Thesis (MComm)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The main topics of study in this thesis are the Principal Component Analysis (PCA) and Canonical Variate Analysis (CVA) biplots, with the primary focus falling on the quality measures associated with these biplots. A detailed study of different routes along which PCA and CVA can be derived precedes the study of the PCA biplot and CVA biplot respectively. Different perspectives on PCA and CVA highlight different aspects of the theory that underlie PCA and CVA biplots respectively and so contribute to a more solid understanding of these biplots and their interpretation. PCA is studied via the routes followed by Pearson (1901) and Hotelling (1933). CVA is studied from the perspectives of Linear Discriminant Analysis, Canonical Correlation Analysis as well as a two-step approach introduced in Gower et al. (2011). The close relationship between CVA and Multivariate Analysis of Variance (MANOVA) also receives some attention. An explanation of the construction of the PCA biplot is provided subsequent to the study of PCA. Thereafter follows an in depth investigation of quality measures of the PCA biplot as well as the relationships between these quality measures. Specific attention is given to the effect of standardisation on the PCA biplot and its quality measures. Following the study of CVA is an explanation of the construction of the weighted CVA biplot as well as two different unweighted CVA biplots based on the two-step approach to CVA. Specific attention is given to the effect of accounting for group sizes in the construction of the CVA biplot on the representation of the group structure underlying a data set. It was found that larger groups tend to be better separated from other groups in the weighted CVA biplot than in the corresponding unweighted CVA biplots. Similarly it was found that smaller groups tend to be separated to a greater extent from other groups in the unweighted CVA biplots than in the corresponding weighted CVA biplot. A detailed investigation of previously defined quality measures of the CVA biplot follows the study of the CVA biplot. It was found that the accuracy with which the group centroids of larger groups are approximated in the weighted CVA biplot is usually higher than that in the corresponding unweighted CVA biplots. Three new quality measures that assess that accuracy of the Pythagorean distances in the CVA biplot are also defined. These quality measures assess the accuracy of the Pythagorean distances between the group centroids, the Pythagorean distances between the individual samples and the Pythagorean distances between the individual samples and group centroids in the CVA biplot respectively. / AFRIKAANSE OPSOMMING: Die hoofonderwerpe van studie in hierdie tesis is die Hoofkomponent Analise (HKA) bistipping asook die Kanoniese Veranderlike Analise (KVA) bistipping met die primêre fokus op die kwaliteitsmaatstawwe wat daarmee geassosieer word. ’n Gedetailleerde studie van verskillende roetes waarlangs HKA en KVA afgelei kan word, gaan die studie van die HKA en KVA bistippings respektiewelik vooraf. Verskillende perspektiewe op HKA en KVA belig verskillende aspekte van die teorie wat onderliggend is tot die HKA en KVA bistippings respektiewelik en dra sodoende by tot ’n meer breedvoerige begrip van hierdie bistippings en hulle interpretasies. HKA word bestudeer volgens die roetes wat gevolg is deur Pearson (1901) en Hotelling (1933). KVA word bestudeer vanuit die perspektiewe van Linieêre Diskriminantanalise, Kanoniese Korrelasie-analise sowel as ’n twee-stap-benadering soos voorgestel in Gower et al. (2011). Die noue verwantskap tussen KVA en Meerveranderlike Analise van Variansie (MANOVA) kry ook aandag. ’n Verduideliking van die konstruksie van die HKA bistipping word voorsien na afloop van die studie van HKA. Daarna volg ’n indiepte-ondersoek van die HKA bistipping kwaliteitsmaatstawwe sowel as die onderlinge verhoudings tussen hierdie kwaliteitsmaatstawe. Spesifieke aandag word gegee aan die effek van die standaardisasie op die HKA bistipping en sy kwaliteitsmaatstawe. Opvolgend op die studie van KVA is ’n verduideliking van die konstruksie van die geweegde KVA bistipping sowel as twee veskillende ongeweegde KVA bistippings gebaseer op die twee-stap-benadering tot KVA. Spesifieke aandag word gegee aan die effek wat die inagneming van die groepsgroottes in die konstruksie van die KVA bistipping op die voorstelling van die groepstruktuur onderliggend aan ’n datastel het. Daar is gevind dat groter groepe beter geskei is van ander groepe in die geweegde KVA bistipping as in die oorstemmende ongeweegde KVA bistipping. Soortgelyk daaraan is gevind dat kleiner groepe tot ’n groter mate geskei is van ander groepe in die ongeweegde KVA bistipping as in die oorstemmende geweegde KVA bistipping. ’n Gedetailleerde ondersoek van voorheen gedefinieerde kwaliteitsmaatstawe van die KVA bistipping volg op die studie van die KVA bistipping. Daar is gevind dat die akkuraatheid waarmee die groepsgemiddeldes van groter groepe benader word in die geweegde KVA bistipping, gewoonlik hoër is as in die ooreenstemmende ongeweegde KVA bistippings. Drie nuwe kwaliteitsmaatstawe wat die akkuraatheid van die Pythagoras-afstande in die KVA bistipping meet, word gedefinieer. Hierdie kwaliteitsmaatstawe beskryf onderskeidelik die akkuraatheid van die voorstelling van die Pythagoras-afstande tussen die groepsgemiddeldes, die Pythagoras-afstande tussen die individuele observasies en die Pythagoras-afstande tussen die individuele observasies en groepsgemiddeldes in die KVA bistipping.

