Károly Héberger

• Ph.D., Cand. Sci., D.Sc. t.Prof.
• Professor Emeritus at HUN-REN Research Centre for Natural Sciences; Institute of Excellence Hungarian Academy of Sciences

Sum of Ranking Differences (SRD) is a relatively novel, non-para-metric statistical procedure that has become increasingly popular recently. SRD compares solutions via a reference by applying a rank transformation on the input and calculating the distance from the reference in $L_1$ norm. Although the computation of the test statistics is simple, v...

Although cross-validation (CV) is a standard technique in machine learning and data science, its efficacy remains largely unexplored in ranking environments. When evaluating the significance of differences, cross-validation is typically coupled with statistical testing, such as the Dietterich, Alpaydin, or Wilcoxon test. In this paper, we evaluate...

Extended similarity indices (i.e., generalization of pairwise similarity) have recently gained importance because of their simplicity, fast computation, and superiority in tasks like diversity picking. However, they operate with several meta parameters that should be optimized. Earlier, we extended the binary similarity indices to “discrete non‐bin...

The utility function-based sum of ranking differences (uSRD) method is proposed as a utility function-based multi-criteria decision analysis tool. Our idea is that the transformation functions can be represented by a utility function that can be aggregated with multi-attribute utility functions. We present a framework incorporating utility values a...

Extended similarity indices (i.e. generalization of pairwise similarity) have recently gained importance because of their simplicity, fast computation and superiority in tasks like diversity picking. However, they operate with several meta parameters that should be optimized. Earlier, we extended the binary similarity indices to ‘discrete non-binar...

Background: The development and application of machine learning (ML) methods have become so fast that almost nobody can follow their developments in every detail. It is no wonder that numerous errors and inconsistencies in their usage have also spread with a similar speed independently from the tasks: regression and classification. This work summar...

Background: The development and application of machine learning (ML) methods became so fast that almost nobody can follow their developments in every detail. There is no wonder that numerous errors and inconsistencies in their usage have also spread with a similar speed independently from the tasks: regression and classification.. This work summari...

This brief literature survey groups the (numerical) validation methods and emphasizes the contradictions and confusion considering bias, variance and predictive performance. A multicriteria decision-making analysis has been made using the sum of absolute ranking differences (SRD), illustrated with five case studies (seven examples). SRD was applied...

Non-negative matrix factorization (NMF) efficiently reduces high dimensionality for many-objective ranking problems. In multi-objective optimization, as long as only three or four conflicting viewpoints are present, an optimal solution can be determined by finding the Pareto front. When the number of the objectives increases, the multi-objective pr...

Molecular dynamics (MD) is a core methodology of molecular modeling and computational design for the study of the dynamics and temporal evolution of molecular systems. MD simulations have particularly benefited from the rapid increase of computational power that has characterized the past decades of computational chemical research, being the first...

Predicting the success of National Football League drafts has always been an exciting issue for the teams, fans and even for scientists. Among the numerous approaches, one of the best techniques is to ask the opinion of sport experts, who have the knowledge and past experiences to rate the drafts of the teams. When asking a set of sport experts to...

The screening of compounds for ADME-Tox targets plays an important role in drug design. QSPR models can increase the speed of these specific tasks, although the performance of the models highly depends on several factors, such as the applied molecular descriptors. In this study, a detailed comparison of the most popular descriptor groups has been c...

Molecular dynamics (MD) is a core methodology of molecular modeling and computational design for the study of the dynamics and temporal evolution of molecular systems. MD simulations have particularly benefited from the rapid increase of computational power that has characterized the past decades of computational chemical research, being the first...

Extended (or n-ary) similarity indices have been recently proposed to extend the comparative analysis of binary strings. Going beyond the traditional notion of pairwise comparisons, these novel indices allow comparing any number of objects at the same time. This results in a remarkable efficiency gain with respect to other approaches, since now we...

