The process requires a calibration or training data set, which includes reference values for the properties of interest for prediction, and the measured attributes believed to correspond to these properties. For case 1), for example, one can assemble data from a number of samples, including concentrations for an analyte of interest for each sample (the reference) and the corresponding infrared spectrum of that sample. Multivariate calibration techniques such as partial-least squares regression, or principal component regression (and near countless other methods) are then used to construct a mathematical model that relates the multivariate response (spectrum) to the concentration of the analyte of interest, and such a model can be used to efficiently predict the concentrations of new samples. Techniques in multivariate calibration are often broadly categorized as classical or inverse methods. The principal difference between these approaches is that in classical calibration the models are solved such that they are optimal in describing the measured analytical responses (e.g., spectra) and can therefore be considered optimal descriptors, whereas in inverse methods the models are solved to be optimal in predicting the properties of interest (e.g., concentrations, optimal predictors). Inverse methods usually require less physical knowledge of the chemical system, and at least in theory provide superior predictions in the mean-squared error sense, and hence inverse approaches tend to be more frequently applied in contemporary multivariate calibration. The main advantages of the use of multivariate calibration techniques is that fast, cheap, or non-destructive analytical measurements (such as optical spectroscopy) can be used to estimate sample properties which would otherwise require time-consuming, expensive or destructive testing (such as LC-MS). Equally important is that multivariate calibration allows for accurate quantitative analysis in the presence of heavy interference by other analytes. The selectivity of the analytical method is provided as much by the mathematical calibration, as the analytical measurement modalities. For example, near-infrared spectra, which are extremely broad and non-selective compared to other analytical techniques (such as infrared or Raman spectra), can often be used successfully in conjunction with carefully developed multivariate calibration methods to predict concentrations of analytes in very complex matrices. Supervised multivariate classification techniques are closely related to multivariate calibration techniques in that a calibration or training set is used to develop a mathematical model capable of classifying future samples. The techniques employed in chemometrics are similar to those used in other fields – multivariate discriminant analysis, logistic regression, neural networks, regression/classification trees. The use of rank reduction techniques in conjunction with these conventional classification methods is routine in chemometrics, for example discriminant analysis on principal components or partial least squares scores.