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Interconnection of Restricted Boltzmann machine method with statistical physics and its implementation in the processing of spectroscopic data
Vrábel, Jakub ; Hrdlička, Aleš (referee) ; Pořízka, Pavel (advisor)
Práca sa zaoberá spojeniami medzi štatistickou fyzikou a strojovým učením s dôrazom na základné princípy a ich dôsledky. Ďalej sa venuje obecným vlastnostiam spektroskopických dát a ich zohľadnení pri pokročilom spracovaní dát. Začiatok práce je venovaný odvodeniu partičnej sumy štatistického systému a štúdiu Isingovho modelu pomocou "mean field" prístupu. Následne, popri základnom úvode do strojového učenia, je ukázaná ekvivalencia medzi Isingovým modelom a Hopfieldovou sieťou - modelom strojového učenia. Na konci teoretickej časti je z Hopfieldovej siete odvodený model Restricted Boltzmann Machine (RBM). Vhodnosť použitia RBM na spracovanie spektroskopických dát je diskutovaná a preukázaná na znížení dimenzie týchto dát. Výsledky sú porovnané s bežne používanou Metódou Hlavných Komponent (PCA), spolu so zhodnotením prístupu a možnosťami ďalšieho zlepšovania.
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A point process driven by a Gaussian field
Scheib, Karel ; Beneš, Viktor (advisor) ; Šedivý, Ondřej (referee)
The thesis investigates the search for dimension reduction subspace for the Poisson point process driven by a Gaussian random eld. The work describes the method called sliced inverse regression, which is applied to a point process driven by random eld. Its functionality in mentioned context is then proved. This method is in several ways implemented and tested in R software environment on random data. The individual implementations are described and results are then compared with each other.
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Big data visualization
Lehončák, Michal ; Pelikán, Josef (advisor) ; Horáček, Jan (referee)
Nowadays, data are an integral part of our lives. Their volume is growing every day, and it often prevents us from understanding what these data means. The object of this thesis is to develop an application for large dataset analysis and visualization. Thesis also explores statistical methods used to reduce volume and dimensionality of data and implements selected algorithms from this field. Another goal is to explore the possibilities of modern graphics cards, as their performance increases every year. The visualization should use a graphics processor with data are shown as points in point- cloud in 3D space and user should be able to browse this data interactively.
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Mathematical modelling of thin films of martensitic materials
Pathó, Gabriel ; Kružík, Martin (advisor) ; Kalamajska, Agnieszka (referee) ; Šilhavý, Miroslav (referee)
The aim of the thesis is the mathematical and computer modelling of thin films of martensitic materials. We derive a thermodynamic thin-film model on the meso-scale that is capable of capturing the evolutionary process of the shape-memory effect through a two-step procedure. First, we apply dimension reduction techniques in a microscopic bulk model, then enlarge gauge by neglecting microscopic interfacial effects. Computer modelling of thin films is conducted for the static case that accounts for a modified Hadamard jump condition which allows for austenite--martensite interfaces that do not exist in the bulk. Further, we characterize $L^p$-Young measures generated by invertible matrices, that have possibly positive determinant as well. The gradient case is covered for mappings the gradients and inverted gradients of which belong to $L^\infty$, a non-trivial problem is the manipulation with boundary conditions on generating sequences, as standard cut-off methods are inapplicable due to the determinant constraint. Lastly, we present new results concerning weak lower semicontinuity of integral functionals along (asymptotically) $\mathcal{A}$-free sequences that are possibly negative and non-coercive. Powered by TCPDF (www.tcpdf.org)
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Efficient implementation of dimension reduction methods for high-dimensional statistics
Pekař, Vojtěch ; Duintjer Tebbens, Erik Jurjen (advisor) ; Hnětynková, Iveta (referee)
The main goal of our thesis is to make the implementation of a classification method called linear discriminant analysis more efficient. It is a model of multivariate statistics which, given samples and their membership to given groups, attempts to determine the group of a new sample. We focus especially on the high-dimensional case, meaning that the number of variables is higher than number of samples and the problem leads to a singular covariance matrix. If the number of variables is too high, it can be practically impossible to use the common methods because of the high computational cost. Therefore, we look at the topic from the perspective of numerical linear algebra and we rearrange the obtained tasks to their equivalent formulation with much lower dimension. We offer new ways of solution, provide examples of particular algorithms and discuss their efficiency. Powered by TCPDF (www.tcpdf.org)
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Statistical model of the face shape
Boková, Kateřina ; Pelikán, Josef (advisor) ; Krajíček, Václav (referee)
The goal of this thesis is to use machine learning methods for datasets of scanned faces and to create a program that allows to explore and edit faces represented as triangle meshes with a number of controls. Firstly we had to reduce dimension of triangle meshes by PCA and then we tried to predict shape of meshes according to physical properties like weight, height, age and BMI. The modeled faces can be used in animation or games.
