Academic literature on the topic 'Metoda hlavních komponent (PCA)'

This diploma thesis deals with using laser-induced breakdown plasma spectroscopy for determining the elemental structure of unknown samples. It was necessary to design an appropriate method to qualify material by laser-induced emission spectrum. Pretreatment of data and using a variety of chemometrics methods had to be done in order to qualify the structure of elements. We achieved a required solution by projecting the data to a new PCA space, creating clusters and computing the Euclidean distance between each cluster. The experiment in the practical part was set to detect an interface of two elements. We created a data file simulating the ablation on the interface. This data set was gradually processed applying a mathematical-chemical-physical view. Several data procedures have been compiled: approximation by Lorenz, Gauss and Voigt function and also a pretreatment method such as the detection of outliers, standardization by several procedures and subsequent use of principal components analysis. A summarization of processes for input data is fully described in the thesis.

The aim of this study is evaluation of using multi-dimensional statistical analyses methods as a tool for simulations of reliability of distribution network. Prefered methods are a cluster analysis (CLU) and a principal component analysis (PCA). CLU is used for a division of objects on the basis of their signs and a calculation of the distance between objects into groups whose characteristics should be similar. The readout can reveal a secret structure in data. PCA is used for a location of a structure in signs of multi-dimensional matrix data. Signs present separate quantities describing the given object. PCA uses a dissolution of a primary matrix data to structural and noise matrix data. It concerns the transformation of primary matrix data into new grid system of principal components. New conversion data are called a score. Principal components generating orthogonal system of new position. Distribution network from the aspect of reliability can be characterized by a number of new statistical quantities. Reliability indicators might be: interruption numbers, interruption time. Integral reliability indicators might be: system average interruption frequency index (SAIFI) and system average interruption duration index (SAIDI). In conclusion, there is a comparison of performed SAIFI simulation according to negatively binomial division and provided values from a distribution company. It is performed a test at description of sign dependences and outlet divisions.

This semester thesis is focused on automated measurement of ECG signal. The theoretical part describes the rise and options ECG signal. Furthermore, the issue is staged principal components analysis, whose output is used as input signal for seasons. They describe the basic methods used in measurement to ECG signal. The practical part is designed in measurement algorithm for ECG signal that has been tested on basic CSE database. The results are discussed in the conclusion.

Tato doktorská práce je zaměřena na vývoj algoritmu ke zpracování dat naměřených zařízením pro spektrometrii laserem indukovaného plazmatu (angl. LIBS). Zařízení LIBS s tímto algoritmem by mělo být následně schopno provést třídění vzorků a kvantitativní analýzu analytu in-situ a v reálném čase. Celá experimentální část této práce byla provedena ve Spolkovém institutu pro materiálový výzku a testování (něm. BAM) v Berlíně, SRN, kde byl sestaven elementární LIBS systém. Souběžně s experimentílní prací byl vytvořen přehled literárních zdrojů s cílem podat ucelený pohled na problematiku chemometrických metod používaných k analýze LIBS měření. Použití chemometrických metod pro analýzu dat získaných pomocí LIBS měření je obecně doporučováno především tehdy, jsou-li analyzovány vzorky s komplexní matricí. Vývoj algoritmu byl zaměřen na kvantitativní analýzu a třídění vyvřelých hornin na základě měření pomocí LIBS aparatury. Sada vzorků naměřených použitím metody LIBS sestávala z certifikovaných referenčních materiálů a vzorků hornin shromážděných přímo na nalezištích mědi v Íránu. Vzorky z Íránu byly následně na místě roztříděny zkušeným geologem a množství mědi v daných vzorcích bylo změřeno na Univerzitě v Clausthalu, SRN. Výsledné kalibrační křivky byly silně nelineární, přestože byly sestaveny i z měření referenčních vzorků. Kalibrační křivku bylo možné rozložit na několik dílčích tak, že závislost intenzity měděné čáry na množství mědi se nacházela v jiném trendu pro jednotlivé druhy hornin. Rozdělení kalibrační křivky je zpravidla přisuzováno tzv. matričnímu jevu, který silně ovlivňuje měření metodou LIBS. Jinými slovy, pokud určujeme množství analytu ve vzorcích s různou matricí, je výsledná kalibrační křivka sestavená pouze z jedné proměnné (intenzity zvolené spektrální čáry analytu) nepřesná. Navíc, normalizace takto vytvořených kalibračních křivek k intenzitě spektrální čáry matrčního prvku nevedla k výraznému zlepšení linearity. Je obecně nemožné vybrat spektrální čáru jednoho matričního prvku pokud jsou analyzovány prvky s komplexním složením matric. Chemometrické metody, jmenovitě regrese hlavních komponent (angl. PCR) a regrese metodou nejmenších čtverců (angl. PLSR), byly použity v multivariační kvantitatvní analýze, tj. za použití více proměnných/spektrálních čar analytu a matričních prvků. Je potřeba brát v potaz, že PCR a PLSR mohou vyvážit matriční jev pouze do určité míry. Dále byly vzorky úspěšně roztříděny pomocí analýzy hlavních komponent (angl. PCA) a Kohonenových map na základě složení matričních prvků (v anglické literatuře se objevuje termín ‚spectral fingerprint‘) Na základě teorie a experimentálních měření byl navržen algoritmus pro spolehlivé třídění a kvantifikaci neznámých vzorků. Tato studie by měla přispět ke zpracování dat naměřených in-situ přístrojem pro dálkovou LIBS analýzu. Tento přístroj je v současnosti vyvíjen v Brně na Vysokém učení technickém. Toto zařízení bude nenahraditelné při kvantifikaci a klasifikaci vzorků pouze tehdy, pokud bude použito zároveň s chemometrickými metodami a knihovnami dat. Pro tyto účely byla již naměřena a testována část knihoven dat v zaměření na aplikaci metody LIBS do těžebního průmyslu.