The Promethee-GAIA method is a multicriteria decision support technique that defines the aggregated ranks of multiple criteria and visualizes them based on Principal Component Analysis (PCA). In the case of numerous criteria, the PCA biplot-based visualization do not perceive how a criterion influences the decision problem. The central question is...

This research investigates how to determine whether two rankings come from the same distribution. We evaluate three hybrid tests: Wilcoxon’s, Dietterich’s, and Alpaydin’s statistical tests combined with cross-validation (CV), each operating with folds ranging from 5 to 10, thus altogether 18 variants. We have applied these tests in the framework of...

A novel visualization technique is proposed for the sum of ranking differences method (SRD) based on parallel coordinates. An axis is defined for each variable, on which the data are depicted row-wise. By connecting data, the lines may intersect. The fewer intersections between the variables, the more similar they are and the clearer the figure bec...

In this review, we outline the current trends in the field of machine learning-driven classification studies related to ADME (absorption, distribution, metabolism and excretion) and toxicity endpoints from the past six years (2015–2021). The study focuses only on classification models with large datasets (i.e. more than a thousand compounds). A com...

Quantification of similarities between protein sequences or DNA/RNA strands is a (sub-)task that is ubiquitously present in bioinformatics workflows, and is usually accomplished by pairwise comparisons of sequences, utilizing simple (e.g. percent identity) or more intricate concepts (e.g. substitution scoring matrices). Complex tasks (such as clust...

Quantification of the similarity of objects is a key concept in many areas of computational science. This includes cheminformatics, where molecular similarity is usually quantified based on binary fingerprints. While there is a wide selection of available molecular representations and similarity metrics, there were no previous efforts to extend the...

Despite being a central concept in cheminformatics, molecular similarity has so far been limited to the simultaneous comparison of only two molecules at a time and using one index, generally the Tanimoto coefficent. In a recent contribution we have not only introduced a complete mathematical framework for extended similarity calculations, (i.e. com...

Similarity measures are widely used in various areas from taxonomy to cheminformatics. To this end, a large number of similarity and distance measures (or, collectively, comparative measures) have been introduced, with only a few studies directed to revealing their inner relationships. We present a thorough analytical study of the conditions leadin...

In recent decades, eye-movement detection technology has improved significantly, and eye-trackers are available not only as standalone research tools but also as computer peripherals. This rapid spread gives further opportunities to measure the eye-movements of participants. The current paper provides classification models for the prediction of foo...

Applied datasets can vary from a few hundred to thousands of samples in typical quantitative structure-activity/property (QSAR/QSPR) relationships and classification. However, the size of the datasets and the train/test split ratios can greatly affect the outcome of the models, and thus the classification performance itself. We compared several com...

Recently, 1H NMR (nuclear magnetic resonance) spectroscopy was presented as a viable option for the quality assurance of foods and beverages, such as wine products. Here, a complex chemometric analysis of red and white wine samples was carried out based on their 1H NMR spectra. Extreme gradient boosting (XGBoost) machine learning algorithm was appl...

Finding optimal solutions usually requires multicriteria optimization. The sum of ranking differences (SRD) algorithm can efficiently solve such problems. Its principles and earlier applications will be discussed here, along with meta-analyses of papers published in various subfields of food science, such as analytics in food chemistry, food engine...

Extracellular vesicles (EVs) are lipid bilayer–bounded particles that are actively synthesized and released by cells. The main components of EVs are lipids, proteins, and nucleic acids and their composition is characteristic to their type and origin, and it reveals the physiological and pathological conditions of the parent cells. The concentration...

Sum of Ranking Differences is an innovative statistical method that ranks competing solutions based on a reference point. The latter might arise naturally, or can be aggregated from the data. We provide two case studies to feature both possibilities. Apportionment and districting are two critical issues that emerge in relation to democratic electio...

Quantitation of surface roughness is difficult, if subtle, but significant differences cause an uncommon variance. We used atomic force microscopy to measure the surface roughness of polyethylene terephthalate (PET) fibers before and after a 30 s plasma treatment of 300 W. Samples were measured multiple times at different locations, in four scan si...

