Peter D. Wentzell

Due to the heterogeneity of multi-omics data, exacting their maximum information potential remains a challenge. Whereas some solutions have been offered, most cannot overcome the large linear dynamic range associated with such data, while others require large biological effect sizes to produce meaningful models. Here, we (i) perform a comprehensive benchmarking of multi-omics data analysis tools, and (ii) introduce kurtosis-based projection pursuit analysis, augmented with classification and regression trees (kPPA-CART) as a robust, easy-to-implement alternative. Using ground truth data, we demonstrate that kPPA-CART exhibits superiority in inferring biological significance from low-intensity (low-count) features and studies with small biological effect sizes. Applying it to experimental breast cancer data from The Cancer Genome Atlas, we identify novel genes that cluster the samples into subtypes that mimic the canonical PAM50 classes with notable improvements. Validating with external metastatic breast cancer data from the AURORA US consortium, kPPA-CART identifies genes that are associated with poor event-free survival and additional clustering associated with increased tumor mutational burden. Finally, we provide an R package and an online implementation of kPPA-CART.

To address the growing concern of honey adulteration in Canada and globally, a quantitative NMR method was developed to analyze 424 honey samples collected across Canada as part of two surveys in 2018 and 2019 led by the Canadian Food Inspection Agency. Based on a robust and reproducible methodology, NMR data were recorded in triplicate on a 700 MHz NMR spectrometer equipped with a cryoprobe, and the data analysis led to the identification and quantification of 33 compounds characteristic of the chemical composition of honey. The high proportion of Canadian honey in the library provided a unique opportunity to apply multivariate statistical methods including PCA, PLS-DA, and SIMCA in order to differentiate Canadian samples from the rest of the world. Through satisfactory model validation, both PLS-DA as a discriminant modeling technique and SIMCA as a class modeling method proved to be reliable at differentiating Canadian honey from a diverse set of honeys with various countries of origins and floral types. The replacement method of optimization was successfully applied for variable selection, and trigonelline, proline, and ethanol at a lower extent were identified as potential chemical markers for the discrimination of Canadian and non-Canadian honeys.

Principal components analysis (PCA) is widely used in analytical chemistry, but is only one type of broader range of factor analysis tools that are described in this article.

To perform discriminant analysis through partial least squares (PLS‐DA), it is important to note that the smaller the set of samples and the higher the variable to sample ratio, the higher the chance of a too optimistic classification model. In this sense, it is necessary to use strategies to check for the possibility that the classification achieved is done by chance. In metabolomics studies, it is not uncommon to work with a reduced number of samples, in which discrimination approaches must be evaluated according to its reliability. Considering this issue, this study aimed to show a case study to deal with few samples using PLS‐DA to discriminate lettuce cultivated in the absence and presence of imidacloprid (IMI). The data were acquired by using ultra‐high‐performance liquid chromatography coupled to a quadrupole‐time of flight mass spectrometry, and the model prediction ability was evaluated by permuting the classes. The performance of the PLS‐DA model built using all the variables reached 100% correct classification. Nonetheless, the reliability tests (Wilcoxon, sign test, and Rand t test) indicated that the model has been build choosing variables by chance. By using the variable importance in projection, it was possible to build a model with reliable specificity and sensitivity equals 1. The study showed the need to check the classification ability in PLS‐DA models through strategies such as variable selection and the permutation test in order to allow for the evaluation of the reliability of the results, even in cases in which the classification reaches 100% in the target.

Sparse projection pursuit analysis (SPPA), a new approach for the unsupervised exploration of high-dimensional chemical data, is proposed as an alternative to traditional exploratory methods such as principal components analysis (PCA) and hierarchical cluster analysis (HCA). Where traditional methods use variance and distance metrics for data compression and visualization, the proposed method incorporates the fourth statistical moment (kurtosis) to access interesting subspaces that can clarify relationships within complex data sets. The quasi-power algorithm used for projection pursuit is coupled with a genetic algorithm for variable selection to efficiently generate sparse projection vectors that improve the chemical interpret-ability of the results while at the same time mitigating the problem of over-modeling. Several multivariate chemical data sets are employed to demonstrate that SPPA can reveal meaningful clusters in the data where other unsupervised methods cannot.

A simple procedure is described that can be used to generate 1/f^α noise, also known as power law noise, in simulated analytical measurement vectors. Certain types of power law noise, such as pink noise (α=1), dominate many types of analytical signals, so its simulation is important in optimizing data processing strategies. In this work, simulated 1/f^α error sequences are created directly from white noise via the theoretical measurement error covariance matrix (ECM) by rotation and scaling. The 1/f^α ECM is obtained from the coefficients of a finite impulse response filter and is easily adapted to generate multiplicative 1/f^α noise that is probably more common for analytical systems exhibiting proportional noise characteristics. Simulating 1/f^α noise directly from the ECM offers two main advantages. First, 1/f^α noise can be easily simulated in the presence of other common analytical measurement errors by additive combination of the ECMs. Second, the theoretical ECM can be used to model real experimental measurement noise. It is shown that the power spectral density function of measurement error sequences generated by the proposed method closely approximates the theoretical behaviour of 1/f^α noise. To demonstrate the utility of this method in evaluating data processing methods, simulated data exhibiting 1/f (pink) noise is analyzed by maximum likelihood principal component analysis (MLPCA) that takes measurement error structure into account, and baseline noise is simulated using brown noise to test baseline fitting by asymmetric least squares (AsLS).

The analysis of multivariate chemical data is commonplace in fields ranging from metabolomics to forensic classification. Many of these studies rely on exploratory visualization methods that represent the multidimensional data in spaces of lower dimensionality, such as hierarchical cluster analysis (HCA) or principal components analysis (PCA). However, such methods rely on assumptions of independent measurement errors with uniform variance and can fail to reveal important information when these assumptions are violated, as they often are for chemical data. This work demonstrates how two alternative methods, maximum likelihood principal components analysis (MLPCA) and projection pursuit analysis (PPA), can reveal chemical information hidden from more traditional techniques. Experimental data to compare different methods consists of near-infrared (NIR) reflectance spectra from 108 samples of wood that are derived from four different species of Brazilian trees. The measurement error characteristics of the spectra are examined and it is shown that, by incorporating measurement error information into the data analysis (through MLPCA) or using alternative projection criteria (i.e., PPA), samples can be separated by species. These techniques are proposed as powerful tools for multivariate data analysis in chemistry.