Abstract

It has become easy to obtain multivariate chemical data of high dimensions. However, it may be expensive or time consuming to obtain a large number of samples or to acquire reference measures, so the number of samples available for multivariate calibration modelling may be limited. If data contains nonlinear relationships, nonlinear methods are required for the calibration task. The combination of limited amounts of data of high dimensions and highly flexible nonlinear methods may result in overfitted models which in turn perform badly on new data. Therefore, for real world applications, it is desirable to understand how the sample size affects model prediction performance. For this purpose, we compared partial least squares regression, artificial neural network, and support vector regression applied to three real world nonlinear datasets of which two were of high dimensions. We evaluated the effect of calibration sample size (i) on test set performance, including variation in test set performance due to sampling variation and (ii) tested if the cross-validated performance was adequate for assessing the predictive ability. We demonstrated the applicability of artificial neural network and support vector regression for real world data of limited size and showed that support vector regression had advantages over artificial neural network: (i) fewer calibration samples were required to obtain a desired model performance, (ii) support vector regression was less sensitive to sampling variation for small sample sets and (iii) cross-validation was an approximately unbiased option for evaluating the true support vector regression model performance even for small sample sets.

© 2017 The Author(s)

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