t/T ),σ(t) = σ(0)(1 − t/T ),(6)

where T is the maximum number of the learning.
If the winner SOM is SOMLl , the weight vectors ofneurons in SOMLl are updated, according to;
wLl i (t + 1) = wLl i (t) + hLl cL l ,i (t)(x j − wLl i (t)),(7)

The function hLl cL l ,i (t) is the neighborhood function of
SOML and it is described as follows;ri − rcLl 2
hLl cLl ,i (t) = pcL l (t) exp −,(8)
2σ2 (t)where pcL l (t) is the learning function, and it is explained in
the next subsection.
(TSOM5) The steps from (TSOM1) to (TSOM4) are repeated for all the input data, namely from j = 1 to j = N.
2.3 Learning Function
In our past study, we have proposed the learning function.
The learning function produces the competing behavior andthe accommodating behavior of SOML . The value of thelearning function is determined by the distance between the
input vector x j and the winner neuron cLl of SOMLl , according to;⎛⎞⎜⎜ wLl cLl − x j 2 ⎟⎟⎟⎟⎠ ,pcL l (t) = α(t) exp ⎜⎜⎝−
(9)2σ2P
where wLl cLl is the weight vector of the winner neuron cLl of
SOMLl , σP corresponds to the width of the learning function, and α(t) corresponds to the maximum value of thelearning function according to Eq. (6).
It is desirable to choose σP as a small value such as lessthan 0.1, because this is a key point to decide their competing behavior and accommodating behavior. Namely, whenplural SOML are winner SOM, some winner SOML whose
winner neurons are near the input data are significantly updated and this means that these SOML tend to accommodate
the input data each other. Conversely, some winner SOML
whose winner neurons are far apart from the input data are
updated very little and this means that these SOML keep tocompete with other SOML .
In other words, some SOML , which are located close toeach other, accommodate each other, contrary, some SOML ,which are located far apart, compete against each other.
3.

Application to Data Extraction

3.1 2-Dimensional Input DataFirst, we consider 2-dimensional input data as shown in
Fig. 2(a). The input data is generated artificially as follows. Total number of the input data N is 1600. 25% of
the input data are distributed within a range from 0.2 to 0.3
horizontally and from 0.7 to 0.8 vertically, and these data
are called the cluster C1 . 50% of the input data are distributed in another cluster C2 , whose horizontal-values follow the normal distribution N(0.7, 0.04), and the verticalvalues N(0.2, 0.0016). The remaining 25% of the input data
are distributed between 0 and 1 at random.
Because the input data include 2 clusters, we use one

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(a)

(b)

(c)

(d)

Fig. 2 Clustering of 2-dimensional input data using TSOM. (a) Input data. (b) Simulated result of
TSOM (n = 3). (c) Clusters extracted by SOML1 . (d) Clusters extracted by SOML2 .

(a)

(b)

(c)

(d)

Fig. 3 Comparison of simulation results. (a) Learning result of conventional SOM. (b) Extraction ofCluster1 by k-means method. (c) Extraction of Cluster2 by k-means method. (d) Extraction of noise by
k-means method.

SOMG and two SOML (n = 3). Each SOM has 100 neurons (10 × 10), namely 3 SOMs have totally 300 neurons,
and these neurons are arranged on a 2-dimensional grid. We
repeat the learning four times for all input data. The parameters of the learning are chosen as follows;α(0) = 0.5, σ(0) = 3, σP = 1/16, RLm = 0.2.
The simulation result is shown in Fig. 2(b). We can see that
two SOML stay around the two clusters by the competing
behavior of TSOM method.
In order to extract only clusters of the input data including much noise, we calculate the distance between the
input data x j and the weight vectors in SOMLl after learningof TSOM. If the calculated distance is smaller than a threshold value R, the input data x j is classified into the cluster
corresponding to SOMLl . Figures 2(c) and (d) show the input data classified into the clusters corresponding to SOML1
and SOML2 , respectively (R = 0.05). As we can see fromthe figures, SOML can successfully extract the clusters, andthe noise are removed by SOMG . This is the result of TSOM
when we know the number of the clusters in advance.
We carry out the conventional SOM and the k-means
method for the same input data for the comparison. From
Fig. 3(a), we can confirm that the conventional SOM selforganizes the input data the influence of noise. On the other
hand, Fig. 3(b)–(d) shows the results obtained by using the

k-means method, where the number of the cluster is set as
k = 3 (namely, two clusters and noise). We can see thatthe clusters obtained by the k-means method include muchnoise.
Next, we assume that we do not know the appropriate
number of clusters in advance. We simulate for the same
input data using one SOMG and three SOML , namely the
number of SOML is more than the number of clusters. We
use the same parameters as Fig. 2. Figures 4(a)–(h) show
the learning process of TSOM, and the simulation result is
Fig. 4(h). We can see that all SOML stay around the twoclusters and SOMG self-organizes only noise. We observe
this in more detail, the two SOML , which stay around thesame cluster C2 , are accommodating in one cluster withoutcompeting although one SOML is redundant. On the other
hand, SOML situated on the other cluster C1 is competingwith other two SOML without accommodating.
Let us consider the learning process. In the early stageof learning as Figs. 4(a) and (b), SOMG is self-organizing
the cluster C1 . However, SOML edges out SOMG and isself-organizing this cluster as Fig. 4(d), because SOMG are
updated to the minus direction, according to Eq. (1). In the
meanwhile, two SOML are competing in the same cluster
C2 as Figs. 4(a)–(d), however, these two SOML are accommodating in one cluster as the learning progressed. Thisis because SOML and SOML , which are located close toMATSUSHITA and NISHIO: TENTACLED SELF-ORGANIZING MAP FOR EFFECTIVE DATA EXTRACTION

