Classification of 2-dimensional array patterns: Assembling many small neural networks is better than using a large one

In many pattern classification/recognition applications of artificial neural networks, an object to be classified is represented by a fixed sized 2-dimensional array of uniform type, which corresponds to the cells of a 2-dimensional grid of the same size. A general neural network structure, called an undistricted neural network, which takes all the elements in the array as inputs could be used for problems such as these. However, a districted neural network can be used to reduce the training complexity. A districted neural network usually consists of two levels of sub-neural networks. Each of the lower level neural networks, called a regional sub-neural network, takes the elements in a region of the array as its inputs and is expected to output a temporary class label, called an individual opinion, based on the partial information of the entire array. The higher level neural network, called an assembling sub-neural network, uses the outputs (opinions) of regional sub-neural networks as inputs, and by consensus derives the label decision for the object. Each of the sub-neural networks can be trained separately and thus the training is less expensive. The regional sub-neural networks can be trained and performed in parallel and independently, therefore a high speed can be achieved. We prove theoretically in this paper, using a simple model, that a districted neural network is actually more stable than an undistricted neural network in noisy environments. We conjecture that the result is valid for all neural networks.This theory is verified by experiments involving gender classification and human face recognition. We conclude that a districted neural network is highly recommended for neural network applications in recognition or classification of 2-dimensional array patterns in highly noisy environments.