People
doc. Ing. Ivan Nagy, CSc.

2025, Atmosphere, 16 (3), ISSN 2073-4433

As a consequence of measures imposed during the COVID-19 pandemic, anthropogenic emissions worldwide decreased markedly in impacted sectors, including the aviation industry. The aim of this study is to investigate the effects of the pandemic on aircraft emissions below the mixing height (3000 feet above ground) at Václav Havel Airport Prague during 2020. For this purpose, real aircraft emissions during 2020 were computed using provided surveillance data, while business-as-usual aircraft emissions that could have been expected at the airport that year under normal circumstances were estimated using traffic data from previous years and derived emission factors. We found that the median real emissions at the airport in 2020 were 220.859 t of NOX, 101.364 t of CO, 15.025 t of HC, 44,039.468 t of CO2, 17,201.825 t of H2O and 11.748 t of SO2. The median estimated reduction in emissions due to the pandemic in 2020 was −476.317 t of NOX, −203.998 t of CO, −28.388 t of HC, −95,957.278 t of CO2, −37,476.400 t of H2O and −25.595 t of SO2. Absolute differences between the real and business-as-usual emissions peaked in June 2020, while the relative differences peaked in April/May at −89.4% to −92.0%.

2025, Journal of Computational Science, 85, ISSN 1877-7511

In this paper, we address the task of modeling and predicting count data, with an application to traffic counts on selected urban roads in Prague. We investigated the relationship between multiple counts, designating one of them as the target variable (e.g., data from a key road section) and the others as explanatory counts. Defining traffic count data as the number of vehicles passing through a selected road section per unit of time, we use a framework based on Poisson models to develop a progressive methodology, which we compared with existing models. Working with multimodal count data, we propose the following main steps for the methodology: (i) cluster analysis of explanatory counts using recursive Bayesian estimation of Poisson mixtures; (ii) target count model estimation via local Poisson regressions at identified locations, capturing local relationships between target and explanatory counts; and (iii) prediction of target counts through real-time location detection. The algorithm’s properties were first investigated using simulated data and then validated with real traffic counts. Experimental results indicate that the proposed algorithm outperforms classical Poisson and negative binomial regressions, decision tree and random forest classifiers, as well as a multi-layer perceptron, in predicting traffic count data across various quality metrics, even for weakly correlated data. Applied to traffic count data, the promising performance demonstrated by the proposed algorithm offers an optimistic vision for traffic prediction and urban planning, suggesting its potential as a valuable tool for enhancing transportation efficiency by optimizing the timing of city traffic lights to improve traffic flow.

2024, 2024 Smart City Symposium Prague (SCSP), New York, IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC), p. 1-5), ISBN 979-8-3503-6095-0, ISSN 2691-3666

The paper deals with a comparative analysis of three widely used data analysis methods: logistic regression, random forest, and neural networks. These methods have been evaluated in terms of accuracy, and computational efficiency and applied to different types of data sets, including both simulated and real MaaS data. The study aims to compare the efficiency of each method in classification tasks. The study leads to specific recommendations on which method to use under various circumstances, contributing to the decision-making process in data analysis projects. We have shown that random forests generally provide better accuracy and are resistant to over-training. Neural networks can achieve comparable performance under certain conditions, although at a high computational cost. Logistic regression shows limitations in dealing with complex data structures.

2024, Applied Sciences, 14 (8), ISSN 2076-3417

Contrails created by aircraft are a very hot topic today because they contribute to the warming of the atmosphere. Air traffic density is very high, and current forecasts predict a further significant increase. Increased air traffic volume is associated with an increased occurrence of contrails and induced cirrus clouds. The scientific level of contrails and their impact on the Earth’s climate is surprisingly low. The scientific studies published so far are mainly based on global models, in situ measurements, and satellite observations of contrails. The research is based on observations of contrails in flight paths in the vicinity of Děčín and Prague, and the collection of flight and meteorological data. It focused on the influence of the meteorological situation on the formation of persistent contrails. The collected data on contrails and meteorological variables were statistically processed using machine learning methods for classification models. Several models were developed to predict and simulate the properties of contrails as a function of given air traffic and meteorological conditions. The Random Forests model produced the best results. Dependencies between meteorological conditions, formation, and contrail lifetime were found. The aim of the study was to identify the possibility of using available meteorological data to predict persistent contrails.

