Development of adaptive B-splines using CMAC neural networks

Summary form only given. Adaptive splines can be used to construct smooth approximations to unknown functions as data are received online. When the adaptive spline is multidimensional with a large number of knot points, the computational requirements of conventional implementations can limit the utility of an adaptive spline approach. Artificial neural networks have shown that multidimensional nonlinear functions can be learned from training data by adjusting the weights of simple neuron-like processing elements. It is shown that by formulating the problem using B-spline receptive field excitation functions the computational architecture of a CMAC (cerebellar model articulation controller) neural network is naturally suited for implementing adaptive splines and learning the spline coefficients. The use of B-spline receptive field excitation functions also enables higher order CMAC neural networks to be developed that can learn both functions and function derivatives. This ability coupled with the computational efficiency of a CMAC neural network will allow the real-time construction of multidimensional functions and their Jacobian matrices on traditional computing architectures.<>