How far-reaching is the influence of the urban area over the mineral composition of the Russula cyanoxantha mushroom? To answer this question, we monitored the metal uptake behavior of this fungus relying on the soil properties. We sampled mushroom and soil from six forests according to an urbanization gradient, and two city parks in Cluj-Napoca (R...

Machine learning classification algorithms are widely used for the prediction and classification of the different properties of molecules such as toxicity or biological activity. the prediction of toxic vs. non-toxic molecules is important due to testing on living animals, which has ethical and cost drawbacks as well. The quality of classification...

Eating insects have raised significant scientific interest in the past few years. Insect-based food product development is one of the most promising areas, which open the door to new foods on the shelves. Consumers face new products containing insects in various forms day-by-day. However, there is a lack of appropriate scientific literature on prod...

Ensemble docking is a widely applied concept in structure-based virtual screening—to at least partly account for protein flexibility—usually granting a significant performance gain at a modest cost of speed. From the individual, single-structure docking scores, a consensus score needs to be produced by data fusion: this is usually done by taking th...

Edible insects have become popular in the past few years not only in the scientific literature but in other media as well. One of the major advantages of entomophagy (eating insects) is said to be the great nutritional composition. Many sources report that insects (generally) have better nutritional characteristics than traditional protein sources....

The old debate is revived: Definite differences can be observed in suggestions of estimation for prediction performances of models and for validation variants according to the various scientific disciplines. However, the best and/or recommended practice for the same data set cannot be dependent on the field of usage. Fortunately, there is a method...

Background: Interaction fingerprints (IFP) have been repeatedly shown to be valuable tools in virtual screening to identify novel hit compounds that can subsequently be optimized to drug candidates. As a complementary method to ligand docking, IFPs can be applied to quantify the similarity of predicted binding poses to a reference binding pose. Fo...

Prediction performance often depends on the cross- and test validation protocols applied. Several combinations of different cross-validation variants and model-building techniques were used to reveal their complexity. Two case studies (acute toxicity data) were examined, applying five-fold cross-validation (with random, contiguous and Venetian blin...

Fat and dry material contents (connected to moisture) are one of the most important parameters in the quality control of butters, margarines and margarine spreads (dairy spreads). More than a hundred margarine samples were used to model their fat and dry material content based on Fourier Transformed – Near Infrared (FT-NIR) spectroscopy in transmis...

This study aims to compare three extraction techniques of four sequential element extraction steps from soil and sediment samples that were taken from the location of the Pan�cevo petrochemical industry (Serbia). Elements were extracted using three different techniques: conventional, microwave and ultrasound extraction. A novel procedure e sum of t...

The Agaricus campestris mushroom widespread in the metropolitan areas could be an alternative food source to the cultivated and widely commercialized Agaricus bisporus. Our aim was to elaborate the elemental profile of the A. campestris in the urban and peri-urban environment, and to determine the levels of some highly toxic elements. The A. campes...

Modern chromatographic and spectrometric techniques abundantly provide digitalized data. This chapter describes the importance of data preprocessing in chemometrics. It distinguishes the essentials of various data analysis methods and discusses the difference between supervised and unsupervised pattern recognition. The chapter also distinguishes th...

Contemporary metabolomic fingerprinting is based on multiple spectrometric and chromatographic signals, used either alone or combined with structural and chemical information of metabolic markers at the qualitative and semi-quantitative level. However, signal shifting, convolution, and matrix effects may compromise metabolomic patterns. Recent incr...

This study aims to compare three extraction techniques of four sequential element extraction steps from soil and sediment samples that were taken from the location of the Pančevo petrochemical industry (Serbia). Elements were extracted using three different techniques: conventional, microwave and ultrasound extraction. A novel procedure – sum of th...

In this chapter we strive to provide a comprehensive but reasonably compact overview of the various possibilities for the computational representation of molecules. This includes a detailed introduction to the most commonly used chemical file formats (complemented with a few novel or more specific representations), a thorough overview of the theore...

