Biomedical Engineering Reference
In-Depth Information
To create the encoder structure, we have to select the subspaces for each neuron
block. For example, if the subspace size is 3, in each neuron block j we will use only
three input parameters whose numbers we select randomly from the range 1,
,
n
(where
n
is the dimension of the input space; in our case,
n
= 48). After that, we
calculate the thresholds for each pair of neurons
l
i
j
and
h
i
j
of three selected neurons
a
i
j
of the block
j
. For this purpose, we select the point
x
i
j
randomly from the range [0,
...
,
X
i
]. After that, we select the random number
y
i
j
uniformly distributed in the range [0,
...
...
, GAP], where GAP is the parameter of the encoder structure. Then we calculate
the thresholds of neurons
l
i
j
and
h
i
j
in accordance with the following formulas:
Trl
i
¼
x
i
y
i
;
then Trl
i
¼
(3.1)
if Trl
i
<
X
i
min
X
i
min
;
Trh
i
¼
x
i
þ
y
i
;
then Trh
i
¼
(3.2)
if Trh
i
>
X
i
max
X
i
max
;
where
Trl
i
and
Trh
i
are the thresholds of neurons
l
i
j
and
h
i
j
respectively, and
X
i
min
and
X
i
max
are the minimum and maximum possible values for a component
X
i
of
the input vector (
X
1
,
,
b
s
)
corresponding to the feature vector. This vector is presented to the input of the one-
layer classifier. The training rule of our one-layer classifier is the same as the
training rule of the one-layer perceptron.
,
X
n
). Then the encoder forms a binary vector (
b
1
,
...
...
3.2 LIRA Neural Classifier for Handwritten Digit Recognition
There are many applications for handwritten digit recognition, such as for bank
checks and custom declaration automatic reading. Various methods were proposed
to solve this problem [
20
-
22
]. To estimate a method's effectiveness, the most
important parameter is recognition rate. This parameter shows the proportion of
samples in the test database that is recognized correctly.
The MNIST database contains 60,000 handwritten digits in the training set and
10,000 handwritten digits in the test set. Different classifiers tested on this database
by LeCun [
21
] had shown recognition rates from 88% to 99.3% (Table
3.1
). In
recent years, new results were obtained using shape matching and Support Vector
Machine methods [
23
,
24
].
We have developed the new neural classifier LIRA (LImited Receptive Area
classifier) based on Rosenblatt's perceptron principles. To adapt Rosenblatt's
perceptron for handwritten digit recognition problems, we made some changes in
perceptron structure, training, and recognition algorithms. Rosenblatt's perceptron
contains three layers of neurons. The first layer
S
corresponds to the retina. In
technical terms it corresponds to input image. The second layer
A
, called the