Στο πλαίσιο της εργασίας αυτής πραγματοποιείται ανάλυση και εφαρμογή του διαχωρισμού ακουστικών σημάτων, τα οποία έχουν ληφθεί από το ανθρώπινο σώμα, όταν αυτό βρίσκεται σε κατάσταση ύπνου. Τα σήματα αυτά έχουν ληφθεί με τη βοήθεια μιας συσκευής πιεζοκρυστάλλων και ο διαχωρισμός τους επιτυγχάνεται με τη μέθοδο Ανάλυσης Ανεξάρτητων Συνιστωσών (ICA). Κύριος σκοπός όλων των παραπάνω είναι να χρησιμοποιηθεί η εν λόγω μεθοδολογία στη διάγνωση της αποφρακτικής άπνοιας (OSA). Στο πρώτο κεφάλαιο, παρουσιάζεται αναλυτικά η μέθοδος ICA και το μαθηματικό μοντέλο που την περιγράφει, όπως επίσης και όλα τα βήματα προεπεξεργασίας της. Στη συνέχεια αναλύεται διεξοδικά η λειτουργία του αλγορίθμου FastICA και οι ιδιότητες του, με τον οποίο υλοποιείται το πειραματικό μέρος της εργασίας αυτής. Στο δεύτερο κεφάλαιο, μελετάται η ασθένεια της αποφρακτικής άπνοιας (OSA), οι παράγοντες και η παθολογία της καθώς και το κύριο διαγνωστικό σύμπτωμα της: το ροχαλητό. Ύστερα, πραγματεύεται την διάγνωση και τους γνωστότερους τρόπους θεραπείας αυτής της νόσου και τελικά τη μέθοδο του Snoring Detection. Στο τρίτο κεφάλαιο γίνεται μια εισαγωγή στον πιεζοηλεκτρισμό, και μία μελέτη του πιεζοηλεκτρικού φαινομένου και του μαθηματικού του μοντέλου. Ακολουθεί αναφορά των ειδών πιεζοηλεκτρικών αισθητήρων με τους οποίους λαμβάνονται τα σήματα που εξετάζονται σε αυτή την εργασία. Στο επόμενο κεφάλαιο γίνεται μία σύνδεση των δεδομένων θεωρίας που αναφέρονται στα προηγούμενα κεφάλαια και μία εισαγωγή στην πειραματική μέθοδο. Στο κεφάλαιο πέντε παρατίθενται κάποια παραδείγματα εφαρμογής του αλγορίθμου FastICA με τυχαία σήματα, τα οποία έχουν σκοπό να δοκιμάσουν την απόδοση του. Στο κεφάλαιο έξι, 5 γίνεται η πειραματική διαδικασία όπου τώρα τα σήματα που διαχωρίζονται με τον αλγόριθμο FastICA προέρχονται από το ανθρώπινο σώμα. Η υλοποίηση της γίνεται σε Matlab. Έτσι, γίνεται εξαγωγή του ζητούμενου σήματος ροχαλητού και αναγράφονται κάποια συμπεράσματα για την απόδοση του αλγορίθμου. Στο τέλος της εργασίας παρατίθενται σε ένα παράρτημα όλοι οι κώδικες της MATLAB που χρησιμοποιήθηκαν για την ολοκλήρωση του πειραματικού της μέρους στα κεφάλαια πέντε και έξι. / In this particular thesis, analysis and application of separation of acoustic signals is carried out. These signals have been taken from the human body in a sleeping state. They are obtained by means of a piezocrystallic device and their separation is achieved by the method of Independent Component Analysis (ICA). The main purpose of all this is to use this methodology in order to diagnose the Obstructive Sleep Apnea (OSA). The first chapter presents the method of ICA and the mathematical model that describes it as well as all the pre-processing steps. Then it analyses, in detail, the algorithm FastICA, which is used in the experimental part of this thesis and its properties. The second chapter studies the disease of obstructive sleep apnea (OSA), its factors and its pathology and the major diagnostic symptom: snoring. Then, it discusses the diagnosis and the best known ways of treating this disease and eventually the method of Snoring Detection. The third chapter is an introduction to piezoelectricity and a study of the piezoelectric effect and its mathematical description. This is followed by a reference to the types of piezoelectric sensors which are used to obtain the signals used in this paper. In chapter five we have listed some examplesapplications of the FastICA algorithm with random signals, which are designed to test the performance. Section six is where the experimental procedure takes place. The signals derived from the human body are separated by the algorithm FastICA and the implementation is done in Matlab. In addition, some conclusions regarding the performance of the algorithm. At the end of this paper, all the MATLAB codes used for the completion of the experimental part of the chapters five and six are listed in an Annex.

