Data outliers can carry very valuable information and might be most informative for the interpretation. Nevertheless, they are often neglected. An algorithm called cellwise outlier diagnostics using robust pairwise log ratios (cell-rPLR) for the identification of outliers in single cell of a data matrix is proposed. The algorithm is designed for metabolomic data, where due to the size effect, the measured values are not directly comparable. Pairwise log ratios between the variable values form the elemental information for the algorithm, and the aggregation of appropriate outlyingness values results in outlyingness information. A further feature of cell-rPLR is that it is useful for biomarker identification, particularly in the presence of cellwise outliers. Real data examples and simulation studies underline the good performance of this algorithm in comparison with alternative methods.

The instrument Cometary Secondary Ion Mass Analyzer (COSIMA) on board of the European Space Agency mission Rosetta to the comet 67P/Churyumov‐Gerasimenko is a secondary ion mass spectrometer with a time‐of‐flight mass analyzer. It collected near the comet several thousand particles, imaged them, and analyzed the elemental and chemical compositions of their surfaces. In this study, variables have been generated from the spectral data covering the mass ranges of potential C‐, H‐, N‐, and O‐containing ions. The variable importance in binary discriminations between spectra measured on cometary particles and those measured on the target background has been estimated by the univariate t test and the multivariate methods discriminant partial least squares, random forest, and a robust method based on the log ratios of all variable pairs. The results confirm the presence of organic substances in cometary matter—probably a complex macromolecular mixture.

While analyzing chromatographic data, it is necessary to preprocess it properly before exploration and/or supervised modeling. To make chromatographic signals comparable, it is crucial to remove the scaling effect, caused by differences in overall sample concentrations. One of the efficient methods of signal scaling is Probabilistic Quotient Normalization (PQN) [1]. However, it can be applied only to data for which the majority of features do not vary systematically among the studied classes of signals. When studying the influence of the traditional "fermentation" (oxidation) process on the concentration of 56 individual peaks detected in rooibos plant material, this assumption is not fulfilled. In this case, the only possible solution is the analysis of pairwise log-ratios, which are not influenced by the scaling constant. To estimate significant features, i.e., peaks differentiating the studied classes of samples (green and fermented rooibos plant material), we propose the application of rPLR (robust pair-wise log-ratios) as proposed by Walach et al. [2]. It allows for fast computation and identification of the significant features in terms of original variables (peaks) which is problematic, while working with the unfolded pair-wise log ratios. As demonstrated, it can be applied to designed data sets and in the case of contaminated data, it allows proper conclusions.

A new method, robust Pair-wise Log-Ratios (rPLR), is proposed for the identification of biomarkers, distinguishing between two groups of observations. The method can cope with the size effect problem, since it is based on log-ratios between the values of all pairs of variables. rPLR makes use of the variance of pairwise log-ratios, computed for the single groups and for all data jointly. When using a robust estimator of variance (or scale), the method is highly robust against data outliers. The robustness weights are aggregated and displayed in a diagnostics plot, which allows to reveal outlying cells in the data matrix.

Cilem teto bakalařske prace je vytvořit malou databazi mluvených ceských samohlasek a použit linearni predikcni model na extrakci formantů ze spektra jednotlivých samohlasek. Dalsim cilem je vytvořit program v prostředi MATLAB, který je schopen rozeznat jednotlive samohlasky podle jejich formantů a urcit jejich kvalitu.