Math @ Duke

Publications [#243832] of Mauro Maggioni
Papers Published
 Ferrari, S; Maggioni, M; Borghese, NA, Multiscale approximation with hierarchical radial basis functions networks.,
IEEE Transactions on Neural Networks, vol. 15 no. 1
(January, 2004),
pp. 178188, ISSN 10459227 [15387258], [doi]
(last updated on 2017/12/14)
Abstract: An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a selforganizing (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 quasireal time. Through harmonic analysis, it is demonstrated that, although a HRBF cannot be reduced to a traditional waveletbased 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 threedimensional (3D) 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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