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Statistical model of the face shape
Boková, Kateřina ; Pelikán, Josef (advisor) ; Krajíček, Václav (referee)
The goal of this thesis is to use machine learning methods for datasets of scanned faces and to create a program that allows to explore and edit faces represented as triangle meshes with a number of controls. Firstly we had to reduce dimension of triangle meshes by PCA and then we tried to predict shape of meshes according to physical properties like weight, height, age and BMI. The modeled faces can be used in animation or games.
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Interconnection of Restricted Boltzmann machine method with statistical physics and its implementation in the processing of spectroscopic data
Vrábel, Jakub ; Hrdlička, Aleš (referee) ; Pořízka, Pavel (advisor)
Práca sa zaoberá spojeniami medzi štatistickou fyzikou a strojovým učením s dôrazom na základné princípy a ich dôsledky. Ďalej sa venuje obecným vlastnostiam spektroskopických dát a ich zohľadnení pri pokročilom spracovaní dát. Začiatok práce je venovaný odvodeniu partičnej sumy štatistického systému a štúdiu Isingovho modelu pomocou "mean field" prístupu. Následne, popri základnom úvode do strojového učenia, je ukázaná ekvivalencia medzi Isingovým modelom a Hopfieldovou sieťou - modelom strojového učenia. Na konci teoretickej časti je z Hopfieldovej siete odvodený model Restricted Boltzmann Machine (RBM). Vhodnosť použitia RBM na spracovanie spektroskopických dát je diskutovaná a preukázaná na znížení dimenzie týchto dát. Výsledky sú porovnané s bežne používanou Metódou Hlavných Komponent (PCA), spolu so zhodnotením prístupu a možnosťami ďalšieho zlepšovania.
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Big data visualization
Lehončák, Michal ; Pelikán, Josef (advisor) ; Horáček, Jan (referee)
Nowadays, data are an integral part of our lives. Their volume is growing every day, and it often prevents us from understanding what these data means. The object of this thesis is to develop an application for large dataset analysis and visualization. Thesis also explores statistical methods used to reduce volume and dimensionality of data and implements selected algorithms from this field. Another goal is to explore the possibilities of modern graphics cards, as their performance increases every year. The visualization should use a graphics processor with data are shown as points in point- cloud in 3D space and user should be able to browse this data interactively.
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Efficient implementation of dimension reduction methods for high-dimensional statistics
Pekař, Vojtěch ; Duintjer Tebbens, Erik Jurjen (advisor) ; Hnětynková, Iveta (referee)
The main goal of our thesis is to make the implementation of a classification method called linear discriminant analysis more efficient. It is a model of multivariate statistics which, given samples and their membership to given groups, attempts to determine the group of a new sample. We focus especially on the high-dimensional case, meaning that the number of variables is higher than number of samples and the problem leads to a singular covariance matrix. If the number of variables is too high, it can be practically impossible to use the common methods because of the high computational cost. Therefore, we look at the topic from the perspective of numerical linear algebra and we rearrange the obtained tasks to their equivalent formulation with much lower dimension. We offer new ways of solution, provide examples of particular algorithms and discuss their efficiency. Powered by TCPDF (www.tcpdf.org)
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