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Mining Module of Data Mining System FIT-Miner
Zapletal, Petr ; Bartík, Vladimír (referee) ; Zendulka, Jaroslav (advisor)
This master's thesis deals with with FIT-Miner, the system for knowledge discovery in databases. The first part of this paper describes the data-mining process, mixture model's issues and FIT-Miner system. Second part deals with design, implementation and testing of created module, which is used for cluster analysis with Expectation-Maximalization algorithm. The end of the paper is focused to design of modules using Java Store Procedures Technology.
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Occupancy grids
Herman, Ivo ; Pohl, Jan (referee) ; Šolc, František (advisor)
This thesis deals with theoretical analysis and practical use of different sensor models for occupancy grids. In the first part was theoretically derived one-dimensional sensor model with Gaussian noise, which was subsequently converted into second dimension. In the second part were compared several of the sensor models: the model by R. Murphy, maps generated by the EM algorithm and also by our implementation of 2D model. Another result of the thesis is computer programme, which allows measurement generating for models in simulated world and incorporating real--sensor data.
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Statistical analysis of samples from the generalized exponential distribution
Votavová, Helena ; Popela, Pavel (referee) ; Michálek, Jaroslav (advisor)
Diplomová práce se zabývá zobecněným exponenciálním rozdělením jako alternativou k Weibullovu a log-normálnímu rozdělení. Jsou popsány základní charakteristiky tohoto rozdělení a metody odhadu parametrů. Samostatná kapitola je věnována testům dobré shody. Druhá část práce se zabývá cenzorovanými výběry. Jsou uvedeny ukázkové příklady pro exponenciální rozdělení. Dále je studován případ cenzorování typu I zleva, který dosud nebyl publikován. Pro tento speciální případ jsou provedeny simulace s podrobným popisem vlastností a chování. Dále je pro toto rozdělení odvozen EM algoritmus a jeho efektivita je porovnána s metodou maximální věrohodnosti. Vypracovaná teorie je aplikována pro analýzu environmentálních dat.
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Algorithms of Electrical Drives State Estimation
Herman, Ivo ; Vavřín, Petr (referee) ; Václavek, Pavel (advisor)
This thesis deals with state estimation methods for AC drives sensorless control and with possibilities of the estimation. Conditions for observability for a synchronous drive were derived, as well as conditions for the moment of inertia and the load torque observability for both drive types - synchronous and asynchronous. The possibilities of the estimation were confirmed by experimental results. The covariance matrices for all filters were found using an EM algorithm. Both drives were also identified. The algoritms used for state estimation are Extended Kalman Filter, Unscented Kalman Filter, Particle Filters and Moving Horizon Estimator.
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Gaussian mixtures in R
Marek, Petr ; Malá, Ivana (advisor) ; Zimmermann, Pavel (referee)
Using Gaussian mixtures is a popular and very flexible approach to statistical modelling. The standard approach of maximum likelihood estimation cannot be used for some of these models. The estimates are, however, obtainable by iterative solutions, such as the EM (Expectation-Maximization) algorithm. The aim of this thesis is to present Gaussian mixture models and their implementation in R. The non-trivial case of having to use the EM algorithm is assumed. Existing methods and packages are presented, investigated and compared. Some of them are extended by custom R code. Several exhaustive simulations are run and some of the interesting results are presented. For these simulations, a notion of usual fit is presented.
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Approximating Probability Densities by Mixtures of Gaussian Dependence Trees
Grim, Jiří
Considering the probabilistic approach to practical problems we are increasingly confronted with the need to estimate unknown multivariate probability density functions from large high-dimensional databases produced by electronic devices. The underlying densities are usually strongly multimodal and therefore mixtures of unimodal density functions suggest themselves as a suitable approximation tool. In this respect the product mixture models are preferable because they can be efficiently estimated from data by means of EM algorithm and have some advantageous properties. However, in some cases the simplicity of product components could appear too restrictive and a natural idea is to use a more complex mixture of dependence-tree densities. The dependence tree densities can explicitly describe the statistical relationships between pairs of variables at the level of individual components and therefore the approximation power of the resulting mixture may essentially increase.
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Mixture distributions
Nedvěd, Jakub ; Malá, Ivana (advisor) ; Bílková, Diana (referee)
Object of this thesis is to construct a mixture model of earnings of the Czech households. In first part are described characteristics of mixtures of statistical distributions with the focus on the mixtures of normal distibutions. In practical part of this thesis are constructed models with parameters extimations based on the data from EU-SILC. Models made by graphical method, EM algorithm and method of maximum likelihood. The quality of models is measured by Akaike information criterion.
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Detekce lineární části Patlak-Rutlandova grafu
Šmídl, Václav
Detection of linear part of a graph is a common problem in data analysis. Specifically for the Patlak-Rutland plot, this step is an important part of functional analysis of renal activity. An automated method for detection is proposed and tested on 16 data sets of real medical data.
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Informační shlukování kategoriálních dat
Hora, Jan
The EM algorithm has been used repeatedly to identify latent classes in categorical data by estimating finite distribution mixtures of product components. Unfortunately, the underlying mixtures are not uniquely identifiable and, moreover, the estimated mixture parameters are starting-point dependent. For this reason we use the latent class model only to define a set of ``elementary'' classes by estimating a mixture of a large number components. As such a mixture we use also an optimally smoothed kernel estimate. We propose a hierarchical ``bottom up'' cluster analysis based on unifying the elementary latent classes sequentially. The clustering procedure is controlled by minimum information loss criterion.
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Application of generalized linear model for mixture distributions
Pokorný, Pavel ; Malá, Ivana (advisor) ; Pavelka, Roman (referee)
This thesis is intent on using mixtures of probability distributions in generalized linear model. The theoretical part is divided into two parts. In the first chapter a generalized linear model (GLM) is defined as an alternative to the classical linear regression model. The second chapter describes the mixture of probability distributions and estimate of their parameters. At the end of the second chapter, the previous theories are connected into the finite mixture generalized linear model. The last third part is practical and shows concrete examples of these models.
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