The scope of applicability of the selected class-modelling methods

Abstract

Class-modelling methods are applied to construct a mathematical model based on the similarities among samples belonging to the same category, i.e., the target class. This model is used to study the belongingness of a new sample to the class for which the model was constructed. If the sample is recognised as not belonging to the target class, it is considered as an outlier. Therefore, the class-modelling techniques are widely used for food or drug authentication and confirmation of the product origin, in order to detect samples of poor quality or potential counterfeits. Structure of the target class data might suggest which of the available class-modelling approaches is well suited for model construction. Data structure can generally be described as normal, or heterogeneous. Normal structure exhibits Gaussian distribution, whereas heterogeneous data deviates from normal distribution, e.g., the objects can have multimodal distributions, create subgroups, and form complex shapes in the feature space. Class-modelling of the normally structured data can directly be performed on an original dataset, whereas heterogeneous datasets are usually subjected to kernel transformation prior to modelling. In this study, several datasets of various structures are analysed with different class-modelling methods to test their scope of applicability and the pros and cons from the practical point of view. It is revealed that in most cases, the Support Vector Domain Description (SVDD) leads to the best classification results. However, it is also discussed and illustrated that SVDD applied to a multimodal data can lead to sub-optimal model. In that case, the Potential Functions Method (PFM) is recommended for model construction. The PFM model is based on local densities of samples in the multivariate space and in that way, it tends to be more accurate than SVDD model. Additionally, some practical remarks are given on optimisation of the Gaussian kernel width.