2024

This data was provided by the mobile measuring laboratory MobiLab from the Czech Technical University in Prague (https://mobilab.fd.cvut.cz). It presents four data sets with traffic counts measured every minute over a 24-hour period at the following four selected areas in Prague: Stodůlky (September 2021), Barrandov (June 2022), Radlice (September 2022), and Velká Chuchle (October 2022). At each location, 3 to 6 points were chosen where traffic counts were collected in all possible directions along the corresponding road section or intersection. Directions are denoted by numbers 1-4 in the columns of each measured point. This data will be used in the research paper, where detailed information about the traffic counts will be available. References to the paper will be added later.

2024

Tato disertační práce se zabývá koncepcemi vícestupňové obsluhy území ve veřejné dopravě se zaměřením na pásmovou obsluhu v monocentrických sítích. Cílem této práce je navrhnout model optimalizace pásmového jízdního řádu na základě přepravních a provozně-ekonomických kritérií. Nejprve jsou v práci shrnuty běžné formy vícestupňové obsluhy území a jejich přepravní a provozně-ekonomické charakteristiky, stejně jako jejich vliv na čerpání kapacity dráhy. Poté jsou shrnuty nejdůležitější aspekty, které vstupují do rozhodování o poloze pásmových stanic, tedy hranic mezi jednotlivými aglomeračními pásmy. V následném rozboru současného stavu poznání jsou analyzovány práce zaměřující se na optimalizace jízdních řádů a provozu z přepravního a provozně-ekonomického hlediska. Dále byl prověřen současný stav v oblasti metod a přístupů k volbě pásmových stanic. Následně je představen samotný návrh optimalizačního modelu a způsobu jeho použití. Součástí představení modelu je jeho testování, navržený model byl úspěšně otestován na 4 reálných železničních tratích v ČR. V závěru bylo následně formulováno možné směřování dalšího návazného výzkumu souvisejícího s řešenou problematikou.

2024, Neural Network World, 34 (2), p. 89-110), ISSN 2336-4335

This paper deals with the analysis of the relationship between locations and types of crime observed in the Czech Republic. Cluster analysis of crime data based on the recursive Bayesian mixture estimation algorithm is used to identify crime hotspots and estimate local models of crime type. The experiments report that the 2D configuration of the algorithm allows the detection of crime hotspots online. The 3D configuration provides 29% more accurate crime type models than 2D clustering and alternative data mining algorithms. For the data set used, it was determined in which crime hotspots the most serious and most frequent types of crime can be expected to occur with the highest probability. The limitation of the study is the artificial support of the 3D clusters by the fully continuous data vector with the recoded values of the crime type. The potential use of the algorithm is expected in online web applications for sharing information on criminal offenses managed by the Police of the Czech Republic with the public and local government entities in the Czech Republic.

2023, 2023 Smart City Symposium Prague, New York, IEEE Press), p. 1-6), ISBN 979-8-3503-2162-3, ISSN 2691-3666

The paper deals with the analysis of histograms of discrete data collected in questionnaires obtained for individual realizations of the target variable. The main aim of the analysis isto explore the influence of combinations of explanatory variables, represented by responses to the questionnaire, on the behavior of the target variable of the questionnaire. In this paper, an automated approach to histogram comparison is proposed based on coding combinations of data and detecting significant differences in frequencies using the Marascuilo procedure. This is the main contribution of the paper. The approach is validated using a simulated questionnaire in which respondents answered regarding their intention to purchase an electric vehicle subject to finance, leasing, and charging availability, as well as their driving style. The results of the experiments are demonstrated.

2023, Proceedings of the The 12th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS) IDAACS’2023, Dortmund, IEEE), p. 51-56), ISBN 979-8-3503-5804-9, ISSN 2770-4254

The paper considers the problem of online prediction of a count variable based on real-time explanatory data of mixed count and categorical nature. The presented solution is based on (i) recursive Bayesian estimation of a mixture model of Poisson-distributed explanatory counts, using the categorical explanatory variable as a measurable pointer of the mixture, (ii) construction of a mixture of local Poisson regressions on the clustered data, and (iii) use of the pre-estimated mixtures for online prediction of the target count using actual measured explanatory data. The latter is one of the main contributions of the proposed approach. In addition, the dynamic model of the categorical explanatory variable preserves the functionality of the algorithm in case of its measurement failure. The experiments with simulations and real data report lower prediction errors compared to theoretical counterparts.

