Determination of the optimal number of components in independent components analysis.

Independent components analysis (ICA) may be considered as one of the most established blind source separation techniques for the treatment of complex data sets in analytical chemistry. Like other similar methods, the determination of the optimal number of latent variables, in this case, independent components (ICs), is a crucial step before any modeling. Therefore, validation methods are required in order to decide about the optimal number of ICs to be used in the computation of the final model. In this paper, three new validation methods are formally presented. The first one, called Random_ICA, is a generalization of the ICA_by_blocks method. Its specificity resides in the random way of splitting the initial data matrix into two blocks, and then repeating this procedure several times, giving a broader perspective for the selection of the optimal number of ICs. The second method, called KMO_ICA_Residuals is based on the computation of the Kaiser-Meyer-Olkin (KMO) index of the transposed residual matrices obtained after progressive extraction of ICs. The third method, called ICA_corr_y, helps to select the optimal number of ICs by computing the correlations between calculated proportions and known physico-chemical information about samples, generally concentrations, or between a source signal known to be present in the mixture and the signals extracted by ICA. These three methods were tested using varied simulated and experimental data sets and compared, when necessary, to ICA_by_blocks. Results were relevant and in line with expected ones, proving the reliability of the three proposed methods.