Objektų klasterizavimas – tai viena iš duomenų gavybos (angl. data mining) sričių. Šių algoritmų pagrindinis privalumas – gebėjimas atpažinti grupavimo struktūrą be jokios išankstinės informacijos. Magistriniame darbe yra pristatomas vaizdų klasterizavimo algoritmas, naudojantis savaime susitvarkančius neuroninius tinklus (angl. Self-Organizing Map). Darbe analizuojami vaizdų apdorojimo, ypatingųjų taškų radimo bei palyginimo metodai. Nustatyta, kad SIFT (angl. Scale Invariant Feature Transform) ypatingųjų taškų radimas bei aprašymas veikia patikimiausiai, todėl būtent SIFT taškiniai požymiai yra naudojami klasterizavime. Darbe taip pat analizuojamas atstumo tarp paveikslėlių radimo algoritmas, tiriami skirtingi jo parametrai. Algoritmų palyginimui yra naudojamos ROC (angl. Receiver Operating Characteristic) kreivės ir EER (angl. Equal Error Rate) rodiklis. Vaizdų klasterizavimui yra naudojamas ESOM (Emergent Self-Organizing Map) neuroninis tinklas, jis vizualizuojamas U-Matrix (angl. Unified distance Matrix) pagalba ir tinklo neuronai skirstomi į klasterius vandenskyros algoritmu su skirtingu aukščio parinkimu. Magistriniame darbe demonstruojami klasterizavimo rezultatai su pavyzdinėmis paveikslėlių duomenų bazėmis bei realiais gyvenimiškais vaizdais. / Clustering algorithms – a field of data mining – aims at finding a grouping structure in the input data without any a-priori information. The master thesis is dedicated for image processing and clustering algorithms. There are point-feature detection, description and comparison methods analyzed in this paper. The SIFT (Scale Invariant Feature Transform) by D. Lowe has been shown to behave better than the other ones; hence it has been used for image to image distance calculation and undirectly in clustering phase. Finding distances between images is not a trivial task and it also has been analysed in this thesis. Several methods have been compared using ROC (Receiver Operating Curve) and EER measurements. Image clustering process is described as: (1) training of ESOM (Emergent Self-Organizing Map), (2) its visualization in U-Matrix, (3) neuron clustering using waterflood algorithm, and (4) image grouping according to their best-matching unit neurons. The paper demonstrates the image clustering algorithm on public object image databases and real life images from the Internet as well.

Darbe yra vertinami stochastinio genetinio modelio ir CKLS lygties parametrai pasinaudojant sprendinio stacionariuoju tankiu. Atlikti skaičiavimai parodo, kad SDL parametrai yra ,,gerai" įvertinami, esant pakankamai dideliam stebėjimų skaičiui, pvz.: N = 10 000. Skaičiavimams atlikti sukurta kompiuterinė programa. / In this work estimation of parameters of stochastic genetic model and CKLS equation using process stationary density is presented. The research shows that SDE parameters are estimated "well" when we have large number of observations, e.g. N = 10 000. Application is created to carry out calculations.

Šiame darbe, remiantis radialiniu medžių vaizdavimu, Maple programos aplinkoje buvo realizuotas algoritmas, skirtas numeruotųjų medžių vizualizacijai plokštumoje. Po to, atsitiktinai generuojant tūkstančius įvairios eilės medžių, empiriškai nustatyta, jog ne visais atvejais tenkinami estetiniai reikalavimai. Iškilusi problema spręsta įvedant papildomus parametrus, suteikiančius medžiui lankstumo, ilgiausius takus vaizduojant vienoje iš koncentrinių elipsių, medį „užtempiant“ ant erdvinių spiralinių paviršių. Taigi mes apibendrinome radialino medžių vaizdavimo algoritmą; pasiūlėme medžio centro paieškos metodą taikyti ilgiausių takų radimui; sukūrėme iki šiol neaprašytą laurų vainiko algoritmą, skirtą vaizduoti įvairiems medžiams plokštumoje; patogumo dėlei pritaikėme Priuferio sugalvotą kodą medžiams generuoti bei išvesti apibrėžto medžio Priuferio kodą; modifikuodami radialinį medžių vizualizacijos algoritmą pavaizdavome medžius koncentrinių elipsoidų sistemoje. Darbe pasiūlyta originali idėja vizualizuoti paiešką į plotį ir į gylį įterpiant papildomas procedūras, tam tikruose algoritmo realizacijos etapuose vaizduojančias grafus bei keičiančias jų briaunų ir viršūnių spalvas. / In this paper, referring to radial tree drawing, through the medium of Maple program, an algorithm has been realized. It was meant to carry out the visualization of rooted trees on a plane. After that, randomly generating thousands of trees of a different order, it has been empirically identified that aesthetic requirements are not suitable in all cases. The arisen problem has been tackled by introducing additional parameters: they have added flexibility to trees, the longest paths representing in one of the concentric ellipsis, pulling the tree on dimensional spiral surfaces. So we have summarized the algorithm of radial tree drawing, we have suggested to apply the method of finding the tree centre in identifying the longest trails. We have created a not described yet method of the algorithm of the laurel wreath, which is meant for portraying various trees on a plane. For ease of application we have also adjusted the code introduced by Prüfer: it is meant for generating trees and for deducing Prüfer‘s code of a determined tree. By modifying the algorithm of radial tree drawing, we have pictured the trees in a system of concentric ellipsoids. The paper suggests an original idea to visualize the breadth first search and the depth first search by inserting additional procedures, showing graphs and changing the colors of their edges and summits at certain stages of the realization of the algorithm.

