Calculation of the reliability of classification in discriminant partial least-squares binary classification

A classification decision must include the degree of confidence in that decision. We have modified the binary classification method Discriminant Partial Least Squares (DPLS) to provide the reliability of the classification of an unknown object. This method, called Probabilistic Discriminant Partial Least Squares (p-DPLS), integrates DPLS, density methods and Bayes decision theory in order to take into account the uncertainty of the predictions in DPLS. The reliability of classification is also used to derive a new classification rule, so that an unknown object is classified in the class for which it has the highest reliability. This new methodology is tested with two data sets, the benchmark Iris data set and an Italian olive oil data set. The results show that the proposed method is comparable with other methodologies, with percentages of correct classification higher than 95%, with the advantage of providing a measurement of the reliability of classification that agrees with the distribution of the samples in the training set.