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 information are everyday situations. Furthermore, the number of points per sample typically reaches several hundreds. Consequently, the sample-to-data ratio does not satisfy the requirements of most of the mathematical treatments. We thus discuss the use of different approaches in order to reduce the number of parameters of the networks in case of data sets with extremely small number of samples. Therefore, more or less new approaches using wavelet or Fourier-transform coefficients for the reduction of spectra have been offered for a few years. Moreover, the necessity emerges to associate these various pre-processing methods with the construction of input–output relationships models. Combinations of different artificial neural networks (ANNs) for non-linear hierarchical modelling are thus examined. ctice, we apply these methods to infrared spectra in three different situations:• ative analysis of complex mixtures (identification) uantitative analysis of a major compound tative and precise analysis of minor compounds. tudy demonstrates that, when real data are investigated, a combination of compression methods and multilevel modelling offers accuracy advantages compared with more classical architecture networks.