A Calibration Method Free of Optimum Factor Number Selection for Automated Multivariate Analysis. Experimental and Theoretical Study

Several analytical applications of multivariate calibration methods require human decisions, the most difficult being the number of factors involved. Thus, eliminating the optimum factor number may contribute to the improvement of automatic calibration processes. We propose a factor analysis method that does not need the factor number. It is particularly suitable for indirect calibration of a system under indirect observation. The algorithm is based on composing a subspace excluding the contribution from the component of interest and calculating its net analyte signal through an orthogonal projection to an orthogonal space. This method is applicable as long as the spectral vector dimension (i.e., the number of data points) is larger than the calibration set size. This condition readily satisfied in spectroscopic analysis. The relevant effects, including the effect of the spectral vector dimension and of the calibration set size upon prediction errors, have been investigated using extensive computer simula...