Study of Efficiency of Dividing the Problem Space as a Means to Improve Solution of Multi-parameter Inverse Problem by Adaptive Methods⁎

The considered multi-parameter inverse problem is determination of concentrations of salts or ions in multi-component water solutions of inorganic salts by Raman spectroscopy with subsequent spectra analysis by a non-linear adaptive method (multilayer perceptron type artificial neural networks (ANN) and by a linear adaptive method (partial least squares (PLS) method based on principal component analysis). Dividing the problem space into parts by data clustering simplifies the problem within each cluster but reduces the number of samples. This study compares efficiency of application of this approach for problems with different complexity (determination of concentrations of five salts, or ten salts, or ten ions) and with various distributions of samples over concentration range of the components. Based on experimental results, limitations and areas of application of the approach are discussed.