Establishing Structure for Artificial Neural Networks Based-on Fractal

The artificial neural network (ANN) is a widely used mathematical model composed of interconnected simple artificial neurons, which has been applied in a variety of applications. However, how to determine number of neurons in the hidden layers is an important part of deciding overall neural network architecture. Many rule-of-thumb methods for determining the appropriate number of neurons in the hidden layers are suggested. In this study, to the puzzling problem of establishing structure for the Artificial Neural Networks (ANN), from a microscopical view, two concepts called the fractal dimension of connection complexity (FDCC) and the fractal dimension of the expectation complexity (FDEC) are introduced. Then a criterion reference for establishing ANN structure based on the two proposed concepts is presented that, the FDCC might not be lower than its (FDEC), and when FDCC is equal or approximate to FDEC, the ANN structure might be an optimal one. The proposed criterion is examined with good results.