由於金融事件層出不窮，控管風險已成為銀行、證券、保險各種金融產業的重要課題。其中Value-at-Risk(VaR)模型為銀行與證券業最常用來衡量其市場風險的模型。VaR模型中的蒙地卡羅模擬法是將投資組合持有部位以適當的市場風險因子來表示，接著產生市場風險因子的各種情境，再結合評價公式以求得投資組合在某一段持有期間內、某一信心水準之下的最低價值，再將最低價值減去原來之價值，便為可能的最大損失(Jorion, 2007)。 / 使用蒙地卡羅模擬法產生市場風險因子的各種情境，必須先估計市場風險因子的共變異數矩陣，再藉此模擬出數千種市場風險因子情境。本研究便是將蒙地卡羅模擬法加入隨著時間改變之共變異數矩陣(time-varying covariance matrix)的概念並減少市場風險因子個數，利用蒙地卡羅模擬法配合Constant模型、UWMA模型、EWMA模型、Orthogonal EWMA模型、Orthogonal GARCH模型、PCA EWMA模型、PCA GARCH模型來產生市場風險因子未來的情境並比較各方法對長天期與短天期風險衡量之優劣。結果顯示PCA EWMA模型的效果最好，因此建議各大金融機構可採用PCA EWMA模型來控管其投資組合短天期與長天期的市場風險。

摘要 近幾年發展的區間型態資料之主成份分析，運用在某些領域的資料上尚未成熟，例如股票價格的資料，這些資料是與時間息息相關地，於是有了時間相關的區間資料分析 (Irpino, 2006. Pattern Recognition Letters 27, 504-513)。本文延續這個分析，針對時間相關之區間型台灣股價資料進行研究。Irpino (2006) 的方法只考慮每週的開盤價與收盤價，為了得到更多資訊，我們提出三種方法，第一個方法，將每週的最高價(最低價)納入分析，由兩點的分析變成三點的分析；第二個方法，我們同時考慮最高價與最低價，變成四點的分析，這兩個方法都能得到原始方法不能得到的資訊－公司的穩定度，其中又以第二個方法較為準確；第三種方法引用Irpino (2006) 的建議，我們改變區間的分配，而此方法得到的結果與原 始的方法差異不大。 本文分別收集了台灣金融市場三十家半導體與台指五十中的四十七家公司於民國九十七年九月一號到十二月二十六號共十七週的股價資料進行實證分析。以台指五十為例，分析結果顯示編號17的台達電子工業股份有限公司、編號24的鴻海科技集團，這兩家公司的未來被看好；而編號10的聯陽半導體股份有限公司、編號35的統一超商股份有限公司，此兩家公司的未來不被看好，這四家公司在民國九十八年一月五號到一月七號三天的走勢確實是如此！此外，結果顯示 金融體系的公司比電子體系的公司來得穩定。 關鍵字：主成份分析，區間型資料，時間相關 / ABSTRACT The methods for principal component analysis on interval data have not been ripe yet in some areas, for example, the data of stock prices that are closely related to the time, so the analysis of time dependent interval data was proposed (Irpino, 2006. Pattern Recognition Letters 27, 504-513). In this paper, we apply this approach to the stock prices data in Taiwan. The original “Spaghetti” PCA in Irpino (2006) considered only the starting and the ending prices for each week. In order to get more information we propose three methods. We consider the highest (lowest) price for each week to our analysis in Method 1, and the analysis changes from two points to three points. In Method 2, we consider all information to our analysis which considers four points. These two methods can get more information than the original one. For example, we can get the information of stability degree of the company. For the Method 3, we quote the suggestion from Irpino (2006) to change the distribution of intervals from uniform to beta. However, the result is similar to the original result. In our approach, we collect data of stock prices from 37 companies of semiconductor and 47 companies of TSEC Taiwan 50 index in Taiwan financial market during the 17 weeks from September 1 to December 26, 2008. For TSEC Taiwan 50 index, the results of this analysis are that the future trend of Delta (Delta Electronics Incorporation) which numbers 17 and Foxconn (Foxconn Electronics Incorporation) which numbers 24 are optimistic; And ITE (Integrated Technology Express) which numbers 10 and 7-ELEVEn (President Chain Store Corporation) which numbers 35 are not good. In fact, the trends of these four companies are indicated these results during January 5th to 7th. What’s more, the financial companies are steadier than the electronic industry. Keywords: Principal component analysis; Interval data; Time dependent

Baigiamajame magistro darbe yra nagrinėjamas bekontaktis pulso matavimo metodas. Darbo tikslams pasiekti naudota Logitech C310 internetinė vaizdo kamera. Įrašomo vaizdo dydis yra 640X480 pikselių. Filmavimo sparta – 15 kadrų per sekundę. Vaizdo įrašo ilgis – 30 sekundžių. Tiriamieji buvo filmuojami apie 0,5 m atstumu nuo kameros. Tiriamųjų amžius nuo 24 iki 64 metų. Vaizdas buvo įrašomas, esant įvairiam apšvietimui: tiek dienos metu, tiek šviečiant skirtingo galingumo lempoms. Rezultatams palyginti buvo naudojamas ant riešo uždedamas pulso matavimo prietaisas ReliOn, kurio veikimas pagrįstas kraujagyslėse pulsuojančio kraujo spaudimo kitimu. Išgautam pulso signalui apdoroti, palyginimui buvo panaudoti du nepriklausomų