Neural network modelling for very small spectral data sets: reduction of the spectra and hierarchical approach

For studies on industrial materials, scarcity of samples and incomplete inf ormation are everyday situations. Furthermore, the number of points per sam ple typically reaches several hundreds. Consequently, the sample-to-data ra tio does not satisfy the requirements of must of the mathematical treatment s. We thus discuss the use of different approaches in order to reduce the n umber of parameters of the networks in case of data sets with extremely sma ll number of samples. Therefore. more or less new approaches using wavelet or Fourier-transform coefficients for the reduction of spectra have been of fered for a few years. Moreover, the necessity emerges to associate these v arious pie-processing methods with the construction of input-output relatio nships models. Combinations of different artificial neural networks (AMNs) for non-linear hierarchical modelling are thus examined. In practice, we apply these methods to infrared spectra in three different situations: qualitative analysis of complex mixtures (identification) semi-quantitative analysis of a major compound quantitative and precise analysis of minor compounds. This study demonstrates that, when real data are investigated, a combinatio n of compression methods and multilevel modelling offers accuracy advantage s compared with more classical architecture networks. (C) 2000 Elsevier Sci ence B.V. All rights reserved.