Geometrical multi-resolution network based on ridgelet frame

Ridgelet has multi-resolution properties in direction besides scale and position. This paper proposes a geometrical multi-resolution network (GMN) based on ridgelet frame by taking ridgelet as the activation function in the hidden layer. For ridgelet is efficient in describing line, hyperplane, and other non-point like structures in high dimension, the network is capable of catching essential features in ‘direction-rich’ signals and thus representing high-dimensional data sparsely. With the binary ridgelet frame providing the foundation for designation, the network is characteristic of more flexible structure and more accurate description of directions. The construction and learning of the network are presented, as well as a theoretical analysis on its approximation property. At last, the superiority of GMN is demonstrated by simulation results of regression and classification.