A new directional multi-resolution ridgelet network

In this paper, we propose a new directional multi-resolution ridgelet network (DMRN) based on the ridgelet frame theory, which uses the ridgelet as the activation function in a hidden layer. For the multi-resolution properties of the ridgelet function in the direction besides scale and position, DMRN has great capabilities in catching essential features of direction-rich data. It proves to be able to approximate any multivariate function in a more stable and efficient way, and optimal in approximating functions with spatial inhomogeneities. Besides, using binary ridgelet frame as the mathematical foundation in its construction, DMRN is more flexible with a simple structure. The construction and the learning algorithm of DMRN are given. Its approximation capacity and approximation rate are also analyzed in detail. Possibilities of applications to regression and recognition are included to demonstrate its superiority to other methods and feasibility in practice. Both theory analysis and simulation results prove its high efficiency.

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