Model validation is the most important part of building a supervised model. For building a model with good generalization performance one must have a sensible data splitting strategy, and this is crucial for model validation. In this study, we conducted a comparative study on various reported data splitting methods. The MixSim model was employed to generate nine simulated datasets with different probabilities of mis-classification and variable sample sizes. Then partial least squares for discriminant analysis and support vector machines for classification were applied to these datasets. Data splitting methods tested included variants of cross-validation, bootstrapping, bootstrapped Latin partition, Kennard-Stone algorithm (K-S) and sample set partitioning based on joint X–Y distances algorithm (SPXY). These methods were employed to split the data into training and validation sets. The estimated generalization performances from the validation sets were then compared with the ones obtained from the blind test sets which were generated from the same distribution but were unseen by the training/validation procedure used in model construction. The results showed that the size of the data is the deciding factor for the qualities of the generalization performance estimated from the validation set. We found that there was a significant gap between the performance estimated from the validation set and the one from the test set for the all the data splitting methods employed on small datasets. Such disparity decreased when more samples were available for training/validation, and this is because the models were then moving towards approximations of the central limit theory for the simulated datasets used. We also found that having too many or too few samples in the training set had a negative effect on the estimated model performance, suggesting that it is necessary to have a good balance between the sizes of training set and validation set to have a reliable estimation of model performance. We also found that systematic sampling method such as K-S and SPXY generally had very poor estimation of the model performance, most likely due to the fact that they are designed to take the most representative samples first and thus left a rather poorly representative sample set for model performance estimation.

Individuals are thought to have their own distinctive scent, analogous to a signature or fingerprint. To test this idea, we collected axillary sweat, urine and saliva from 197 adults from a village in the Austrian Alps, taking five sweat samples per subject over 10 weeks using a novel skin sampling device. We analysed samples using stir bar sorptive extraction in connection with thermal desorption gas chromatograph–mass spectrometry (GC–MS), and then we statistically analysed the chromatographic profiles using pattern recognition techniques. We found more volatile compounds in axillary sweat than in urine or saliva, and among these we found 373 peaks that were consistent over time (detected in four out of five samples per individual). Among these candidate compounds, we found individually distinct and reproducible GC–MS fingerprints, a reproducible difference between the sexes, and we identified the chemical structures of 44 individual and 12 gender-specific volatile compounds. These individual compounds provide candidates for major histocompatibility complex and other genetically determined odours. This is the first study on human axillary odour to sample a large number of subjects, and our findings are relevant to understanding the chemical nature of human odour, and efforts to design electronic sensors (e-nose) for biometric fingerprinting and disease diagnoses.

Missing values are known to be problematic for the analysis of gas chromatography-mass spectrometry (GC-MS) metabolomics data. Typically these values cover about 10%–20% of all data and can originate from various backgrounds, including analytical, computational, as well as biological. Currently, the most well known substitute for missing values is a mean imputation. In fact, some researchers consider this aspect of data analysis in their metabolomics pipeline as so routine that they do not even mention using this replacement approach. However, this may have a significant influence on the data analysis output(s) and might be highly sensitive to the distribution of samples between different classes. Therefore, in this study we have analysed different substitutes of missing values namely: zero, mean, median, k-nearest neighbours (kNN) and random forest (RF) imputation, in terms of their influence on unsupervised and supervised learning and, thus, their impact on the final output(s) in terms of biological interpretation. These comparisons have been demonstrated both visually and computationally (classification rate) to support our findings. The results show that the selection of the replacement methods to impute missing values may have a considerable effect on the classification accuracy, if performed incorrectly this may negatively influence the biomarkers selected for an early disease diagnosis or identification of cancer related metabolites. In the case of GC-MS metabolomics data studied here our findings recommend that RF should be favored as an imputation of missing value over the other tested methods. This approach displayed excellent results in terms of classification rate for both supervised methods namely: principal components-linear discriminant analysis (PC-LDA) (98.02%) and partial least squares-discriminant analysis (PLS-DA) (97.96%) outperforming other imputation methods.

Support Vector Machines (SVMs) are a new generation of classification method. Derived from well principled Statistical Learning theory, this method attempts to produce boundaries between classes by both minimising the empirical error from the training set and also controlling the complexity of the decision boundary, which can be non-linear. SVMs use a kernel matrix to transform a non-linear separation problem in input space to a linear separation problem in feature space. Common kernels include the Radial Basis Function, Polynomial and Sigmoidal Functions. In many simulated studies and real applications, SVMs show superior generalisation performance compared to traditional classification methods. SVMs also provide several useful statistics that can be used for both model selection and feature selection because these statistics are the upper bounds of the generalisation performance estimation of Leave-One-Out Cross-Validation. SVMs can be employed for multiclass problems in addition to the traditional two class application. Various approaches include one-class classifiers, one-against-one, one-against-all and DAG (Directed Acyclic Graph) trees. Methods for feature selection include RFE (Recursive Feature Elimination) and Gradient Descent based approaches.