Neural networks are one of the most efficient classifier methods. One of such classifying neural networks we are trying to teach in this work by using genetic algorithms. In this work we test two types of genetic algorithms. One may be called parameterized genetic algorithm. It is built on the basic ideas of genetic algorithms. The other one is called parameter less genetic algorithm. It was presented by F. G. Lobo and D. E. Goldberg. Both genetic algorithms are tested and compared to the other well known optimization methods such as Bayes and Monte Carlo search. Experiments show the relevance of use genetic algorithms in teaching classifying neural network. Also stated that parameter less genetic algorithm works more efficient than parametric genetic algorithm in general cases. Created programs will be used in future studies.

In the context of adaptive intellectual learning environment (VLE) possibility of using conceptual clustering algorithms is analyzed, trying to accomplish the ability of software agent to "feel" the changing environment and recognise the states it is in. Agent environment is understood as interface between the user of VLE and the students model, which is stored in the VLE and is constantly changing. Agents ability to "feel" is understood as agents ability to classify students, based on their knowledge level, which changes in the learning process. Using conceptual clustering algorithms found in the literature, we are trying to choose one which is most suited for the problem area, modifying it to model real data.

In this work, the Traveling Salesman Problem (TSP) is discussed. The Hybrid Genetic Algorithm for solving the TSP is presented. The traveling salesman problem is formulated as follows: given matrix D=(dij)nxn of distances between n objects and the set P of permutations of the integers from 1 to n, find a permutation p=(p(1), p(2), ..., p(n)) P that minimizes. Many heuristic algorithms can be applied for the TSP. Recently, genetic algorithms (GAs) are among the advanced heuristic techniques for the combinatorial problems, like the TSP. genetic algorithms are based on the biological process of natural selection. The original concepts of GAs were developed in 1970s. Many simulations have demonstrated the efficiency of GAs on different optimization problems, among them, bin–packing, generalized assignment problem, graph partitioning, job–shop scheduling problem, set covering problem, vehicle routing. One of the main operators in GAs is the crossover (i.e. solution recombination). This operator plays a very important role by constructing competitive GAs. In this work, we investigate several crossover operators for the TSP, among them, CX (cycle crossover), PMX (partialy mapped crossover), POS (position based crossover), ER (edge recombination crossover), edge-NN (edge recombination crossover, nearest neighbour) and AP (alternating-positions crossover). Comparison of these crossover operators was performed. The results show high efficiency of the edge-NN, ER and PMX crossovers.

This Master thesis presents a study of computer equipment support services providing company’s business processes, specifics of the ongoing communication between end-users and supporting engineers-consultants and presents review of some information systems designed to automate certain technical support activities. Core aim of this study is to alleviate the daily work of above mentioned consultants when supporting end-users to locate and resolve issues in owned computer equipment. This paper outlines requirements set for software which could be capable to support business processes of a company operating in a computer equipment maintenance industry, describes specially designed technical support system’s architecture as well as its programming and testing results. The presented prototype of an information system might be treated as new step in computer equipment support services enhancement. This prototype might serve as a core for knowledge management system development; it is suitable for use in businesses which are other than the IT equipment support business.