2023, Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), Manassas, VA, The Institute of Navigation (ION)), p. 4145-4152), ISBN 978-0-936406-35-0, ISSN 2331-5954

The growing dependence of critical infrastructure on Global Navigation Satellite Systems (GNSS) as an accurate and reliable positioning, navigation and timing (PNT) source gives rise to the importance of GNSS interference detection. Although jamming detection capabilities are present in the current market, predominately in the form of specialised GNSS interference detectors or GNSS receivers add-ons. These provide a limited coverage area and their implementation into critical infrastructure operations is rather slow. Therefore, this paper focuses on the detection of GNSS interference using widespread Automatic Dependent Surveillance-Broadcast (ADS-B) technology. The research builds upon previous work and addresses some of its limitations by developing a discrete mathematical model for GNSS jamming detection based on ADS-B quality parameters. To develop and validate the model, a series of experiments involving GNSS jamming in live-sky environments were conducted. The controlled experiments enabled close monitoring of the aircraft navigation systems allowing for precise determination of the aircraft’s jammed/unjammed status. Approximately 75% of the jamming experiment data was used for model development and tuning, while the remaining 25% was reserved for evaluation. The model evaluation leveraging the confusion matrix showed a positive jamming detection rate of over 99% and a false positive jamming detection rate of under 1%. Additionally, the model was tested on ADS-B data from the Atlantic Ocean where no GNSS jamming is expected. Using this data set the model exhibited an under 1% false positive jamming detection rate.

2023

Nastavení parametrů stavební úpravy železniční trati je velmi složitý a komplexní proces, neboť v jeho průběhu je zpravidla nutné utřídit a prioritizovat velké množství variant a podvariant. Tyto jsou následně ohodnoceny na základě přepravní prognózy a hodnocení ekonomické efektivity a v závěru celého procesu je vybrána vítězná varianta. Celý proces je velkou měrou ovlivněn budoucím využitím stavebně upravené infrastruktury cestujícími, které je predikováno zmíněnou přepravní prognózou. Tato práce si klade za cíl revizi stávajícího přístupu k nastavování parametrů železničních infrastrukturních staveb s důrazem na vztah mezi úpravou a budoucím využitím tratě cestujícími.

2023, Informatics in Control, Automation and Robotics. ICINCO 2021. Lecture Notes in Electrical Engineering, vol 1006, Springer, Cham), p. 163-184), ISBN 978-3-031-26474-0, ISSN 1876-1119

The chapter focuses on the description of the relationship of the count variable and explanatory Gaussian variables. The cluster-based model is proposed, which is constructed on conditionally independent Gaussian clusters captured in real time using recursive algorithms of the Bayesian mixture estimation theory. The resulting model is expected to be used for predicting count data using real time Gaussian observations. The Poisson distribution of the count data is used as a basic model. However, in reality, count data often do not satisfy the Poisson assumption of equal mean and variance. For this case, five cluster-based Poisson-related models of overdispersed data have been studied. The experimental part of the chapter demonstrates a comparison of the prediction accuracy of the considered models with two theoretical counterparts for the case of weak and strong overdispersion with the help of simulations. The paper reports that the most accurate prediction in average has been provided by the cluster-based Generalized Poisson models.

2023, Neural Network World, 33 (4), p. 291-315), ISSN 2336-4335

The development of traffic state prediction algorithms embedded in intelligent transportation systems is of great importance for improving traffic conditions for drivers and pedestrians. Despite the large number of prediction methods, existing limitations still confirm the need to find a systematic solution and its adaptation to specific traffic data. This paper focuses on the relationship between traffic flow states in different urban locations, where these states are identified as clusters of traffic counts. Extending the recursive Bayesian mixture estimation theory to the Poisson mixtures, the paper uses the mixture pointers to construct the traffic state prediction model. Using the predictive model, the cluster at the target urban location is predicted based on the traffic counts measured in real time at the explanatory urban location. The main contributions of this study are: (i) recursive identification and prediction of the traffic state at each time instant, (ii) straightforward Poisson mixture initialization, and (iii) systematic theoretical background of the prediction approach. Results of testing the prediction algorithm on real traffic counts are presented.

