Artificial neural networks sigmoid function

An example of a non-covalent MIP sensor array is shown in Fig. 21.14. Xylene imprinted poly(styrenes) (PSt) and poly(methacrylates) (PMA) with 70 and 85% cross-linker have been used for the detection of o- and p-xylene. The detection has been performed in the presence of 20-60% relative humidity to simulate environmental conditions. In contrast to the calixarene/urethane layers mentioned before, p-xylene imprinted PSts still show a better sensitivity to o-xylene. The inversion of the xylene sensitivities can be gathered with PMAs and higher cross-linker ratios. As a consequence of the humidity, multivariate calibration of the array with partial least squares (PLS) and artificial neural networks (ANN) is performed, The evaluated xylene detection limits are in the lower ppm range (Table 21.2), whereas neural networks with back-propagation training and sigmoid transfer functions provide the most accurate data for o- and p-xylene concentrations as compared to PLS analyses. 

The constants a, b, and c define the sigmoid curve, which has the asymptotic values zero for x —> —X and a for x 4-Y (a and c are expected to have positive values). The position and steepness of the curve between the two asymptotic values depend on the parameters b and c. A logistic function is the result of a logistic regression analysis, where b + cx is replaced by a linear combination of all x-variables. With values 1, 0, and 1 for a, b, and c, respectively, the logistic function is often used as a transfer function for back-propagation networks, a type of artificial neural network. See Neural Networks in Chemistry. 

The hyperbolic tangent (tanh) function, with a sigmoid shape, is the most used transfer function for artificial neural networks. The corresponding kernel has the formula ... 

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