This thesis deals with the design and implementation of a tool for generating drums triggers from a downmix record. The work describes the preprocessing of the input audio signal and methods for the classification of strokes. The drum classification is based on the similarity of the signals in the frequency domain. Principal component analysis (PCA) was used to reduce the number of dimensions and to find the characteristic properties of the input data. The method support vector machine (SVM) was used to classify the data into individual classes representing parts of the drum kit. The software was programmed in Matlab. The classification model was trained on a set of 728 drum samples for seven categories (kick, snare, hi-hat, crash, ride, kick + hi-hat, snare + hi-hat). The success of the system in the classification is 75 %.

The mortality is historically one of the most important demographic indicator and definitely reflects the maturity of each country. The objective of this diploma thesis is the comparison of mortality rates in analyzed countries around the world over time and among each other using the principle component analysis that allows assessing data different way. The big advantage of this method is minimal loss of information and quite understandable interpretation of mortality in each country. This thesis offers several interesting graphical outputs, that for example confirm higher mortality rate in Eastern European countries compared to Western European countries and show that Czech republic is country where mortality has fallen most in context of post-communist countries between 1990 and 2010. Source of the data is Human Mortality Database and all data were processed in statistical tool SPSS.

The diploma thesis deals with multivariate statistical methods and their environmental applications. The theoretical part is devoted to selected methods of linear regression analysis, method of principal components and the model of classical and robust factor analysis is also described. In the practical part of thesis, the main emission sources of PM1 aerosols in summer and winter period in Brno and Šlapanice are determined by using the classical factor analysis. The main aerosol emission sources in summer and winter in Šlapanice are also identified by using the robust factor analysis. Furthermore, the prediction of concentrations of PM1 aerosols in summer and winter period in Brno and Šlapanice is performed by using the linear regression model.

This thesis deals with the increasingly developing field of biometric systems which is the identification of faces. The thesis deals with the possibilities of face localization in pictures and their normalization, which is necessary due to external influences and the influence of different scanning techniques. It describes various techniques of localization of dominant features of the face such as eyes, mouth or nose. Not least, it describes different approaches to the identification of faces. Furthermore a it deals with an implementation of the Dominant Face Features Recognition application, which demonstrates chosen methods for localization of the dominant features (Hough Transform for Circles, localization of mouth using the location of the eyes) and for identification of a face (Linear Discriminant Analysis, Kernel Discriminant Analysis). The last part of the thesis contains a summary of achieved results and a discussion.

The master thesis deals with the joint EEG-fMRI analysis based on a heuristic model that describes the relationship between changes in blood flow in active brain areas and in the electrical activity of neurons. This work also discusses various methods of extracting of useful information from the EEG and their influence on the final result of joined analysis. There were tested averaging methods of electrodes interest, decomposition by principal components analysis and decomposition by independent component analysis. Methods of averaging and decomposition by PCA give similar results, but information about a stimulus vector can not be extracted. Using ICA decomposition, we are able to obtain information relating to the certain stimulation, but there is the problem in the final interpretation and selection of the right components in a blind search for variability coupled with the experiment. It was found out that although components calculated from the time sequence EEG are independent for each to other, their spectrum shifts are correlated. This spectral dependence was eliminated by PCA / ICA decomposition from vectors of spectrum shifts. For this method, each component brings new information about brain activity. The results of the heuristic approach were compared with the results of the joined analysis based on the relative and absolute power approach from frequency bands of interest. And the similarity between activation maps was founded, especially for the heuristic model and the relative power from the gamma band (20-40Hz).

Neural networks with algorithm back-propagation will be presented in this work. Theoretical background of the algorithm will be explained. The problems with training neural nets will be solving there. The work discuss some techniques of image preprocessing and image extraction features, which is one of main part in classification. Some part of work discuss few experiments with neural nets with chosen image features.