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Discriminant-type analyses arise from the need to classify samples based on their measured characteristics (variables), usually with respect to some observable property. In the case of samples that are difficult to obtain, or using advanced instrumentation, it is very common to encounter situations with many more measured characteristics than samples. The method of Partial Least Squares Regression (PLS-R), and its variant for discriminant-type analyses (PLSDA) are among the most ubiquitous of these tools. PLS utilises a rank-deficient method to solve the inverse least-squares problem in a way that maximises the co-variance between the known properties of the samples (commonly referred to as the Y-Block), and their measured characteristics (the X-block). A relatively small subset of highly co-variate variables are weighted more strongly than those that are poorly co-variate, in such a way that an illposed matrix inverse problem is circumvented. Feature selection is another common way of reducing the dimensionality of the data to a relatively small, robust subset of variables for use in subsequent modelling. The utility of these features can be inferred and tested any number of ways, this are the subject of this review. [ABSTRACT FROM AUTHOR]

Comprehensive gas chromatography with time of flight mass spectrometry is a powerful tool in the analysis of complex samples. Chemometric analysis of raw chromatographic data is more useful in one‐ and two‐dimensional separations relative to peak tables. The data volume from such experiments generally necessitates the use of data reduction tools. Such tools often sacrifice some of the multivariate information in the mass to charge ratio dimension. The unique ion filter reduces the over‐redundancy in two‐dimensional gas chromatography‐mass spectrometry data by limiting the data to a few unique/pseudo‐unique ions, sub‐peaks/slices in the first dimension, and spectra in the second dimension. We explore the performance of this algorithm through careful inspection of two‐dimensional gas chromatography‐mass spectrometry data before and after application of the filter. A reduction (99%) in the number of variables in a two‐dimensional gas chromatography‐mass spectrometry chromatogram passed on to subsequent analysis was observed. Feature selection times for model optimization reduced from 229 (±13) to 6.8 (±0.5) min when the filter was applied. An estimate of two unique/pseudo‐unique ions, one sub‐peak in the first dimension and five spectra in the second dimension were considered to provide a true representation of each chromatogram and provided enough information to achieve 100% model prediction accuracy. [ABSTRACT FROM AUTHOR]

Cluster resolution (CR) is a useful metric for guiding automated feature selection of classification models. CR is a measure of class separation in a linear subspace for variable subsets via the determination of maximal, non‐intersecting confidence ellipses. Feature selection by cluster resolution (FS‐CR) is most commonly used to extract panels of useful, discriminating features from sparsely populated chromatographic peak tables, optimizing models from raw signals, or when working with datasets with many more variables than samples. The absence of a numerical method for calculating CR necessitates a great deal of dynamic programming and algorithmic complexity. In this work, we present a numerical determination of the CR metric, which reduces computation time by about 65 times when compared with the dynamic programming approach and simplifies the operating principles of FS‐CR algorithm. Cluster resolution is a measure of class separation in a linear subspace, which has been used to guide feature selection algorithms. In this contribution, a numerical method for calculating cluster resolution is presented. An algorithm implementing the numerical determination of cluster resolution is 65× faster than the current implementation, which relies on dynamic programming. [ABSTRACT FROM AUTHOR]

Abstract: A novel metric termed cluster resolution is presented. This metric compares the separation of clusters of data points while simultaneously considering the shapes of the clusters and their relative orientations. Using cluster resolution in conjunction with an objective variable ranking metric allows for fully automated feature selection for the construction of chemometric models. The metric is based upon considering the maximum size of confidence ellipses around clusters of points representing different classes of objects that can be constructed without any overlap of the ellipses. For demonstration purposes we utilized PCA to classify samples of gasoline based upon their octane rating. The entire GC–MS chromatogram of each sample comprising over 2×106 variables was considered. As an example, automated ranking by ANOVA was applied followed by a forward selection approach to choose variables for inclusion. This approach can be generally applied to feature selection for a variety of applications and represents a significant step towards the development of fully automated, objective construction of chemometric models. [ABSTRACT FROM AUTHOR]

Partial least-squares discriminant analysis (PLS-DA) and support vector machine (SVM) techniques were applied to develop a crystal structure predictor for binary AB compounds. Models were trained and validated on the basis of the classification of 706 AB compounds adopting the seven most common structure types (CsCl, NaCl, ZnS, CuAu, TlI, β-FeB, and NiAs), through data extracted from Pearson's Crystal Data and ASM Alloy Phase Diagram Database. Out of 56 initial variables (descriptors based on elemental properties only), 31 were selected in as unbiased manner as possible through a procedure of forward selection and backward elimination, with the quality of the model evaluated by measuring the cluster resolution at each step. PLS-DA gave sensitivity of 96.5%, specificity of 66.0%, and accuracy of 77.1% for the validation set data, whereas SVM gave sensitivity of 94.2%, specificity of 92.7%, and accuracy of 93.2%, a significant improvement. Radii, electronegativity, and valence electrons, previously chosen intuitively in structure maps, were confirmed as important variables. PLS-DA and SVM could also make quantitative predictions of hypothetical compounds, unlike semiclassical approaches. The new compound RhCd was predicted to have the CsCl-type structure by PLS-DA (0.669 probability) and, at an even stronger confidence level, by SVM (0.918 probability). RhCd was synthesized by reaction of the elements at 800 °C and confirmed by X-ray diffraction to adopt the CsCl-type structure. SVM is thus a superior classification method in crystallography that is fast and makes correct, quantitative predictions; it may be more broadly applicable to help identify the structure of unknown compounds with any arbitrary composition. [ABSTRACT FROM AUTHOR]