A thorough survey of classification data sets and a rigorous comparison of classification methods clearly show the unambiguous superiority of other techniques over soft independent modeling of class analogies (SIMCA) in the case of classification – which is a frequent area of usage for SIMCA, even though it is a class modeling (one class or disjoin...

We have revisited the vivid discussion in the QSAR-related literature concerning the use of external versus cross-validation , and have presented a thorough statistical comparison of model performance parameters with the recently published SRD (sum of (absolute) ranking differences) method and analysis of variance (ANOVA) . Two case studies were in...

Comparison and selection of chromatographic columns is an important part of development as well as validation of analytical methods. Presently there is abundant number of methods for selection of the most similar and orthogonal columns, based on the application of limited number of test compounds as well as quantitative structure retention relation...

Several different approaches have been introduced for analysis of just-about-right (JAR) data; however, their results are sometimes deviating or even contradictory. More reliable results are gained, if a consensus of many methods is determined. A specific approach is presented to compare and select JAR attributes of food products. Overall liking wa...

Almost a hundred commercially available energy drink samples from Hungary, Slovakia, and Greece were collected for the quantitative determination of their caffeine and sugar content with FT-NIR spectroscopy and high-performance liquid chromatography (HPLC). Calibration models were built with partial least-squares regression (PLSR). An HPLC-UV metho...

Needs for fast, yet reliable means of assessing the lipophilicities of diverse compounds resulted in the development of various in silico and chromatographic approaches that are faster, cheaper, and greener compared to the traditional shake-flask method. However, at present no accepted "standard" approach exists for their comparison and selection o...

Four classification methods were compared using receiver operating characteristic (ROC) curves to identify the best one: two common ones (linear discriminant analysis, LDA and partial least squares, PLS) and another two (random forest, boosted tree) that are not applied as frequently as LDA or PLS yet. A dataset with 90 commercially available (in H...

Recent implementations of QSAR modelling software provide the user with numerous models and a wealth of information. In this work, we provide some guidance on how one should interpret the results of QSAR modelling, compare and assess the resulting models, and select the best and most consistent ones. Two QSAR datasets are applied as case studies fo...

Abstract In product development using JAR (Just-About-Right) scales, it is important to identify precisely, which direction of a given attribute affects hedonic scores the most. The Generalized Pairwise Correlation Method (GPCM) is a non-parametric one and it is useful to rank JAR variables according to their impact on liking. This is done using ap...

Cheminformaticians are equipped with a very rich toolbox when carrying out molecular similarity calculations. A large number of molecular representations exist, and there are several methods (similarity and distance metrics) to quantify the similarity of molecular representations. In this work, eight well-known similarity/distance metrics are compa...

Seven antioxidant capacity assays were compared and evaluated (ranked and grouped) with several statistical methods. The aim of the research was to compare the results of different antioxidant capacity assays and choose preferably one (or two) method(s), which could reproduce on its own the consensus results of all of the others. The two datasets (...

H‐NMR spectral data and H and C isotope abundances of virgin olive oils (VOOs) and their unsaponifiable fractions were analyzed by pattern recognition techniques, such as principal component analysis (PCA) and partial‐least squares discriminant analysis (PLS‐DA). The aim was to develop chemical tools for the authentication of VOOs according to thei...

A novel, time- and money-sparing method has been developed and validated for the quantitative determination of coenzyme Q10 (CoQ10) from several dietary supplements. FT-NIR spectroscopy was applied for the examination, and a calibration model was built by partial least-square regression (PLS-R) using 50 dietary supplements. The combination of FT-NI...

Most multivariate calibration methods require selection of tuning parameters, such as partial least squares (PLS) or the Tikhonov regularization variant ridge regression (RR). Tuning parameter values determine the direction and magnitude of respective model vectors thereby setting the resultant predication abilities of the model vectors. Simultaneo...

