Η ομαδοποίηση ομαδοποιεί τα δεδομένα βασισμένη μόνο σε πληροφορία που βρίσκεται σε αυτά η οποία περιγράφει τα αντικείμενα και τις σχέσεις τους. Ο στόχος είναι τα αντικείμενα που βρίσκονται σε μια ομάδα να είναι όμοια(ή σχετικά) μεταξύ τους και διαφορετικά απο τα αντικείμενα των άλλων ομάδων. Όσο μεγαλύτερη είναι η ομοιότητα(ή η ομοιογένεια) σε μια ομάδα και όσο μεγαλύτερη είναι η διαφορετικότητα ανάμεσα στις ομάδες τόσο καλύτερη είναι η ομαδοποίηση. Οι μεθόδοι ομαδοποίησης μπορούν να διακριθούν σε τρείς κατηγορίες, ιεραρχικές, διαχωριστικές, και στις βασισμένες στη πυκνότητα. Οι ιεραρχικοί αλγόριθμοι μας δίνουν ιεραρχίες ομάδων σε μία top-down(συγχωνευτική) ή bottom-up(διαχωριστική) μορφή. Η εργασία αυτή επικεντρώνεται στην ιεραρχική διαχωριστική ομαδοποίηση. Ανάμεσα στους ιεραρχικούς διαχωριστικούς αλγορίθμους ξεχωρίζουμε τον αλγόριθμο Principal Direction Divisive Partitioning (PDDP). Ο PDDP χρησιμοποιεί την προβολή των δεδομένων στα κύρια συστατικά της αντίστοιχης μήτρας συνδιασποράς. Αυτό επιτρέπει την εφαρμογή σε δεδομένα υψηλής διάστασης. Στην εργασία αυτή προτείνεται μια βελτίωση του αλγορίθμου \Principal Direction Divisive Partitioning. Ο προτεινόμενος αλγόριθμος συνδυάζει στοιχεία από την εκτίμηση πυκνότητας και τις μεθόδους βασισμένες στην προβολή με έναν γρήγορο και αποδοτικό αλγόριθμο, ικανό να αντιμετωπίσει δεδομένα υψηλής διάστασης. Τα πειραματικά αποτελέσματα δείχνουν βελτιωμένη απόδοση ομαδοποίησης σε σύγκριση με άλλες δημοφιλείς μεθόδους. Επίσης ερευνάται το πρόβλημα του αυτόματου καθορισμού του πλήθους των ομάδων που είναι πολύ σημαντικό την ανάλυση ομάδων. / Cluster analysis groups data objects based only on information found in the data that describes the objects and their relationships. The goal is that the objects within a group be similar (or related) to one another and different from (or unrelated to) the objects in other groups. The greater the similarity (or homogeneity) within a group and the greater the difference between groups, the better or more distinct the clustering. Clustering methods can be broadly divided into three categories, hierarchical, partitioning and density-based (while there are other categorisations). Hierarchical algorithms provide nested hierarchies of clusters in a top-down (agglomerative), or bottom-up (divisive) fashion. This work is focused on the class of hierarchical divisive clustering algorithms. Amongst the class of divisive hierarchical algorithms, the Principal Direction Divisive Partitioning (PDDP) algorithm is of particular value. PDDP uses the projection of the data onto the principal components of the associated data covariance matrix. This allows the application to high dimensional data. In this work an improvement of the algorithm PDDP is proposed. The proposed algorithm merges concepts from density estimation and projection-based methods towards a fast and efficient clustering algorithm, capable of dealing with high dimensional data. Experimental results show improved partitioning performance compared to other popular methods. Moreover, we explore the problem of automatically determining the number of clusters that is central in cluster analysis.

The current surge of interest in search and comparison tasks in natural language processing has brought with it a focus on vector space approaches and vector space dimensionality reduction techniques. Presenting data as points in hyperspace provides opportunities to use a variety of welldeveloped tools pertinent to this representation. Dimensionality reduction allows data to be compressed and generalised. Eigen decomposition and related algorithms are one category of approaches to dimensionality reduction, providing a principled way to reduce data dimensionality that has time and again shown itself capable of enabling access to powerful generalisations in the data. Issues with the approach, however, include computational complexity and limitations on the size of dataset that can reasonably be processed in this way. Large datasets are a persistent feature of natural language processing tasks. This thesis focuses on two main questions. Firstly, in what ways can eigen decomposition and related techniques be extended to larger datasets? Secondly, this having been achieved, of what value is the resulting approach to information retrieval and to statistical language modelling at the ngram level? The applicability of eigen decomposition is shown to be extendable through the use of an extant algorithm; the Generalized Hebbian Algorithm (GHA), and the novel extension of this algorithm to paired data; the Asymmetric Generalized Hebbian Algorithm (AGHA). Several original extensions to the these algorithms are also presented, improving their applicability in various domains. The applicability of GHA to Latent Semantic Analysisstyle tasks is investigated. Finally, AGHA is used to investigate the value of singular value decomposition, an eigen decomposition variant, to ngram language modelling. A sizeable perplexity reduction is demonstrated.