This paper investigates three methods of one variable function optimizing methods, executes the comparison of their efficiency and generalizes the results of this research. At first there is a review of historical aspects of optimization theory, definition of optimization concept, introduction to task formulation. Presentation of optimization importance, the role of objective function in the process of optimization. Introduction to the classification of optimization tasks and optimization of various systems. In this paper there is an analysis of three methods of optimization: “Half distribution”, “Golden cut”, “Powell”. There was created a program for calculating and comparing of the selected optimization methods. During the investigation it was determined that when there is a small precision (0,1; 0,01), the change of minimum of the function and the value of that point are great. When you increase the value of precision the change of minimum of the function and the value of that point are very small. When the precision value is about (0,0001 .. 0,000001) there is a difference in only 6-th – 9-th value after the comma. The use of “Powell” method requires least steps of calculating, the use of “Half distribution” method requires mostly steps of calculating. In about 80 % of calculation the shortest interval of the search was using the “Powell” method of optimizing, in 20 % of calculation the shortest interval of the search was using the “Golden cut” method of optimization... [to full text]

Savo magistriniame darbe nagrinėju vienos draudimo kompanijos KASKO sistemos funkcionavimą. Visų pirma sukonstruoju KASKO draudimo sistemos matematinį modelį. Tuomet atlieku išsamias analizes polisų sutartims, draudiminiams įvykiams, įmokoms ir išmokoms, bei jų kitimo dinamikai. Apskaičiuoju 2006 m. kiekvieno mėnesio pelno pasikliovimo intervalus ir padarau prognozę 2007 metams. Galiausiai patikrinu draudimo kompanijos padalinių ir filialų darbo efektyvumą. / My work analyses CASCO insurance system’s behavior of one insurance company. At first I made a mathematical model of CASCO insurance. Then I properly described analyses of policies’ contracts, insurance events, insurance premiums and payouts. Later I estimated approximate confidence intervals of profit and made a forecast for 2007 year. And finally I analysed the work efficiency of subdivisions and branches. The mathematical model of CASCO insurance system let us to do various experiments in mathematical space when we analyses incomes of insurance company.

Baigiamajame darbe nagrinėjami nekilnojamojo turto kadastro žemėlapio žemės sklypų ribų topologiniai nesutapimai, atsirandantys dėl riboženklių koordinačių netikslumų. Nagrinėjama bendras ribas turinčių 5 žemės sklypų grupė, kurios ribos nustatytos kadastrinių matavimu metu, valstybinėje koordinačių sistemoje. Matavimais gautos tų pačių riboženklių koordinačių reikšmės nesutapma dydžiu, kuris yra ne didesnis kaip teisės aktais reglamentuojamas leistinas riboženklių nesutapimas. Nesutapimams panaikinti atliekamas žemės sklypų koordinčių optimizavimas genetinio algoritmo metodu. Optimizavimo uždavinui suformuluoti pasirinkta optimizavimo sąlygą ir ribojimų sistema, paremti teisės aktų reikalavimais. Atliekamas nesutampančių koordinačių optimizavimas, rezultatai analizuojami pagal žemės sklypų plotų pokyčius. Darbe pateikiami tyrimo rezultatai ir išvados. Darbą sudaro: įvadas, keturi skyriai, išvados, literatūros sąrašas. Darbo apimtis - 82 p. Teksto be priedų, 25 iliustr., 33 lent., 25 bibliografiniai šaltiniai. Atskirai pridedami darbo priedai. / In the final work of Master’s degree are analysed topological misalignments between Real Estate Cadastral Map parcel boundaries, that occures due to imprecision of landmark coordinates. The investigation involves a group of 5 parcels with common boundaries, whose cadastral measurements were carried out in the national system of geodetic coordinates. Measured same landmark coordinates, satisfies the required juridical difference between the coordinates of common boundary marks. In order to liquidate misalignments of parcel boundaries, genetic algorithm optimization method of land coordinates is performed. On purpose to develop optimization task, the optimization condition and limitation system were chosen, according to the juridical requirements. The optimization of misaligned coordinates is performed, results of this investigation are analysed by differences of parcel area. Structure: introduction, four sections, conclusions, references. Final work consist of 82 p. text without extras, 25 pictures, 33 tables, 25 bibliographical entries. Appendixes included.