Information Technology Reference
In-Depth Information
which is a memory overhead of the design. A
k
-attractor two class classifier needs
log
2
(
k
) bits.
To classify pattern set into two classes, we should ideally find an
MACA
with two attractor basins - each basin having the members of the specific class.
Even if this ideal situation is not attained, the algorithm should design a
MACA
based classifier having minimum number of attractor basins - while one subset
of basins accommodates the elements of one class, the remaining subset houses
the elements of the other class.
MACA based two class classifier.
The design of the
MACA
based Classifier
for two pattern sets
P
1
and
P
2
should ensure that elements of one class (say
P
1
)
are covered by a set of attractor basins that do not include any member from the
class
P
2
. Any two patterns
a ∈ P
1
and
b ∈ P
2
should fall in different attractor
basins. According to
Theorem 2
, the pattern derived out of
modulo-2
sum of
a
and
b
(
a ⊕ b
) should lie in a non-zero attractor basin. Let X be a set formed
from
modulo-2
sum of each member of
P
1
with each member of
P
2
that is,
X
=
{x
l
| x
l
=(
a
i
∈ P
1
)
⊕
(
b
j
∈ P
2
)
∀
i,j
}
. Therefore, all members of
X
should fall in non-zero basin. This implies that the following set of equations
should be satisfied.
T
d
· X
= 0
(1)
where
T
is a valid
MACA
to be employed for designing two class classifier.
Design of Multi-class Classifier.
A two class classifier can be viewed as a
single stage classifier. For designing a multi-class classifier, this scheme of single
stage classification will be repeatedly employed leading to a multi-stage classifier
consisting of multiple
CA
, each
CA
corresponds to a single stage (
Fig.3
).
Hence, in the rest of the paper, we concentrate on designing an e
%
cient
CA
based two class classifier.
T0
S1, S2, S3, S4
S = {S1, S2, S3, S4}
T1
S1, S2
S3, S4
T2
S1
S2
S3
S4
Fig. 3.
MACA
based multi-class classifier. Note : A leaf node represents a class in the
input set
S
=
{
S
1
,
S
2
,
S
3
,
S
4
}
3 Genetic Algorithm for Evolution of
MACA
The aim of this evolution scheme is to arrive at the desired
MACA
(
T
matrix)
that can perform the task of classification with minimum number of attractors.
