Sudaryta ir išbandyta Matchad‘o programiniu paketu Gauso funkcijų splino programa glodinanti didelio matavimo skaičiaus eksperimentinį masyvą. Glodinimo funkciją sudaro polinomų ir Gauso funkcijų sandaugos suma. Glodinimo procedūra suvedama į algebrinių lygčių sistemą neapibrėžtiems koeficientams Cn,l rasti. Sudaryta Matchad‘o programa, kuri panaudojus suglodintą funkciją apruoksimuoja ją tik teigiamų Gauso funkcijų suma.Šis uždavinys realizuotas programa, kuri remiasi didžiausio nuolydžio metodu. Glodinimo ir aproksimavimo rezultatai tenkina eksperimentatorių reikalavimus. / Formed and, used MathCad software, tested Gauss function spline program, which smoothes big measure number experimental array. Smoothing function contains polynomial and Gauss functions multiplication sum. Smoothing procedure is reduced to algebraic equation system to find indeterminate coefficients Cn,l. Created MathCad program, which, by using smoothed function, approximates it to positive Gauss functions sum. This task was solved with program, which refers to biggest pitch method. Smoothing and approximation results fit experimenters’ requirements.

Darbe aprašytas modelis, naudojant aktyvacijos funkcijas su Gauso branduoliais. Vienu atveju buvo paimtos aktyvacijos funkcijos, maksimizuojančios Shannon entropija, kitu – maksimizuojančios Renyi entropiją. Manoma, kad tokio tipo funkcijos turėtų geriau tikti prognozavimui. / In this thesis a novel technique is used to construct sparse generalized Gaussian Kernel regression model- so called neural network. Kernel which maximize Renyi entropy is used too. Experimental results obtained using these models are promising.

Problem of the dissertation. The Gaussian random values are very common in practice, because if a random value depends on many additive factors, according to the Central Limit Theorem (if particular conditions are satisfied), the sum is approximately from Gaussian distribution. If the observed random value belongs to one of the several classes, it is from the Gaussian distribution mixture model. The mixtures of the Gaussian distributions are common in various fields: biology, medicine, astronomy, military science and many others. The most important statistical problems are problems of mixture identification and data clustering. In case of high data dimension, these tasks are not completely solved. The new parameter estimation of the multivariate Gaussian distribution mixture model and data clustering methods are proposed and analysed in the dissertation. Since it is much easier to solve these problems in univariate case, the projection-based approach is used. The aim of the dissertation. The aim of this work is the development of constructive algorithms for distribution analysis and clustering of data from the mixture model of the Gaussian distributions.

Problem of the dissertation. The Gaussian random values are very common in practice, because if a random value depends on many additive factors, according to the Central Limit Theorem (if particular conditions are satisfied), the sum is approximately from Gaussian distribution. If the observed random value belongs to one of the several classes, it is from the Gaussian distribution mixture model. The mixtures of the Gaussian distributions are common in various fields: biology, medicine, astronomy, military science and many others. The most important statistical problems are problems of mixture identification and data clustering. In case of high data dimension, these tasks are not completely solved. The new parameter estimation of the multivariate Gaussian distribution mixture model and data clustering methods are proposed and analysed in the dissertation. Since it is much easier to solve these problems in univariate case, the projection-based approach is used. The aim of the dissertation. The aim of this work is the development of constructive algorithms for distribution analysis and clustering of data from the mixture model of the Gaussian distributions.

Gaussian distribution is the most applied in practice and because of that reason there is a great amount of studies done in this area. In this report we look at Gaussian distribution from a point of view of extreme value theory. More concretely, moments of maximum of normally distributed values are discussed. There are methods to calculate moments of extremes of independent identically distributed normal values, values with different variances and asymptotical results. In this work a case of dependant variables is analyzed and aim is to look for results in similar cases that is done for independent variables. Continuing Bachelor’s work formula for moment calculation of maximum of two dependent normal variables with all different parameters is presented. Also there is a proof of formula for calculation of odd order moments of three dependent variable maximum. This result is generalized for random variable vectors of any length. There is a theorem stated, according to which moments of length n vector maximum could be expressed by same order moments of shorter vectors. Unfortunately, because of requirements for numbers n and m, no recursion method could be applied. Using computer, maximum of various length random vectors with dependent components is simulated and average is analyzed. In experiments relation between mean values of dependent and independent variable maximums is observed. This relation is stated in a form of a formula and proved for vectors of any length. In this... [to full text]

