Multiscale approximation with hierarchical radial basis functions networks

IEEE Transactions on Neural Networks
Stefano FerrariN A Borghese

Abstract

An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a self-organizing (by growing) multiscale version of a radial basis function (RBF) network. It is constituted of hierarchical layers, each containing a Gaussian grid at a decreasing scale. The grids are not completely filled, but units are inserted only where the local error is over threshold. This guarantees a uniform residual error and the allocation of more units with smaller scales where the data contain higher frequencies. Only local operations, which do not require any iteration on the data, are required; this allows to construct the network in quasi-real time. Through harmonic analysis, it is demonstrated that, although a HRBF cannot be reduced to a traditional wavelet-based multiresolution analysis (MRA), it does employ Riesz bases and enjoys asymptotic approximation properties for a very large class of functions. HRBF networks have been extensively applied to the reconstruction of three-dimensional (3-D) models from noisy range data. The results illustrate their power in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by MRA.

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Citations

Jun 10, 2009·Journal of Neuroscience Methods·M SciarabbaN A Borghese
Mar 14, 2009·IEEE Transactions on Visualization and Computer Graphics·M Alper Selver, Cüneyt Güzeliş
Dec 17, 2009·IEEE Transactions on Neural Networks·Stefano FerrariN Alberto Borghese
Jun 9, 2009·IEEE Transactions on Neural Networks·Jean-François Connolly, Richard Labib
Jul 22, 2006·IEEE Transactions on Neural Networks·David WedgeZuhair Bandar
Feb 7, 2007·IEEE Transactions on Neural Networks·Stefano FerrariN Alberto Borghese
Feb 14, 2008·IEEE Transactions on Neural Networks·J I Mulero-Martinez
Mar 11, 2006·IEEE Transactions on Neural Networks·Jinn-Tsong TsaiTung-Kuan Liu
Sep 1, 2012·IEEE Transactions on Neural Networks and Learning Systems·Francesco BellocchioNunzio Alberto Borghese
Aug 10, 2010·IEEE Transactions on Neural Networks·Muzhou Hou, Xuli Han
Aug 27, 2005·IEEE Transactions on Neural Networks·Stephen A Billings, Hua-Liang Wei

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