Sigma-Pi$_{t}$ Cascaded Hybrid Neural Network and its Application to the Spirals and Sonar Pattern Classification Problems

A cascade structured neural network called Sigma-Pi$_{t}$ Cascaded Hybrid Neural Network ($\sigma$$\pi$$_{t}$-CHNN) is Proposed. It is an extended version of the Sigma-Pi Cascaded extended Hybrid Neural Network ($\sigma$$\pi$-CHNN), where the classical multiplicative neuron ($\pi$-neuron) is replaced by the translated multiplicative ($\pi$$_{t}$-neuron) model. The learning algorithm of $\sigma$$\pi$$_{t}$-CHNN is composed of an evolutionary programming method, responsible for determining the network architecture, and of a Levenberg-Marquadt algorithm, responsible for tuning the weights of the network. The $\sigma$$\pi$$_{t}$-CHNN is evaluated in 2 pattern classification problems: the 2 spirals and the sonar problems. In the 2 spirals problem, $\sigma$$\pi$$_{t}$-CHNN can generate neural networks with 10％ less hidden neurons than that in previous neural models. In the sonar problem, $\sigma$$\pi$$_{t}$-CHNN can find the optimal solution for the problem i.e., a network with no hidden neurons. These results confirm the expanded information processing capabilities of $\sigma$$\pi$$_{t}$-CHNN, when compared to previous neural network models. network models.