平成19年度電気関係学会四国支部連合大会

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17-25

Fuzzy ARTMAP with Group Learning
Haruka Isawa, Masato Tomita, Haruna Matsushita and Yoshifumi Nishio(Tokushima University)

1. Introduction
Fuzzy ARTMAP achives a synthesis of fuzzy logic andadaptive resonance theory (ART). In this study, we adapt
an additional step called “Group Learning” to Fuzzy
ARTMAP. This new algorithm is called Fuzzy ARTMAP
with Group Learning (FAM-GL). The important featureof the group learning is that creating connections between
similar categories. In other words, the FAM-GL learns not
only categories but also its connections, namely, groups ofthe categories. We investigate the behavior of FAM-GL,and discuss the results.

2. Proposed Fuzzy ARTMAP
Fuzzy ARTMAP system incorporates two fuzzy ART
modules, ARTa and ARTb , that are linked together
through map field Fab . ARTa is composed of Fa1 (inputlayer) and Fa2 (category layer). ARTb also has Fb1 andFb2 . Input to ARTa and ARTb are in the complement code
form, for ARTa , I = A = (a, ac ), and for ARTb , I = B= (b, bc ). For the map field (MF), let xab denote the Fab
output vector, and let wjab denote the weight vector fromthe jth node to Fab .
(FAM-GL1) A and B are inputted to Fa1 and Fb1 , respectively.
(FAM-GL2) For Fa2 , a winning category J is chosen bychoice function Tj . J has maximal TJ . For ARTb , winningcategory K is chosen in the same way. Furthermore, forthe group learning, the second-winning category, denotedby J2 , is found. namely, TJ2 is the second largest.
and the out put vector y b of Fb2 are(FAM-GL3) wabjabgived to MF. x is calculated by| xab |≡| y b ∧ wab
J | .

(1)

By Eq. (1), xab = 0 if the prediction wab
J is disconfirmed
by y b . Such a mismatch event triggers an ARTa search fora better category, as follows.
(FAM-GL4) Match Tracking: At the start of each input presentation to ARTa , vigilance parameter ρa equals abaseline vigilance, ρa . The map field vigilance parameteris ρab . If
| xab | < ρab | y b |,(2)then ρa is increased until it is slightly larger than| A ∧ waj || A |−1 . When this occurs, ARTa
search leads either to activation of another Fa2 node J, if
no such node exists, to shutdown of Fa2 for the remainderof the input presentation. On the other hand, if| xab | ≥ ρab | y b |,(FAM-GL6) The age of all categories which directly connect with the winning category J are increased one;oldagenew
J,j = ageJ,j + 1,CJ,j = 0,then follow step the (FAM-GL8).
(FAM-GL5) In this step, it is decided whether if a connection is formed. Eq. (3) is satisfied, a connection between
the winning category J and the second-winning categoryJ2 is created; CJ,J2 = 0. The age of the connection between
the winning category J and the second-winning categoryJ2 is set to zero “refresh” the age; ageJ,J2 = 0. On thecontrary, if Eq. (3) is not satisfied, the connection is notformed.

(4)age(J,j) ≥ AT (t),(5)t/tmaxAT (t) = ATi (ATf /ATi ),(6)where tmax is the learning length, ATi and ATf is the initial value and the final value of AT , respectively. The steps
from (FAM-GL1) to (FAM-GL7) are repeated for all theinput data. Therefore, Fuzzy ART-GL makes connections
or releases connections at each step.
(FAM-GL8) Learning: If Eq. (3) is satisfied, weight vectors waJ , wbK , wab
J are updated, as follows.
a(new)a(old)a(old)wJ= βa (A ∧ wJ) + (1 − βa )wJb(new)b(old)b(old)
wK= βb (B ∧ wK ) + (1 − βb )wKab(new)wJ=| y b ∧ wab
J |(7)

3. Simulation Results
We consider 2-dimensional input data of 300 points,
which are random data. The learning results of Fuzzy
ARTMAP and FAM-GL are shown in Fig. 1. Rectangles represent categories. From these results, we can seethat the categories predicted being outside the circle arerepresented by dashed lines, and the categories predictedbeing inside are represented by straight lines in Fig. 1(a).
Therefore input data are divied into two kinds of categories. However, we can not see an association betweencategories. On the other hand, in Fig. 1(b), we can see
categories are divided into four groups by four marks. Inother words, we can obtain two results of category learningand group learning by FAM-GL.
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j ∈ NJ ,where NJ is set of categories which directly connect withJ.
(FAM-GL7) The connections are removed, if their age
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Figure 1: Simulation result. (a) Simulation resultof the Fuzzy ARTMAP. (b) Simulation result of theFAM-GL.

4. Conclusions
In this study, we have adapted “Group Learning” toFuzzy ARTMAP. We have investigated its behaviors withapplication to categorization of 2-dimensional input data,and confirmed the efficiency of FAM-GL.