2089

each other, accommodate each other, according to Eq. (8),namely, some SOML whose winner neurons are close to the
input data are significantly updated.
We carry out the extraction of clusters from Fig. 4(h).
Figures 5(a)–(c) show that the input data are classified into
the clusters corresponding to SOML1 , SOML2 and SOML3 ,respectively (R = 0.05).
In order to investigate the ability of the TSOM algorithm, we carry out the simulations with excessive number
of SOMs. The parameters are the same as Fig. 2. Figure 6
shows the result using six SOMs for the same input data,
namely 5 SOML just for 2 clusters. As we can see fromthe figures, TSOM can extract 2 clusters as if they know thenumber of the clusters.
In order to evaluate the clustering ability of TSOM
quantitatively, we define the correct answer rate RC I as fol-lows;
RC I =

Nr I − NeI,
NC I(I = 1, 2, · · · ),(10)

where NC I is the true number of the input data within thecluster C I , Nr I is the obtained number of the desired input
data within C I , and NeI is the obtained number of undesired
input data out of C I . The calculated results are summarizedin Table 1. When the number of SOML is equal to the number of the clusters (n=3), we can evaluate the eﬀectivenessof the method of using TSOM method by this index value.
3.2 3-Dimensional Input Data
Next, we carry out simulation for 3-dimensional input data
shown in Fig. 7(a). The input data include two clusters and

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 4 Clustering using TSOM with inappropriate number of SOML . (a) Initial state (t = 0). (b) t =200. (c) t = 400. (d) t = 600. (e) t = 1000. (f) t = 2000. (g) t = 3000. (h) Simulation results (t = 6400).

(a)

(b)
Fig. 5

Input data extracted by SOML of TSOM. (a) SOML1 . (b) SOML2 . (c) SOML3 .

(c)

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 6 Cluster extraction using excessive number of SOMs. (a) Learning result of TSOM (n = 6).
(b) SOML1 . (c) SOML2 . (d) SOML3 . (e) SOML4 . (f) SOML5 .

(a)

(b)

(c)

Fig. 7 Clustering of 3-dimensional input data using TSOM. (a) Input data. (b) Learning result of
TSOM (n = 3) (c) Result from another angle.

much noise out of the clusters.
Figure 7(b) shows the learning result of TSOM (n = 3),
and the same result from another angle is shown in Fig. 7(c).
We can see that two SOML stay around the two clusters
and SOMG self-organizes the area of noise. The input dataclassified into the clusters corresponding to each SOML are
shown in Figs. 8(a) and (b), respectively (R = 0.15). We canconfirm that the noise are removed by SOMG and only thecluster part can be extracted very well.
Furthermore, we carry out this simulation for the same
input data using TSOM (n = 5) and k-means method (k =3). The correct answer rates are summarized in Table 2.
As we can see from this table, the clustering ability of using TSOM method is eﬀectual whether or not we know the

Table 1n3
4
6Correct answer rate [%] for 2-dimensional input data.

Methodk-means
TSOM
TSOM
TSOM

1
81.78
87.36
85.48
96.50

2
66.00
97.73
95.62
84.01

SOMLl
3
83.08
96.97

4
86.09

5
96.74

number of clusters.
3.3 5-Dimensional Input Data
Furthermore, we perform the simulation for 5-dimensional
input data of 1600 points. This data include four clusters andMATSUSHITA and NISHIO: TENTACLED SELF-ORGANIZING MAP FOR EFFECTIVE DATA EXTRACTION

2091

much noise, and the four clusters are generated by random
Gaussian data as shown in Table 3.
We carry out simulations for the cases of n = 5 (whichis the same number of clusters) and n = 7 (we do not know
the number of cluster). The parameters of the learning forn = 5 and n = 7 are chosen as follows;(For n = 5)

(For n = 7)(b)
3-D input data extracted by SOML . (a) SOML1 . (b) SOML2 .

n
3
5

4.

Conclusions

References(a)

Table 2

The results of the calculated correct answer rates (R =0.3) are summarized in Table. 4. We can confirm that thecorrect answer rates are high.

