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In-Depth Information
While some of these are biologically inspired approaches such as neural networks [7],
genetic algorithms [8], AIS approaches remained unexplored for this application; though
AIS techniques have been applied to several pattern recognition problems [9-14].
The rest of the paper is organized as follows. Section-2 describes the CSA with the
proposed retraining scheme. Section-3 provides the experimental details and report re-
sults highlighting the performance of the CSA in classifying handwritten numerals. This
section also exhibits the performance of the new retraining scheme over the previously
used single-pass approach. In addition, section-3 discusses the effect of CSA control
parameters on its performance, and section-4 provides some concluding remarks.
2 Classification Using Clonal Selection Algorithm
Let
AG
represent a set of training data (antigens) and
ag
i
represents an individual
member of this set:
AG
= {
ag
1
,
ag
2
, …,
ag
k
}. Each
ag
i
has two attributes:
class
:
ag.c
∈
C
={
c
1
,
c
2
,………
c
n
} (
n
= 10 for digit classification) and
feature vector
:
ag.f
. Let the
immune memory,
IM
={
m
1
,
m
2
, …,
m
m
} where
m
i
is a memory cell having two attrib-
utes similar to those of an individual antigen. For any
m
i
,
m
i
.c
∈
C
= {
c
1
,
c
2
,………
c
n
}
is the class information and
m
i
.f
is the feature vector.
Binary images of handwritten numerals are first size-normalized in a 48x48 matrix
whose each element is binary. This matrix is used as a feature map for the experi-
ments. Similarity between two such feature matrices
S
(
F
1
,
F
2
) a measure of auto-
correlation coefficient between
F
1
and
F
2
as defined below:
s
s
−
s
s
1
10
01
00
11
S
(
F
,
F
)
=
−
(1)
1
2
2
2
(
s
+
s
)(
s
+
s
)(
s
+
s
)(
s
+
s
)
11
10
01
00
11
01
10
00
where
s
00
,
s
11
,
s
01
, and
s
10
denote the number of zero matches, one matches, zero mis-
matches, and one mismatches, respectively. It is to be noted that
S
gives values in the
range [0, 1], where
1
indicates the highest and
0
signifies the lowest similarity be-
tween two samples. We used this metric to measure similarity/affinity during anti-
body-antibody or antigen-antibody interactions.
Training has two phases: Phase-I is the same as was used in [6], while Phase-II in-
corporates a refinement process. Phase-I involves three stages namely, initialization
of immune memory, clone generation, and selection of clones to update the immune
memory. These stages are briefly discussed below.
Initialization:
This stage deals with choosing some antigens as initial memory cells to
initialize the immune memory. In the present study, only one antigen from each class is
randomly chosen to initialize the immune memory (
IM
). It is to be noted that the num-
ber of initial cells has certain effect on system's performance as illustrated in [6].
Clone generation:
For a given antigen
ag
i
, its closest match (say,
m
i
) is, at first, cho-
sen from the existing
IM
as follows:
stim
(
ag
i
, m
i
)
i
and
m
j
.c=ag
i
.c
(2)
The function
stim
() is used to measure the response of a
b-
cell to an antigen or to
another
b-
cell and is directly proportional to the similarity between the feature
matrices as defined in equation (1). After a memory cell
m
i
(renamed as
m
match
) is
≥
stim
(
ag
i
, m
j
), for all
j
≠