Baigiamajame magistro darbe sprendžiamas klasikinis uždavinys, kai tikimybinis skirstinys aproksimuojamas Gauso skirstiniu, panaudojus kelis žinomus metodus. Darbe skirstiniai iš GZD tikimybinių skirstinių klasės aproksimuojami Gauso tikimybiniais skirstiniais. Pritaikytas D. Alfers ir H. Dinges metodas apie beta skirstinio aproksimavimą normaliuoju skirstiniu darbe nagrinėjamiems GZD. Užrašyti neaprėžtai dalių tikimybinių skirstinių formalūs charakteristinių funkcijų bei tankių asimptotiniai skleidiniai panaudojant Apelio daugianarius. Gautos formulės bus naudingos matematinės statistikos specialistams ir ekonomistams, nagrinėjantiems finansuose iškilusias problemas. / In this paper are solved classical problem, i.e. there are used normal approximations employed few well-known methods. In this paper normal approximations are developed for Br. Grigelionis GZD distributions. We are shown what normal approximations used for beta distributions are applied for GZD distributions. In this paper we are applying D. Alfers ir H. Dinges statements about beta distributions asymptotical treatments. It is written down formal characteristic function and density for infinite divisible distributions asymptotical expansion used Apelis polynomial. The results will help to mathematical statistics specialists and cea who are researching problems in finance theory.

Baigiamajame magistro darbe sprendžiamas klasikinis uždavinys, kai tikimybinis skirstinys aproksimuojamas Gauso skirstiniu, panaudojus kelis žinomus metodus. Darbe skirstiniai iš GZD tikimybinių skirstinių klasės aproksimuojami Gauso tikimybiniais skirstiniais. Pritaikytas D. Alfers ir H. Dinges metodas apie beta skirstinio aproksimavimą normaliuoju skirstiniu darbe nagrinėjamiems GZD. Užrašyti neaprėžtai dalių tikimybinių skirstinių formalūs charakteristinių funkcijų bei tankių asimptotiniai skleidiniai panaudojant Apelio daugianarius. Gautos formulės bus naudingos matematinės statistikos specialistams ir ekonomistams, nagrinėjantiems finansuose iškilusias problemas. / In this paper are solved classical problem, i.e. there are used normal approximations employed few well-known methods. In this paper normal approximations are developed for Br. Grigelionis GZD distributions. We are shown what normal approximations used for beta distributions are applied for GZD distributions. In this paper we are applying D. Alfers ir H. Dinges statements about beta distributions asymptotical treatments. It is written down formal characteristic function and density for infinite divisible distributions asymptotical expansion used Apelis polynomial. The results will help to mathematical statistics specialists and cea who are researching problems in finance theory.

Baigiamajame magistro darbe “Interaktyvus transporto numerio atpažinimas” nagrinėjami bei pritaikomi stebėjimo zonos išskyrimo, fono eliminavimo, Gauso, Sobel metodai ir algoritmai. Taip pat atliekama metodų bei filtrų analizė. Tyrimo eigoje buvo sukurta programa skirta duomenų įvedimui į kompiuterį iš vaizdo kameros, vaizdo failo arba interneto. Atlikti eismo filtravimo eksperimentai, vartotojų patogumui įgyvendintas įrankis skirtas gauti ir pateikti apdorojimo rezultatus į mobilujį telefoną. / This work presents an approach to license plate localization and recognition. A proposed method is designed to perform recognition of any kind of license plates under any environmental conditions. The main assumption of this method is the ability to recognize all kinds of license plates which can be found in an individual picture. The algorithm takes a raster image as an input, and yields the position of a plate in the image. After the position is determined, the algorithm can determine the locations of characters on the license plate, which could be easily combined with an OCR algorithm to convert the license plate number into an ASCII string. User could view collected license plate localizations results with mobile phone, which has JAVA (MIDP 1.0) support and internet access. Future work could focus on determining the positions of characters more precisely. Determining the correct positions of all characters in a license plate would dramatically improve the results of the license plate recognition.

