A linear ridgelet network

Abstract

The multiscale properties of the reception field of the human visual cortex have illuminated the research of wavelet neural network (WNN). Findings in neurophysiology indicate that in the human visual system there are specialized areas in the visual cortex that respond for particular orientations. In other words, the reception field of visual cortex has the multiresolution properties in direction, as well as in localization and scale. Enlightened by these facts, a three layer feed-forward neural network (FNN) is presented by employing ridgelet as the activation function in the hidden layer. To get rapid learning when dealing with high dimensional samples, we proposed an efficient linear learning algorithm inspired by traditional kernel smoothing method, which has low computation complexity proportional to the number and dimension of samples. At the cost of a little degradation in accuracy, the network can achieve rapid learning. Some simulation experiments about function approximation are taken, and several commonly used regression ways are considered under the same conditions to give a comparison result. The results show that the proposed linear ridgelet network can overcome the curse of dimensionality in the training of FNNs and exhibit better performance in high dimension than its counterparts, especially when some spatial inhomogeneities exist in the function.