Scalar wavelet networks for time series prediction
Bruce A. Whitehead · 1995
1 1 2 - layer neural networks whose basis functions are scalar wavelets, trained with the quickprop gradient descent algorithm, appear to train more quickly and yield lower prediction errors on the Mackey-Glass chaotic time series than comparable networks of conventional sigmoid units. 1. INTRODUCTION A "1 1 2 - layer" neural network attempts to approximate an arbitrary real-valued multivariate function f as a linear combination of basis functions h i ; i = 1; : : : ; m. The basis functions h i are typically constrained to be affine transformations of a prototype basis function h. Wavelet basis functions, by virtue of being localized in both the input-space domain and its corresponding frequency domain, form theoretically attractive candidates for the prototype basis function h. Regularly-spaced grids of wavelets, arranged in a hierarchy of meshes at successively finer resolutions, have been shown capable of approximating a large class of target functions f to any desired accuracy ...