Neural Classifiers - Neural Networks and Micromechanics - page 42

Table 3.4 Error numbers in the final experiments
Number of experiments 1 2 3

Number of errors 60 59 64

Mean number of errors 61.33

3.6 Discussion

The novel neural classifier LIRA was developed, which contains three neuron
layers: sensor, associative, and output layers. The sensor layer is connected with
the associative layer with no modifiable random connections, and the associative
layer is connected with the output layer with trainable connections. The training
process converges sufficiently fast. This classifier does not use floating-point and
multiplication operations, and this property, in combination with the parallel
structure of the classifier, permits it to be implemented in low-cost, high-speed
electronic devices. The classifier LIRA, tested on the MNIST database, shows good
recognition rates. It contains 60,000 handwritten digit images for the classifier
training and 10,000 handwritten digit images for the classifier testing.
The results obtained on the MNIST database seem sufficient for applications, but
there are many uses for handwritten number recognition. If the number contains, for
example, ten digits and the recognition rate of one digit is 0.994 (as in our case), the
whole number recognition rate could be 0.994 10 = 0.942 = 94.2%. This recognition
rate is insufficient for many applications. For this reason, additional investigations
are needed to improve handwritten digit recognition rate.
The recognition time of each handwritten digit is also an important parameter. In
many cases, to estimate the recognition time, the authors of different methods give
the number of multiply-accumulate operations for one symbol recognition. For
example, for the RS-SVM method it equals 650,000, and LeNet-5 is about 60% less
expensive [ 21 ]. It is difficult to compare our classifier using this parameter because
our classifier uses neither multiply operations nor floating-point operations. For one
digit recognition, our classifier needs approximately 50,000 fixed-point add opera-
tions. This may seem very fast, but it is not. For one image coding, it needs
approximately 10 x 256,000 readings from memory and logical operations. During
recognition, we must code not only the initial image, but also, for example, four
distortions. This whole process demands nearly ten million operations for each digit
recognition, which is difficult to compare with the number of floating-point opera-
tions. In general, our classifier has lower recognition speed than methods by LeCun
and SVM.
The other method to compare recognition time is testing classifiers on similar
computers. Belongie [ 23 ] gives the time of the shape matching as 200 ms on a
Pentium III, 500 MHz workstation. Using the regular nearest neighbor method,
it is necessary to make N matchings for each digit recognition, where N is the size
of the training set (Belongie used from 15,000 to 20,000 images). In this case,
the recognition time of one digit could be from 3,000 seconds to 4,000 seconds.