Diesel oil biodegradation by different bacteria-yeast-rhamnolipids consortia was tested. Chromatographic analysis of post-biodegradation residue was completed with chemometric tools (ANOVA, and a novel ranking procedure based on the sum of ranking differences). These tools were used in the selection of the most effective systems. The best results o...

Classification is an important part of chemometrics and mostly based on optimization by vector rotations. The present study is a continuation of the classification of medieval Hungarian silver coins including the 16 kings of the Hungarian Árpád Dynasty (ad 997–1301) (Rácz et al.: Heritage Science 2013 1:2). The Rácz et al. paper identified three hi...

The purpose of this study was to evaluate the influence of preparation/storage conditions on the sorption, solubility, and mass changes of new proposed hydroxyapatite-containing resin-based composites. Seventy cylindrical samples of composite were prepared according to the ISO 4049 and stored in different storage solutions (distilled water, artific...

Performance parameters (coefficient of determination - R2, cross-validated correlation coefficients - Q2(external), R2(leave-one-out) R2(leave-many-out), R2(bootstrap), etc.) are frequently used to test the predictive performance of models. It is relatively easy to check whether the performance parameters for linear fits stem from the same distribu...

Coefficient of determination (R (2)) and its leave-one-out cross-validated analogue (denoted by Q (2) or R cv (2) ) are the most frequantly published values to characterize the predictive performance of models. In this article we use R (2) and Q (2) in a reversed aspect to determine uncommon points, i.e. influential points in any data sets. The ter...

Sum of ranking differences (SRD) was applied for comparing multianalyte results obtained by several analytical methods used in one or in different laboratories, i.e., for ranking the overall performances of the methods (or laboratories) in simultaneous determination of the same set of analytes. The data sets for testing of the SRD applicability con...

Significant progress has been achieved since the introduction of the new similarity measure: the sum of absolute ranking differences (SRDs) [TrAC — Trends in Anal. Chem. 29 (2010) 101–109]. Empirical evidences were accumulated about scaling, selection of the reference (benchmark) vector, cross-validation and grouping of variables (features, models,...

The surface properties of hybrid materials (potential carriers for sustained release of active agents) have been examined by inverse gas chromatography. A nonsteroidal anti-inflammatory agent, ibuprofen, was used as a model for active compound. The following parameters have been used to characterize the interactions between the constituents of the...

The genotoxic potential of waters in six rivers and reservoirs from Serbia was monitored in different tissues of chub (Squalius cephalus L. 1758) with the alkaline comet assay. The comet assay, or single-cell gel electrophoresis, has a wide application as a simple and sensitive method for evaluating DNA damage in fish exposed to various xenobiotics...

Inverse gas chromatography was used to estimate surface activity expressed by the dispersive component of the surface free energy, γ SD, as well as parameters K A and K D describing surface ability to act as electron acceptor and donor, respectively. These parameters characterize the ability of the surface to specific interactions. The method was a...

Background A set of silver coins from the collection of Déri Museum Debrecen (Hungary) was examined by X-ray fluorescent elemental analysis with the aim to assign the coins to different groups with the best possible precision based on the acquired chemical information and to build models, which arrange the coins according to their historical perio...

A data set containing acute toxicity values (96-h LC 50) of 69 substituted benzenes for fathead minnow (Pimephales promelas) was investigated with two Quantitative Structure-Activity Relationship (QSAR) models, either using or not using molecular descriptors, respectively. Recursive Neural Networks (RNN) derive a QSAR by direct treatment of the mol...

Empirical equations known from literature have been interpreted thermodynamically and their performance was checked for alkylbenzenes and for stationary phases of low and medium polarity. These equations relate Kováts retention index (I) and boiling point (TB) in a linear and a reciprocal way: {I=ATB+B and I=C/TB+D}. It was possible to attribute th...

Mineral, spring and tap water samples of different geographical origins (7 classes) were distinguished by various methods, such as sensory evaluation, electronic tongue measurement, inductively coupled plasma atomic emission spectroscopy and ion chromatography. Samples from the same geographical origin were correctly classified by chemical analysis...