The advent of modern computer technologies provided a powerful tool in numerical simulations. One of the most frequently used method for the discretization of the physical domain is Finite element Method (FEM). One of the main problems in a finite element analysis is the adequacy of the finite element mesh. Since the quality of the finite element solution directly depends on the quality of meshes, the additional process to improve the quality of meshes is necessary for reliable finite element approximation. In order to perform quality-assessed numerical simulation, the adaptive finite element strategies have been developed. These strategies integrate the finite element analysis with error estimation and fully automatic mesh modification, user interaction with this process is limited by initial geometry data and possible error tolerance definition. The finite element solution, obtained during adaptive finite element strategy process, approximates quite good different engineering structures. Despite many works in this area the problem of the adequate finite element mesh is not fully solved and additional developments are needed in order to improve adaptive mesh refinement strategy process. The aim and tasks of the work – to obtain methodology for quality assessed discretization to finite elements for complex geometry engineering structures by adaptive finite element strategies. To realize this purpose the following scientific tasks have been dealt: to develop an automatic... [to full text]

The advent of modern computer technologies provided a powerful tool in numerical simulations. One of the most frequently used method for the discretization of the physical domain is Finite element Method (FEM). One of the main problems in a finite element analysis is the adequacy of the finite element mesh. Since the quality of the finite element solution directly depends on the quality of meshes, the additional process to improve the quality of meshes is necessary for reliable finite element approximation. In order to perform quality-assessed numerical simulation, the adaptive finite element strategies have been developed. These strategies integrate the finite element analysis with error estimation and fully automatic mesh modification, user interaction with this process is limited by initial geometry data and possible error tolerance definition. The finite element solution, obtained during adaptive finite element strategy process, approximates quite good different engineering structures. Despite many works in this area the problem of the adequate finite element mesh is not fully solved and additional developments are needed in order to improve adaptive mesh refinement strategy process. The aim and tasks of the work – to obtain methodology for quality assessed discretization to finite elements for complex geometry engineering structures by adaptive finite element strategies. To realize this purpose the following scientific tasks have been dealt: to develop an automatic... [to full text]

Magistro baigiamajame darbe nagrinėjama antrosios eilės tiesinė nehomogeninė diferencialinė lygtis intervale, kurio kairysis kraštas yra nagrinėjamosios lygties koeficientų ireguliarusis ypatingasis taškas. Ištirta sprendinių asimptotika ypatingojo taško aplinkoje ir išnagrinėti trys šios lygties kraštiniai uždaviniai, kurių formulavimas iš esmės priklauso nuo lygties parametro ženklo. / The present Master thesis analyses the second order linear differential equation in interval which left side coincides with irregular singular point of this equation. The asymptotics of the solutions in the neighbourhood of singular point is investigated and three boundary value problems, statement of which principally depends on equation parameter sign, have been analyzed.

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Šiandieninėje visuomenėje tiek komercinė, tiek socialinė reklama užima svarbią vietą. Komercinė reklama ragina pirkti, įsigyti vienokį ar kitokį daiktą. Socialinė reklama aprėpia opiausias žmonių problemas ir bando parodyti vartotojams tinkamo elgesio normas. Iki šiol bakalauro darbo tema „Liepiamosios nuosakos vartojimas komercinėje ir socialinėje reklamoje“ nėra plačiai nagrinėta. Šiame darbe pabandyta pasižiūrėti į liepiamosios nuosakos funkcijas bei paskirtį reklamose. Palyginta, kokia forma, vienaskaitos ar daugiskaitos, labiau vartojama reklamose. / In today's society, both commercial and social advertising plays an important role. Commercial advertising prompts to buy, to possess some sort of object. Social advertising covers the most acute problems of people and tries to show its consumers the proper norms of behavior. So far, the Bachelor thesis on the use of imperative mood in commercial and social advertising is not widely examined. The thesis attempted to look at the imperative mood functions and purpose in advertising. The comparison was made of what form, singular or plural, is used more in commercials.

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Functionally graded materials processed by the thermal spray techniques such as electron beam physical vapor deposition and plasma spray forming are known to have an orthotropic structure with reduced mechanical properties. Debonding related failures in these types of material systems occur due to embedded cracks that are perpendicular to the direction of the material property gradation. These cracks are inherently under mixed-mode loading and fracture analysis requires the extraction of the modes I and II stress intensity factors. The present study aims at developing semi-analytical techniques to study embedded crack problems in graded orthotropic media under various boundary conditions. The cracks are assumed to be aligned parallel to one of the principal axes of orthotropy. The problems are formulated using the averaged constants of plane orthotropic elasticity and reduced to two coupled integral equations with Cauchy type dominant singularities. The equations are solved numerically by adopting an expansion - collocation technique. The main results of the analyses are the mixed mode stress intensity factors and the energy release rate as functions of the material nonhomogeneity and orthotropy parameters. The effects of the boundary conditions on the mentioned fracture parameters are also duly discussed.