平成20年度電気関係学会四国支部連合大会

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17-4

Fuzzy ART Relieving Vigilance
Haruka Isawa, Haruna Matsushita and Yoshifumi Nishio(Tokushima University)

1. Introduction
Fuzzy ART (Adaptive Resonance Theory) is oneof the unsupervised neural networks introduced by
G.A.Carpenter and S.Grossberg. Fuzzy ART is applied toassociation, clustering and memory of input pattern. Thismodel put focus on stability- plasticity dilemma by using
a vigilance parameter. In this study, we propose a new
type of Fuzzy ART algorithm, which is called Fuzzy ART
Relieving Vigilance (R-FART). The important feature ofR-FART is that the vigilance parameter varies. We investigate the behavior of R-FART and compare R-FART withthe conventional Fuzzy ART.

2. Proposed Fuzzy ART (R-FART)
R-ART is composed of F1 (input layer) and F2 (categorylayer). F1 and F2 are connected by the bottom-up-weightvector wij and the top-down-weight vector wji . m neuronsof the input layer F1 correspond to the an input vector I.
Input vector: Each input I is an m-dimensional vector
I = (I1 , · · · , Im ), where Ii ∈ [0, 1]m .
Weight vector: Each category j corresponds to a vector
wj = (wj1 , · · · , wjm ), (j = 1, · · · , n) of adaptive weight.
Parameters: R-FART dynamics are determined by achoice parameter α > 0; a learning parameter β ∈ [0, 1];
and the vigilance parameter ρ(t) ∈ [0, 1]. The vigilance parameter is ﬁxed value in the conventional Fuzzy ART. However, in R-FART, the vigilance parameter is varied withlearning.
(RFART1) An input vector I is inputted to the categorylayer F2 from the input layer F1 .
(RFART2) A winning category J is chosen. For the input
vector I and category j, choice function Tj is deﬁned by
Tj (I) =| I ∧ wj |,(α+ | wj |)(1)

where the fuzzy AND operator ∧ and the norm | · | aredeﬁned by(p ∧ q)i ≡ min(pi , qi ), | P |≡m∑| pi |.

(2)

i=1

The winning category J, whose Tj is maximum, is found;
TJ = max{Tj : j = 1 · · · n}.

(3)

If more than one Tj is maximal, the category j with thesmallest index is chosen as the winner J.
(RFART3) The similarity of I and the current winningcategory wJ is measured by the vigilance criterion. We
check whether| I ∧ wJ |≥ ρ(t).
(4)|I|

algorithm, the vigilance parameter ρ(t) is varied according
to the learning step t as following gaussian function;
ρ(t) = √−(t − µ)21exp{}.
2σ 22πσ(6)(RFART4) wJ is updated byold= β(I ∧ woldwnew
J ) + (1 − β)w J ,J(7)if there is J which satisﬁes Eq. (4). On the contrary, if allavailable F2 nodes do not satisfy Eq. (4), a new category
is established in F2 ;wn+1 = I.

(8)(RFART5) The steps from (FART1) to (FART4) are repeated for all the input data.
(Complement coding) To prevent weight vector frommonotone decreasing, let input I preprocess into the complement coding form.
I = (a ; ac ) = (a1 , · · · , aM , ac1 , · · · , acM ),(9)

4. Simulation Results
We apply R-FART to the real world clustering problem.
We use the iris data as real data. This data set is widelyused to be found in pattern recognition literatures, andcontains three classes of 50 instances each, where each classrefers to a type of iris plant. One class is linearly separablefrom the other 2; the latter are not linearly separable fromeach other. The parameters for the learning are chosen as
follows; (For Fuzzy ART) α = 0.2, β = 1, ρ = 0.8, (For RFART) α = 0.2, β = 1, N (0, 1). We perform the learning
simulation 10 times. Table 1 shows percent recognition
for Fuzzy ART and R-FART. The correct answer rate isobtained by;
Ncr× 100 [%],(10)Ncwhere Nr is the obtained number of the desired input data
within the class c and Nc is the total number of the input
data belonging to the class c. From the simulation resultof Fuzzy ART, Fuzzy ART can not recognize class 3 wellbecause iris data has linearly inseparable classes. In contrast, we can see that the recognition percent is improvedin every case from the simulation result of R-FART.
Iris data
Best [%]
Fuzzy ART
Worst [%]
Average[%]Best [%]
R-FART
Worst [%]
Average[%]

Class 1887480.01009899.5

Class 2682238.61005492.0Class 3
102
8.8
7230
56.2

If Eq. (4) is not satisﬁed, namely| I ∧ wJ |< ρ(t),|I|

4. Conclusions(5)

a new index J is chosen by Eq. (3). The search processcontinues until the chosen J satisﬁes Eq. (4). In R-FARTIn this study, we have proposed Fuzzy ART Relieving
Vigilance (R-FART). We have investigated its behaviors
with application to iris data, and conﬁrmed the eﬃciencyof R-FART.