Page 44 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

MODELING OF BIOMEDICAL SYSTEMS 21

The error gradient can be expressed as
m m
(δE /δW ) = (δE /δF)(dF/dW ) (1.58)
i,j i,j
For a sigmoid function (F), it turns out that the differential is a simple function of the sigmoid as
follows:
dF = b(1 − F)F (1.59)

where b is a constant. Thus,
(dF/dW ) = b(1 − F(W ))F(W ) (1.60)
i,j i,j i,j
For adjusting the weights for connections between the input and the hidden layer neurons, the error
is back propagated by calculating the partial derivative of the error E with respect to the weights w j,k
similarly (Haykin, 1999).
The whole process of calculating the weights using the sample data sets is called the training
process. There is a neural network package in the MATLAB which can be easily used in the train-
ing process. There are several algorithms in the package, including the back propagation, modified
back propagation, etc. which the user can choose in the MATLAB software. Once the weights are
calculated using MATLAB or any other software, it becomes a matter of obtaining the output vector
for a given input vector using matrix multiplications. The most important aspect of a neural network
is that it should be tested with data not used in the training process.
Neural networks have been used for classification and control. For instance, Reddy et al. (1995)
used neural networks to classify the degree of the disease in dysphagic patients using noninvasive
measurements (of throat acceleration, swallow suction, pressure, etc.) obtained from dysphagic
patients during swallowing. These measurements were the inputs to the network and the outputs
were normal, mild, moderate, and severe. Neural network performance depends on the sample data,
initial weights, etc. Reddy et al. (1995) trained several networks with various initial conditions and
activation functions. Based on some initial testing with known data, they recruited the best five net-
works into a committee. A majority opinion of the committee was used as the final decision. For clas-
sification problems, Reddy and Buch (2000) and Das et al. (2001) obtained better results with
committee of neural networks (Fig. 1.11) when compared to a single network, and the majority opin-
ion of the committee was in agreement with clinical or actual classification.

Committee of Neural Networks
Classification by majority opinion

NW-1 NW-2 NW-3 NW-4 NW-5

Extracted features/parameters
FIGURE 1.11 The committee of neural networks. Each of the
input parameters is simultaneously fed to several networks working in
parallel. Each network is different from the others in terms of initial
training weights or the activation function (transfer function at the nodes).
A majority opinion of the member networks provides the final decision
of the committee. This committee of networks simulates the parliamen-
tary process, and emulates a group of physicians making the decision.
[Reddy and Buch (2000).]