2022, 2022 New Trends in Civil Aviation (NTCA), Praha, České vysoké učení technické v Praze), p. 63-67), ISBN 978-80-01-06985-1, ISSN 2694-7854

The evolution of airports toward the Smart Airport concept is currently very topical. The Smart Airport concept brings the digitization and new technologies amongst other benefits. This article deals with the impact of smart technologies, implemented to increase the passenger throughput at airport processors, on waiting times in the queue. To enable simulating the impact of various passenger throughputs, a developed generic model, that can be primarily applied to arrival border control at any airport, was used. Based on the simulation results, the difference in the waiting times in the queue depending on different processing times and used technologies can be compared and analyzed. Therefore, the model can also be used to determine the impact of implementation of smart technologies on the passenger flow at the airport. A simulation performed in the model comparing manual, smart and hybrid configurations of the arrival border control is analyzed in this paper.

2022, Neural Network World, 32 (1), p. 15-41), ISSN 1210-0552

The paper deals with the task of modeling discrete questionnaire data with a reduced dimension of the model. The discrete model dimension is reduced using the construction of local models based on independent binomial mixtures estimated with the help of recursive Bayesian algorithms in the combination with the naive Bayes technique. The main contribution of the paper is a three-phase algorithm of the discrete model dimension reduction, which allows to model high-dimensional questionnaire data with high number of explanatory variables and their possible realizations. The proposed general solution is applied to the traffic accident questionnaire analysis, where it takes the form of the classification of the accident circumstances and prediction of the traffic accident severity using the currently measured discrete data. Results of testing the obtained model on real data and comparison with theoretical counterparts are demonstrated.

2021, Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics - ICINCO, Setùbal, SciTePress), p. 641-648), ISBN 978-989-758-522-7, ISSN 2184-2809

This paper aims at presenting the on-line non-iterative form of Bayesian mixture estimation. The model used is composed of a set of sub-models (components) and an estimated pointer variable that currently indicates the active component. The estimation is built on an approximated Bayes rule using weighted measured data. The weights are derived from the so called proximity of measured data entries to individual components. The basis for the generation of the weights are integrated likelihood functions with the inserted point estimates of the component parameters. One of the main advantages of the presented data analysis method is a possibility of a simple incorporation of the available prior knowledge. Simple examples with a programming code as well as results of experiments with real data are demonstrated. The main goal of this paper is to provide clear description of the Bayesian estimation method based on the approximated likelihood functions, called proximities.

2021, Neural Network World, 31 (3), p. 227-238), ISSN 1210-0552

According to the statistics about vehicle accidents, there are many causes such as traffic violations, reduced concentration, micro sleep, hasty aggression, but the most frequent cause of accidents at highways is a carelessness of the driver and violation of keeping a safe distance. Producers of vehicles try to take into account this situation by development of assistance systems which are able to avoid accidents or at least to mitigate its consequences. This urgent situation leaded to the described project of investigation of behavior of drivers in dangerous situations occurring in vehicle driving. The research is to help in solution of the present unsatisfactory situation in driving accidents. The developed decisionmaking algorithm of detection serious driving situations that can lead to accidents was tested in the laboratory of driving simulators in FTS CTU, Prague. The data for its testing resembled highway traffic.

2021, Neural Network World, 31 (2), p. 89-107), ISSN 1210-0552

This study reflects a unique task with significant business potential, on the edge of the wholesale and retail power market, i.e., optimization of power derivatives purchase strategy of retail customers. Even though the definition of the task as well as initial assumptions may be highly complex, essentially, the purpose of this study can be narrowed down to the estimation of buying signals. The price signals are estimated with the use of machine learning techniques, i.e., one-, two- and three-layer perceptron with supervised learning as well as long short-term memory network, which allow modelling of highly complex functional relationships, and with the use of relative strength index, i.e., momentum technical indicator, which on the contrary allows higher flexibility in terms of parameters adjustment as well as easier results interpretation. Thereafter, performance of these methods is compared and evaluated against the established benchmark.

