GMDH Neural Network MATLAB Implementation

The GMDH-type polynomial neural network represents a simplified implementation of the Group Method of Data Handling technique for data processing. This method constructs polynomial neural networks through an iterative layer-building algorithm that automatically determines the network's exact architecture (connection patterns) and size (layer count) during training. The training process employs evaluation criteria that can utilize either additional validation data with performance metrics (following regularity criteria) or explicit complexity control mechanisms such as information criteria (AIC) or minimum description length principles. Key algorithm parameters configurable in the MATLAB implementation include: the number of inputs per individual neuron, maximum polynomial terms allowed within each neuron, flexibility for neurons to receive inputs from both adjacent layers and original input variables (enabling cross-layer connectivity), and progressive reduction of neuron count in subsequent layers to optimize network complexity. The implementation features automatic structural optimization where each iteration evaluates candidate models using defined criteria, selecting optimal architectures through combinatorial selection of polynomial terms and connection patterns. The code includes modular functions for polynomial generation, layer-wise network construction, and validation metrics calculation to ensure computational efficiency while maintaining model accuracy.