2006 IEEE Workshop on Nonlinear Circuit Networks (NCN'06)
Tokushima University, Tokushima, Japan, Dec. 9, 2006

Fuzzy ART with Group Learning
Haruka ISAWA, Masato TOMITA, Haruna MATSUSHITA and Yoshifumi NISHIO
Dept. Electrical and Electronic, Eng.,
Tokushima University
Email: {isawa, tomita, haruna, nishio}@ee.tokushima-u.ac.jp

Abstract— Adaptive Resonance Theory (ART) is an unsupervised neural network based on competitive learning which iscapable of learning stable recognition categories in response
to arbitrary input sequences. In this study, we propose anapplication step, called “Group Learning”, for Fuzzy ART inorder to obtain more effective categorization. This new algorithm
is called Fuzzy ART with Group Learning (Fuzzy ART-GL).
The important feature of the group learning is that creatinga connection between similar categories. We investigate thebehavior of Fuzzy ART-GL with application to the recognition
problems.

I. I NTRODUCTION
Adaptive Resonance Theory (ART) is an unsupervised neural network based on competitive learning which is capable oflearning stable recognition categories in response to arbitrary
input sequences. Fuzzy ART is a variation of ART, allows bothbinary and continuous input pattern. Fuzzy ART has limits ofcategory space size by the vigilance parameter. Thus, input
vectors are classified in each appropriate category. However,Fuzzy ART often makes input data of the common categories
classify several categories.
In this study, we propose an application step, called “GroupLearning”, for Fuzzy ART in order to obtain more effective
categorization. This new algorithm is called Fuzzy ART withGroup Learning (Fuzzy ART-GL). The important feature of
the group learning is that creating a connection between
similar categories. This idea takes some sort of reference toCompetitive Hebbian Learning proposed by Martinetz andSchulten.[1][2] We investigate the behavior of Fuzzy ARTGL with application to recognition problems. We apply theFuzzy ART-GL to 2-dimensional input data and confirm itsefficiency.
II. L EARNING A LGORITHM OF F UZZY ARTWITH G ROUP L EARNING
The proposed Fuzzy ART has an additional step, “GroupLearning”. Each category j corresponds to a vector wj =(wj1 , · · · , wjm ) of adaptive weight. A connection between thewinning category J and the second-winning category J2 iscreated at each step. Fuzzy ART-GL has connections C andthe age of connections, denoted by age. The similarity of input
I and the second-winning prototype wJ2 is measured;| I ∧ w J2 |
≥ ρ.
(1)
|I|
If Eq. (1) is satisfied, a connection between J and J2 iscreated;
C = C ∪ {(J, J2 )}.
(2)

The age of the connection between J and J2 is set to zero(“refresh” the age);
age(J,J2 ) = 0.

(3)

The age of all categories which directly connect with J areincreased;age(J,j) = age(J,j) + 1,j ∈ NJ ,(4)where NJ is the set of categories which directly connect with
J. The connections are removed, if the age is larger thanAT (t);(J, j) ∈/ C,age(J,j) ≥ AT (t),(5)AT (t) = ATi (ATf /ATi )t/tmax ,(6)where tmax is the learning length, ATi and ATf is the initialvalued and the final value of AT , respectively.
III. L EARNING S IMULATION
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Fig. 1. Simulation result. (a) Input data. (b) Learning result of Fuzzy ART.
(c) Learning result of Fuzzy ART-GL.

We consider 2-dimensional input data as Fig.1(a).
The learning results of Fuzzy ART and Fuzzy ART-GL are
shown in Figs. 1(b) and (c). From these results, we can seethat the proliferation of categories occurs with conventional
Fuzzy ART. Furthermore, Fuzzy ART has a lot of categories
in one cluster. In contrast, we can see that the proposed Fuzzy
ART can recognize the group of the input data from its color
as shown in Fig. 1(c). Therefore, the input data is effectively
classified in each appropriate category.
R EFERENCES[1] T. M. Martinetz and K. J. Schulten, “A ‘Neural Gas’ Network Learns
Topologies,” Proc. of ICANN’91, pp. 397-402, 1991.
[2] T. M. Martinetz and K. J. Schulten, “Topology representing networks,”
Neural Networks, vol. 7, no. 3, pp. 507-522, 1994.

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