2021, Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics - ICINCO, Setùbal, SciTePress), p. 600-608), ISBN 978-989-758-522-7, ISSN 2184-2809

The paper deals with predicting a discrete target variable described by the Poisson distribution based on the discretized Gaussian explanatory data under condition of the multimodality of a system observed. The discretization is performed using the recursive mixture-based clustering algorithms under Bayesian methodology. The proposed approach allows to estimate the Gaussian and Poisson models existing for each discretization interval of explanatory data and use them for the prediction. The main contributions of the approach include: (i) modeling the Poisson variable based on the cluster analysis of explanatory continuous data, (ii) the discretization approach based on recursive mixture estimation theory, (iii) the online prediction of the Poisson variable based on available Gaussian data discretized in real time. Results of illustrative experiments and comparison with the Poisson regression is demonstrated.

2021, 2021 Smart City Symposium Prague, Piscataway, IEEE Signal Processing Society), ISBN 9780738131580

Data analysis is very important tool for acquiring information about object of our interest. It involves a lot of various methods, mainly from the area of data mining or statistical analysis. However, most of these methods aim at continuous data. In real applications, especially in the field of Smart Cities, questionnaires are a frequent source of data. They are mainly a source of discrete data. As commonly used data analysis methods, such as regression analysis, naturally work with continuous data, complications can occur. However, the linear regression analysis can be carefully used to to analyze discrete data, but carefully.The paper wants to give a warning before a direct mindless use of regression analysis for discrete data, especially when the independent variables are nominal. Also some ways how to modify values of the independent variables to achieve sensible results with linear regression applied to measured discrete data from the Smart City area are sketched.

2020, 2020 Smart City Symposium Prague, New York, IEEE Press), ISBN 978-1-7281-6821-0

Data analysis is an important method for obtaining information which is useful in many projects such as e.g. Smart Cities. Common data sources are questionnaires, their output mainly purveys discrete data. The most common description of discrete data is through categorical models. These models have several advantages such as flexibility but there are also disadvantages such as a huge dimension of the table expressing this distribution for more variables and values and their overparametrization. The aim of this paper is to replace the categorical distribution by another discrete distribution with a lower number of parameters while maintaining the model quality. Binomial distribution was chosen a suitable one because it is determined only by one parameter and this parameter allows to shape the probability function of binomial distribution well. The output of the paper is the presented model of mixture with binomial components. The suggested estimation algorithms are tested on real traffic data.

2020, Automa, 26 (1), p. 26-31), ISSN 1210-9592

Článek se zabývá modelováním diskrétních dopravních dat pomocí binomického, geometrického, Poissonova a rovnoměrného rozdělení.

2019, METRON, 77 (3), p. 253-270), ISSN 0026-1424

The paper focuses on a problem of comparing clusterings with the same number of clusters obtained as a result of using different clustering algorithms. It proposes a method of the evaluation of the agreement of clusterings based on the combination of the Cohen's kappa statistic and the normalized mutual information. The main contributions of the proposed approach are: (i) the reliable use in practice in the case of a small fixed number of clusters, (ii) the suitability to comparing clusterings with a higher number of clusters in contrast with the original statistics, (iii) the independence on size of the data set and shape of clusters. Results of the experimental validation of the proposed statistic using both simulations and real data sets as well as the comparison with the theoretical counterparts are demonstrated.

2019, Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2019), Madeira, SciTePress), p. 617-624), ISBN 978-989-758-380-3

The paper deals with the problem of modeling the passenger demand in the tram transportation network. The passenger demand on the individual tram stops is naturally influenced by the number of boarding and disembarking passengers, whose measuring is expensive and therefore they should be modeled and predicted. A mixture of Poisson components with the dynamic pointer estimated by recursive Bayesian estimation algorithms is used to describe the mentioned variables, while their prediction is solved with the help of the Poisson regression. The main contributions of the presented approach are: (i) the model of the number of boarding and disembarking passengers. (ii) the real-time data incorporation into the model. (iii) the recursive estimation algorithm with the normal approximation of the proximity function. The results of experiments with real data and the comparison with theoretical counterparts are demonstrated.

2019, Informatics in Control, Automation and Robotics. ICINCO 2017. Lecture Notes in Electrical Engineering., Springer, Cham), p. 679-698), ISBN 978-3-030-11292-9, ISSN 1876-1119

The paper provides a practical guide on initialization of the recursive mixture-based clustering of non-negative data. For modeling the non-negative data, mixtures of uniform, exponential, gamma and other distributions can be used. Initialization is known to be an important task for a start of the mixture estimation algorithm. Within the considered recursive approach, the key point of initialization is a choice of initial statistics of the involved prior distributions. The paper describes several initialization techniques for the mentioned types of components that can be beneficial primarily from a practical point of view.

