Class-modelling and discriminant methods are applied to construct mathematical models that are used to predict whether samples belong to the classes studied. Class-modelling methods, also known as one-class classification methods, are used for the construction of a class-model for the target class studied. The class-model is based on the similarities among samples of the target class. Whether a new sample belongs to the class is based on the similarity measures of this sample to the class modelled. If more than one target class are considered, then for each class an individual model is constructed, and the new sample is tested against each of them. The class-modelling is widely applied for e.g., food and drug authentication, product origin confirming, or process monitoring, since it enables rejecting a sample if it belongs to none of the classes studied, e.g., counterfeits, outliers, or samples of poor quality .
On the other hand, the discriminant model is based on the differences among the classes studied. The multivariate feature space is divided by the discriminant model into regions that correspond to the classes considered. A new sample is always predicted by the discriminant model as belonging to one of the classes accordingly to the region on which the sample is projected. The discrimination in its classical form cannot be used for authentication purposes since nontarget samples are always assigned as a member of one of the classes studied .
However, the class-modelling can lead to unsatisfactory results, when the goal is to authenticate classes which overlap, since samples from different classes are too similar. Thus, individual class models can incorrectly recognize similar samples as belonging to several target classes. In such situations, the discriminant model usually leads to better classification of the samples than individual class models, since it takes advantage of the differences between classes. However, the discrimination cannot be applied for authentication alone, thus we propose the two-step authentication of the overlapping classes that benefit from both class-modelling and discrimination . The first step is the construction of the class-model for the training set consisting of samples from all authentic classes considered. The class-model is meant to identify samples that do not belong to any of the classes studied and can be regarded as potential counterfeits or samples of poor quality. The samples assigned by the class-model as belonging to one of the studied classes are in the second step discriminated into specific classes with a discriminant model. The discriminant model in the second step is constructed for the same training set as the class-model.
The performance of the two-step authentication approach is illustrated for three Cyclopia species, used for the production of honeybush tea. The two-step authentication approach enabled obtaining much higher classification results than in the case of class-models constructed for each of the Cyclopia species studied individually.