In this study, we have proposed the Tentacled SOM (TSOM)
algorithm which is a method of using plural SOMs. TSOM
possesses both abilities of nSOM and PSOM. Each SOM
of TSOM can catch the information of other SOMs existing in its neighborhood and self-organizes with the competing and accommodating behaviors. We have investigated its
behaviors. Furthermore, we have applied TSOM to extract
clusters in the case that we do not know the number of theclusters in advance, and have confirmed its eﬃciency.
From these results, we can say that the proposed
method using TSOM can be applied to not only data extraction, but also data segmentation in the future. In addition,by proposing new visualization methods for TSOM, TSOM
has the possibility of opening up completely new ways tovisualize high-dimensional data.

α(0) = 0.7, σ(0) = 4, σP = 1/16, RLm = 0.2,

Fig. 8α(0) = 0.7, σ(0) = 4, σP = 1/16, RLm = 0.25.

[1] T. Kohonen, Self-organizing Maps, vol.30, Springer, Berlin, 1995.
[2] Y. Cheng, “Clustering with competing self-organizing maps,” Proc.
International Joint Conference on Neural Networks, vol.IV, pp.785–
790, 1992.
[3] W. Wan and D. Fraser, “M2dSOMAP: Clustering and classificationof remotely sensed imagery by combining multiple kohonen selforganizing maps and associative memory,” Proc. International Joint
Conference on Neural Networks, vol.III, pp.2464–2467, 1993.
[4] L. Xu, A. Krzyzak, and E. Oja, “Rival penalized competitive learning for clustering analysis, RBF net, and curve detection,” IEEE
Trans. Neural Netw., vol.4, no.4, pp.636–649, 1993.
[5] B. Fritzke, “Growing Grid — A self-organizing network with constant neighborhood range and adaptation strength,” Neural Process.
Lett., vol.2, no.5, pp.9–13, 1995.
[6] J. Vesanto and E. Alhoniemi, “Clustering of the self-organizing
map,” IEEE Trans. Neural Netws., vol.11, no.3, pp.586–600, 2002.

Correct answer rate [%] for 3-dimensional input data.
Methodk-means
TSOM
TSOM

Table 4

Correct answer rate [%] for 5-dimensional input data.

SOMLl
1
65.98
89.75
93.85

2
59.29
94.26
87.67

3
90.49

4
94.47

n

Method

5
7

TSOM
TSOM

2
97.93
95.15

SOMLl
3
4
96.35
93.69
63.52
95.79

Table 3
No.
C1
C2
C3
C4

Mean value
Variance
Mean value
Variance
Mean value
Variance
Mean value
Variancex1
0.8
0.00160.35
0.00360.6
0.00040.2
0.00165-dimensional Gaussian data.
Coordinate axes
x2
x3
x4
0.3
0.7
0.2
0.00810.00360.00090.8
0.3
0.7
0.00040.01
0.00810.9
0.1
0.1
0.00160.00090.0025
0.1
0.8
0.4
0.01
0.00040.0225

1
80.00
96.77

x5
0.7
0.0081
0.2
0.00360.9
0.00090.3
0.0025

Probability [%]
15
20
15
20

5
70.39

6
98.37

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[7] I. Lapidot, H. Guterman, and A. Cohen, “Unsupervised speakerrecognition based on competition between self-organizing maps,”
IEEE Trans. Neural Netw., vol.13, no.4, pp.877–887, 2002.
[8] H. Matsushita and Y. Nishio, “Competing behavior of two kinds ofself-organizing maps and its application to clustering,” IEICE Trans.
Fundamentals, vol.E90-A, no.4, pp.865–871, April 2007.
[9] H. Matsushita and Y. Nishio, “Competing and accommodating behaviors of peace SOM,” RISP J. Signal Processing, vol.10, no.5,
pp.371–376, 2006.

Haruna Matsushita
was born in Tokushima, Japan, in 1982. She received the B.E.,
M.E. degrees from Tokushima University, Tokushima, Japan, in 2005 and 2007. She is currently working towards Ph.D. degree at the same
university. Her research interests include theory
and application of Self-Organizing Maps. She isa student member of the IEEE.

Yoshifumi Nishio
received B.E., M.E.,
and Ph.D. degrees in electrical engineering from
Keio University, Yokohama Japan, in 1988,
1990, and 1993, respectively. In 1993, he joined
the Department of Electrical and Electronic Engineering at Tokushima University, Tokushima
Japan, where he is currently an Associate Professor. From May 2000 he spent a year in the
Laboratory of Nonlinear Systems (LANOS) at
the Swiss Federal Institute of Technology Lausanne (EPFL) as a Visiting Professor. His research interests include analysis and application of chaos in electrical circuits, analysis of synchronization in coupled oscillatory circuits, development of analyzing methods for nonlinear circuits, theory and applicationof cellular neural networks, and neural network architecture. He was the
Chair of the IEEE CAS Technical Committee on Nonlinear Circuits andSystems (NCAS) during 2004–2005 and is currently the Steering Committee Secretary of the IEICE Research Society of Nonlinear Theory and its
Applications (NOLTA). He is serving as an Associate Editor for the IEEE
Transactions on Circuits and Systems Part I and the RISP Journal of Signal
Processing. He is a senior member of the IEEE, and a member of the RISP.