2019, Transportation Research Part B: Methodological, 128, p. 254-270), ISSN 0191-2615

This paper deals with the task of modeling the driving style depending on the driving environment. The model of the driving style is represented as a two-layer mixture of normal components describing data with two pointers: outer and inner. The inner pointer indicates the actual driving environment categorized as “urban”, “rural” and “highway”. The outer pointer through the determined environment estimates the active driving style from a fuel economy point of view as “low consumption”, “middle consumption” and “high consumption”. All of these driving styles are assumed to exist within each driving environment due to the two-layer model. Parameters of the model and the driving style are estimated online, i.e., while driving using a recursive algorithm under the Bayesian methodology. The main contributions of the presented approach are: (i) the driving style recognition within each of urban, rural and highway environments as well as in the case of switching among them. (ii) the two-layer pointer, which allows us to incorporate the information from continuous data into the model. (iii) the potential use of the data-based model for other measurements using corresponding distributions. The approach was tested using real data.

2018, Practical Issues of Intelligent Innovations. Studies in Systems, Decision and Control, Springer, Cham), p. 313-330)

2018, IEEE Aerospace Conference Proceedings, IEEE Xplore), p. 1-8), ISBN 978-1-5386-2014-4, ISSN 1095-323X

This paper deals with safety performance predictions in the aviation, which address the long-term global efforts to achieve predictive risk management by the year 2028. Predictive risk management regards timely and accurate detection of risk, well before some incident or accident takes place so that effective control actions can be provided. To assure achieving such diagnosis, it is necessary that mathematically well-founded predictions will become part of existing safety management systems with the capability to predict key performance indicators. From current safety metrics and with respect to the data available in the aviation, overall safety performance was selected as suitable candidate for predictions. To obtain the performance signal, Aerospace Performance Factor methodology was utilized. Due to confidentiality restrictions with regard to aviation safety data, this study relies on public data sets from the domain of European Air Traffic Management. Dedicated resampling method was used to fill in the gaps of real data sets by transforming expert knowledge into mathematical functions. This enabled the possibility to build and test mathematical models for predicting safety performance. Because the identified data sources included some data, which are not necessary for computing safety performance but relevant in its context, conditional forecasts were made possible. With respect to this, the goal of this paper was to research and evaluate possibilities for both conditional and unconditional forecasts in the context of future risk management. Time-series analysis of the computed safety performance was conducted using ordinary least squares and maximum likelihood estimation. Each of the methodology led to different mathematical model and different predictions. Specific aspects of each methodology were identified.

2018, 2018 Smart City Symposium Prague, New York, IEEE Press), p. 1-6), ISBN 978-1-5386-5017-2

In this paper we perceive data analysis with empirical probability functions as a data mining method. We propose a way to carry out this type of analysis by employing the LISp-Miner system, namely the CF-Miner procedure and pattern difference quantifiers. In order to confirm that LISp-Miner is a suitable tool for this purpose, we briefly present both methods and then show their equivalence. We do this by providing theoretical description which we then support by analysing a small set of data concerning traffic accidents with methods and comparing results. Afterwards we provide an example of analysis of a full data set concerning rail tickets sold at selected stations in 2014. We show that by considering “difference histograms” it is possible to identify remarkable dissimilarities in histograms of time of ticket sale that would not be found otherwise. Both analyses confirms that the method we propose can provide new and interesting results even if the data has been already analysed.

2018, Young Transportation Engineers Conference 2018, Praha, Fakulta dopravní), p. 53-61), ISBN 978-80-01-06464-1

Bayesian networks are one of the most suitable tools for traffic accident data analysis. A well-designed and trained Bayesian network is the first assumption for obtaining good results. Two sources of information can be used for this purpose. They are information extracted from measured historical data and also information specified by an expert. The latter one can also involve some generally known rules or knowledge based on traffic regulations or safety rules. Mostly, only one of these sources of information is used. After training the network can be evaluated with standard methods based on likelihood or prediction error evaluation. The goal of this paper is to show that if two Bayesian networks are created, e.g. one from the data and second from the expert knowledge, they can be merged into one which joins the objective information from data with the subjective opinion from expert and which has better evaluation than the original ones.

