Multivariate calibration of analytical signals by WILMA (wavelet interface to linear modelling analysis)

A novel algorithm based on coupling of the fast wavelet transform (FWT) with MLR and PLS regression techniques for the selection of optimal regression models between matrices of signals and response variables is presented: wavelet interface to linear modelling analysis (WILMA). The algorithm decomposes each signal into the FWT domain and then, by means of proper criteria, selects the wavelet coefficients that give the best regression models, as evaluated by the leave-one-out cross-validation criterion. The predictive ability of the regression model is then checked by means of external test sets. Moreover, the signals are reconstructed back in the original domain using only the selected wavelet coefficients, to allow for chemical interpretation of the results. The algorithm was tested on different literature data sets: two near-infrared data sets from Kalivas, on which the performances of many calibration algorithms have already been tested, and a data set consisting of lead and thallium mixtures measured by differential pulse anodic stripping voltammetry and giving seriously overlapped responses. Good results were obtained for all the studied data sets; in particular, for the data sets from Kalivas the WILMA models showed improved predictive capability. Copyright