Orthonormal ridgelets and linear singularities
SIAM Journal on Mathematical Analysis
Geometrical multi-resolution network based on ridgelet frame
Signal Processing
Letters: Convex incremental extreme learning machine
Neurocomputing
Neurocomputing
A new adaptive ridgelet neural network
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
Wavelet neural networks for function learning
IEEE Transactions on Signal Processing
The finite ridgelet transform for image representation
IEEE Transactions on Image Processing
Real-time learning capability of neural networks
IEEE Transactions on Neural Networks
Universal approximation using incremental constructive feedforward networks with random hidden nodes
IEEE Transactions on Neural Networks
A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks
IEEE Transactions on Neural Networks
Engineering Applications of Artificial Intelligence
A collaborative decision-making model for orientation detection
Applied Soft Computing
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To approximate the multivariate functions with spatial inhomogeneity, in this paper we proposed an ortho-ridgelet neural network (ORNN) model. By taking orthonormal ridgelet, which is a ''true'' ridgelet function different with the ''classic'' ridgelet, as the activation function of the hidden neurons, the network is characterized of more efficient representation of a set of functions with linear and curvilinear singularities. Although the ortho-ridgelet is initially more complicated to be understood than ridgelet, it can be easily applied to function approximation theory in a more effective manner. Moreover, we extended the ORNN model to the time-varied situation, and the time-varied ortho-ridgelet neural network (TV-ORRN) is established for time-varied function approximation, with an incremental learning of the ridgelets output layer. The theoretical analysis is presented and some experiments are taken, and the experimental results prove its efficiency in approximation of multivariate functions with linear and curvilinear singularities, in both the stationary and time-varied environment.