2018, Intuitionistic Fuzziness and Other Intelligent Theories and Their Applications. Studies in Computational Intelligence., Springer, Cham), ISBN 978-3-319-78931-6, ISSN 1860-9503

The initialization is known to be a critical task for running a mixture estimation algorithm. A majority of approaches existing in the literature are related to initialization of the expectation-maximization algorithm widely used in this area. This study focuses on the initialization of the recursive mixture estimation for the case of normal components, where the mentioned methods are not applicable. Its key part is a choice of the initial statistics of normal components.

2017, ISBN 978-3-319-64670-1, ISSN 2191-544X

This book provides a general theoretical background for constructing the recursive Bayesian estimation algorithms for mixture models. It collects the recursive algorithms for estimating dynamic mixtures of various distributions and brings them in the unified form, providing a scheme for constructing the estimation algorithm for a mixture of components modeled by distributions with reproducible statistics. It offers the recursive estimation of dynamic mixtures, which are free of iterative processes and close to analytical solutions as much as possible. In addition, these methods can be used online and simultaneously perform learning, which improves their efficiency during estimation. The book includes detailed program codes for solving the presented theoretical tasks. Codes are implemented in the open source platform for engineering computations. The program codes given serve to illustrate the theory and demonstrate the work of the included algorithms.

2017, Transportation Research Part C: Emerging Technologies, p. 23-36), ISSN 0968-090X

The paper focuses on a task of stochastic modeling the driving style and its online estimation while driving. The driving style is modeled by means of a mixture model with normal and categorical components as well as a data-dependent pointer. The main contributions of the presented approach are: (i) the online estimation of the driving style while driving, taking into account data up to the current time instant; (ii) the joint model for continuous and discrete data measured on a vehicle; (iii) the data-dependent model of the driving style conditioned by the values of fuel consumption; (iv) the use of the model both for detection of clusters according to the driving style and prediction of the fuel consumption along with other variables; and (v) the universal modeling with the help of mixtures, which allows us to use different combinations of components and pointer models as well as to specify the initialization approach suitable for the considered problem.

2017, Intelligent Systems and Informatics (SISY), 2017 IEEE 15th International Symposium on, Budapest, IEEE Hungary Section, University Obuda), ISBN 978-1-5386-3855-2, ISSN 1949-0488

This paper deals with a modeling of data by several mixtures of different distributions within a task of clustering. This issue can be required from a practical point of view, e.g., for a multi-modal system, which generates measurements described by different distributions. The approach is based on the partition of the data on several parts, the factorization of the joint probability density function according to these parts and the estimation of each conditional mixture separately. Due to the data-based construction of the general model from the estimated components, the most suitable combination of the components is used at each time instant.

2017, Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics, Madeira, SciTePress), ISBN 978-989-758-263-9

The paper deals with a task of initialization of the recursive mixture estimation for the case of uniform components. This task is significant as a part of mixture-based clustering, where data clusters are described by the uniform distributions. The issue is extensively explored for normal components. However, sometimes the assumption of normality is not suitable or limits potential application areas (e.g., in the case of data with fixed bounds). The use of uniform components can be beneficial for these cases. Initialization is always a critical task of the mixture estimation. Within the considered recursive estimation algorithm the key point of its initialization is a choice of initial statistics of components. The paper explores several initialization approaches and compares results of clustering with a theoretical counterpart. Experiments with real data are demonstrated.

2017, Proceedings of International Conference on Intelligent Informatics and BioMedical Sciences ICIIBMS 2017, Okinawa, Okinawa Institute of Science and Technology), p. 63-70), ISBN 978-1-5090-6664-3, ISSN 2189-8723

The paper deals with the mixture-based clustering of anonymized data of patients with leukemia. The presented clustering algorithm is based on the recursive Bayesian mixture estimation for the case of exponential components and the data-dependent dynamic pointer model. The main contribution of the paper is the online performance of clustering, which allows us to actualize the statistics of components and the pointer model with each new measurement. Results of the application of the algorithm to the clustering of hematological data are demonstrated and compared with theoretical counterparts.