Abstract: By combining the ridgelet theory with the neual network, an adaptive rideglet neural network is presented by adopting a directional ridgelet function as the activation function of the hidden layer. For the stability of ridgelet in representing high dimensional data and the sparsity in approximating linear singularity (curvilinear singularity when using a multiscale ridgelet), the proposed network can learn quit a large group of multivariate functions with a reduced scale. On the other hand, it has more flexible structure, rapider processing speed, greater tolerance and robustness than the fixed ridgelet transform. Simulation results are also included to prove its efficiency.

Key words: function approximation, neural network, ridgelet neural network