In this work in-needle technique as the method for liquid samples preparation which faces with the problem of high flow resistance produced by a sorbent layer is considered. The influence of parameters (needle size, sorbent particle size and length of sorbent layer) of in-needle device on the flow rate was examined. Acceptable sampling conditions w...

Quantitative structure-(chromatographic) retention relationship (QSRR) models for prediction of Lee retention indices for polycyclic aromatic hydrocarbons (PAHs) were gathered from the literature and the predictive performances of models were compared. Numerous Lee retention indices (46) were served as a reliable basis for ranking by a recently dev...

Effects of different catalyst components on the catalytic performance in steam reforming of ethanol have been investigated by means of Artificial Neural Networks (ANNs) and Partial Least Square regression (PLSR). The data base consisted of ca. 400 items (catalysts with varied composition), which were obtained from a former catalyst optimization pro...

This paper describes the theoretical background, algorithm and validation of a recently developed novel method of ranking based on the sum of ranking differences [TrAC Trends Anal. Chem. 2010; 29: 101-109]. The ranking is intended to compare models, methods, analytical techniques, panel members, etc. and it is entirely general. First, the objects t...

CP-ANN technique was used to build 54 different QSAR models. The models were built for three sets (assays) of fluo-roquinolones considering their antituberculosis activity and using different technical parameters (dimension of network and number of learning epochs). The models served as a reliable basis for ranking by a new powerful method based on...

The sorbent-eluent systems combined from eight polymeric sorbents and seven solvents as eluents were used for the extraction of phenol and its oxidation products from water samples. The individual interactions between sorbents, eluents and analytes were characterized by Hansen solubility parameters. Principal components analysis (PCA) was used for...

(1)H NMR fingerprints of virgin olive oils (VOOs) from the Mediterranean basin (three harvests) were analyzed by principal component analysis, linear discriminant analysis (LDA), and partial least-squares discriminant analysis (PLS-DA) to determine their geographical origin at the national, regional, or PDO level. Further delta(13)C and delta(2)H m...

A new approach to the geographical characterisation of virgin olive oils (VOOs) based on the 1H NMR fingerprint of the unsaponifiable matter is presented. The 1H NMR spectra of the unsaponifiable fraction of virgin olive oils from Spain, Italy, Greece, Tunisia, Turkey, and Syria were analysed by several pattern recognition techniques (LDA, PLS-DA,...

The comparison of different polarity measures (parameters, descriptors, variables, scales, etc.) indicates that evaluation of interrelations between these measures is important for better understanding and interpretation of chemical and/or analytical data, especially for chromatographic separation. The best linear correlation between gas chromatogr...

This review covers a novel approach to comparing methods, based on the sum of ranking differences (SRD). Many method-comparison studies suffer from ambiguity or from comparisons not being quite fair. This problem can be avoided if there are differences between ideal and actual rankings. The absolute values of differences for the ideal and actual ra...

Absolute rate constants for the addition of the 2-cyano-2-propyl radical to 26 alkenes CH2 = CXY at 315 K were determined in solution by time-resolved electron-spin-resonance spectroscopy. They vary with the alkene substituents from 30 M-1 s-1 to 7′010 M-1 s-1. For styrene the temperature dependence is given by log k/M-1 s-1 = 7.7 - 26.1/Θ where Θ...

Green coffee beans of the two main commercial coffee varieties, Coffea arabica (Arabica) and Coffea canephora (Robusta), from the major growing regions of America, Africa, Asia, and Oceania were studied. The contents of chlorogenic acids, cinnamoyl amides, cinnamoyl glycosides, free phenolic acids, and methylxanthines of green coffee beans were ana...

This chapter provides an introduction to chemoinformatics covering multivariate mathematical-statistical methods for data evaluation. It is expedient to distinguish the variables on the basis of three scales: nominal, ordinal, and numeric. The nominal scales are qualitative only and can be measured solely in terms of whether the individual items be...