Sports are getting more and more benefit from use of information technologies. Information technologies can provide not only collected sport event statistics but also can give more complex analysis results that can be used for planning sport strategies and tactics. Also information technologies are used in sports monitoring, data gathering and result data analysis. Great results are achieved in basketball monitoring and data analysis. Most popular and widely used basketball data analysis methods are rating systems. Other analysis methods can provide predictions on forthcoming basketball games. With aim to provide new possibilities in data analysis area some popular basketball data analysis methods are introduced with discussed possibilities of methods improvements. As a research result possibilities for basketball rating systems improvements are proposed. Also framework for basketball games prediction methods precision research is designed and developed. Using developed framework prediction methods are researched and main results provided.

Questions of speaker’s recognition by voice are investigated in this dissertation. Speaker recognition systems, their evolution, problems of recognition, systems of features, questions of speaker modeling and matching used in text-independent and text-dependent speaker recognition are considered too. The text-independent speaker recognition system has been developed during this work. The Gaussian mixture model approach was used for speaker modeling and pattern matching. The automatic method for voice activity detection was proposed. This method is fast and does not require any additional actions from the user, such as indicating patterns of the speech signal and noise. The system of the features was proposed. This system consists of parameters of excitation source (glottal) and parameters of the vocal tract. The fundamental frequency was taken as an excitation source parameter and four formants with three antiformants were taken as parameters of the vocal tract. In order to equate dispersions of the formants and antiformants we propose to use them in mel-frequency scale. The standard mel-frequency cepstral coefficients (MFCC) for comparison of the results were implemented in the recognition system too. These features make baseline in speech and speaker recognition. The experiments of speaker recognition have shown that our proposed system of features outperformed standard mel-frequency cepstral coefficients. The equal error rate (EER) was equal to 5.17% using proposed... [to full text] / Disertacijoje nagrinėjami kalbančiojo atpažinimo pagal balsą klausimai. Aptartos kalbančiojo atpažinimo sistemos, jų raida, atpažinimo problemos, požymių sistemos įvairovė bei kalbančiojo modeliavimo ir požymių palyginimo metodai, naudojami nuo ištarto teksto nepriklausomame bei priklausomame kalbančiojo atpažinime. Darbo metu sukurta nuo ištarto teksto nepriklausanti kalbančiojo atpažinimo sistema. Kalbėtojų modelių kūrimui ir požymių palyginimui buvo panaudoti Gauso mišinių modeliai. Pasiūlytas automatinis vokalizuotų garsų išrinkimo (segmentavimo) metodas. Šis metodas yra greitai veikiantis ir nereikalaujantis iš vartotojo jokių papildomų veiksmų, tokių kaip kalbos signalo ir triukšmo pavyzdžių nurodymas. Pasiūlyta požymių vektorių sistema, susidedanti iš žadinimo signalo bei balso trakto parametrų. Kaip žadinimo signalo parametras, panaudotas žadinimo signalo pagrindinis dažnis, kaip balso trakto parametrai, panaudotos keturios formantės bei trys antiformantės. Siekiant suvienodinti žemesnių bei aukštesnių formančių ir antiformančių dispersijas, jas pasiūlėme skaičiuoti melų skalėje. Rezultatų palyginimui sistemoje buvo realizuoti standartiniai požymiai, naudojami kalbos bei asmens atpažinime – melų skalės kepstro koeficientai (MSKK). Atlikti kalbančiojo atpažinimo eksperimentai parodė, kad panaudojus pasiūlytą požymių sistemą buvo gauti geresni atpažinimo rezultatai, nei panaudojus standartinius požymius (MSKK). Gautas lygių klaidų lygis, panaudojant pasiūlytą požymių... [toliau žr. visą tekstą]