A Multi-layer ADaptive FUnction Neural Network (MADFUNN) for Analytical Function Recognition

In our previous work, we developed an adaptive function neural network (ADFUNN) [1]. ADFUNN is based on a linear piecewise neuron activation function that is modified by a novel gradient descent supervised learning algorithm. The simulation results of applying ADFUNN to XOR, Iris dataset, and the natural language processing task of phrase recognition [2] reveal that without any hidden neuron ADFUNN offers several advancements over the traditional single-layer perceptron (SLP). Linearly inseparable problems can be solved [1, 2] by ADFUNN, and the learned function of ADFUNN supports intelligent data analysis. In this paper, smoothed learned functions [3] are prepared for recognising their closest fit to a set of analytical functions. We generated 1400 training patterns, for six commonly used analytical function classes plus one non function class, and introduce a Multi-layer ADFUNN (MADFUNN) for this problem [4]. As expected, MADFUNN solves the function recognition task more accurately than a simple back-propagation network and requires fewer hidden neurons.