Class-modelling of overlapping classes. A two-step authentication approach.

Honeybush is an indigenous herbal tea highly valued for its aroma, flavour and medicinal properties. It is protected as Geographical Indication (GI) since it is produced from a number of Cyclopia species that are endemic to South Africa. Most commonly used for honeybush tea production are C. intermedia, C. subternata and C. genistoides, differing slightly, but distinctly in flavour. Demand for species-specific honeybush tea instead of mixtures have increased, meriting a strategy for authentication of C. intermedia, C. subternata and C. genistoides. Samples of these three species were analysed, using hyperspectral imaging (HSI) in the near-infrared spectral range. The data were pre-processed and used for class-modelling, a general approach well suited for authentication purposes. Unfortunately, since the HSI data of Cyclopia species studied are very similar, the classification results obtained with individual class-models are unsatisfactory, e.g., class-models constructed for C. genistoides and C. subternata yielded correct classification rate (CCR) values of 76.4 and 83.1%, respectively. On the other hand, discriminant modelling, which is another type of classification technique, led to good classification outcomes (CCR 98.9%). However, the classical discriminant model cannot be applied for authentication purposes since it always assigns a new sample to one of the classes studied, even if in reality, it belongs to none of them. Counterfeits or non-representative samples would be incorrectly assigned by the discriminant model to one of the authentic classes. Therefore, in this study, a two-step authentication of overlapping classes is proposed, which combines the advantages of class-modelling and discriminant methods. When applied to the authentication of Cyclopia species studied, the two-step approach yielded a CCR of 97.4%, which is a significant improvement compared to results obtained with the individual class-models. The proposed approach is general and can be applied when classes studied are very similar, and individual class-models lead to unsatisfactory results.

Different strategies for class model optimization. A comparative study.

The Class Modelling (CM) approaches like Soft Independent Modelling of Class Analogy (SIMCA) aim at developing a mathematical model for determination of belongingness of new samples to the studied classes. The main feature of CM is that for each target class an individual model is constructed. CM is widely exploited, e.g., in the food and drug quality testing and authenticity or origin verification. It is well known that the most critical stage in construction of a class model is optimization of its parameters. There exist two basic strategies for optimization of class model, i.e., the "compliant" strategy where the target and nontarget class samples are required in the model optimization process, and the "rigorous" strategy where only the target class samples are used. Since the nontarget class samples are usually available, the compliant scenario is more often explored. In the present study, four different resampling methods for optimization of the SIMCA model (applied in both, a compliant and a rigorous fashion) are thoroughly compared. Each method is tested in combination with two distinct decision threshold estimation criteria: i) an a priori fixing it based on a desired statistical significance level and ii) optimizing it through appropriate data-driven procedures. For the sake of a comprehensive assessment of the studied strategies, several real-world datasets are exploited and final results are post-processed by means of ANalysis Of VAriance (ANOVA). The study reveals that both, a compliant approach with an optimized decision threshold and a rigorous approach with a fixed decision threshold can yield satisfactory classification outcomes, no matter which resampling technique is used. Finally, it is shown how unrepresentativeness of the nontarget classes can lead to the biased classification models when a compliant optimization is carried out. Therefore, a rigorous optimization can be considered as a safer option for the SIMCA model parameter tuning.

Working with log-ratios.

Instrumental signals of samples cannot be compared and/or analysed directly if their concentrations are unknown. Differences in overall concentration need to be removed at the data normalization step. The choice of normalization method has a profound effect on the final results of data analysis, and especially on biomarker identification. One of the possible approaches to deal with the 'size effect' is to work with size-irrelevant (log) ratios instead of the original variables. In the presented study, the performance of log-ratio methods, namely pairwise log-ratio (plr) and centered log-ratio (clr), is discussed for real and simulated data sets with different characteristics. It was found that the clr method can lead to distribution of local differences along an entire signal and as such, it should be avoided in all studies aiming to identify biomarkers.