Radial basis functions for multivariable interpolation: a review
Algorithms for approximation
Universal approximation using radial-basis-function networks
Neural Computation
Regularization in the selection of radial basis function centers
Neural Computation
Representation of functional data in neural networks
Neurocomputing
Signal detection using the radial basis function coupled map lattice
IEEE Transactions on Neural Networks
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In this paper, functional prediction is carried out for spatio-temporal systems in which the spatial data is irregularly sampled. We propose a novel method called Kalman Filter Radial Basis Function (KF-RBF) for such a purpose. It casts the problem into a Reproducing Kernel Hilbert Space (RKHS) defined by some continuous, symmetric and positive definite Radial Basis Function (RBF), thereby allowing for irregular sampling in the spatial domain. A Functional Auto-Regressive (FAR) model describing the system evolution in the temporal domain is further assumed. The FAR model is then formulated as a Vector Auto-Regressive (VAR) model embedded into a Kalman Filter (KF). This is achieved by projecting the unknown functions onto a time-invariant functional subspace. Subsequently, the weight vectors obtained become inputs into a Kalman Filter (KF). In this way, nonstationary functions can be forecasted by evolving these weight vectors.