komponenčių analizės algoritmai: Fast ICA bei stSobi. Eksperimentams atlikti buvo naudojama C# programavimo kalba ir Matlab 2008 matematinis skaičiavimo paketas. / The thesis analyses the non-contact cardiac pulse measurement method. To achieve work main goals Logitech C310 web camera was used. Video resolution was 640X480 pixels. Video capture speed was 15 frames per second. Video length was 30 seconds. Distance from web camera to human face was ~ 0,5 m. Participant age varied from 24 to 64 years old. Video was captured with different light sources: sun, lamps with different power. For results comparison ReliOn handy pulse measurement device was used. Pulse signal was filtered using two independent component analysis algorithms: Fast ICA and stSobi. Experiments have been made using C# programming language and Matlab 2008 mathematical package.

Financial ratios are key units of analysis in most quantitative financial research including bankruptcy prediction, performance and efficiency analysis, mergers and acquisitions, and credit ratings, amongst others. Since hundreds of ratios can be computed using available financial data and given the substantial overlap in information provided by many of these ratios, choosing amongst ratios has been a significant issue facing practitioners and researchers. An important contribution of the present thesis is to show that ratios can be arranged into groups where each group describes a separate financial aspect or dimension of a given firm or industry. Then by choosing representative ratios from each group, a small, yet comprehensive, set of ratios can be identified and used for further analysis. Whilst a substantial part of the financial ratio literature has focused on classifying financial ratios empirically and on assessing the stability of the ratio groups over different periods and industries, relatively little attention has been paid to the classifying of financial ratios of the banking sector. This study aims to explore the classification patterns of 56 financial ratios for banks of different type, size and age. Using data from the Uniform Bank Performance Report (UBPR), large samples of commercial, savings, and De Novo (newlychartered) commercial banks were obtained for the period between 2001 and 2005, inclusive. Principal Component Analysis (PCA) was performed on a yearly basis to classify the banks' ratios after applying the inverse sinh transformation to enhance the distributional properties of the data. The number of patterns were decided using Parallel Analysis. The study also uses various methods including visual comparison, correlation, congruency, and transformation analysis to assess the time series stability and cross-sectional similarity of the identified ratio patterns. The study identifies 13 or 14 ratio patterns for commercial banks and 10 or 11 ratio patterns for savings banks over the period on which the study is based. These patterns are generally stable over time; yet, some dissimilarity was found between the ratio patterns for the two types of banks – that is, the commercial and savings banks. A certain degree of dissimilarity was also found between the financial patterns for commercial banks belonging to different asset-size classes. Furthermore, four ratio patterns were consistently identified for the De Novo commercial banks in the first year of their operations. However, no evidence of convergence was found between the ratio patterns of the De Novo commercial banks and the ratio patterns of the incumbent (that is, long established) commercial banks. The findings of this study bring useful insights particularly to researchers who employ bank financial ratios in empirical analysis. Methodologically, this research pioneers the application of the inverse sinh transformation and parallel analysis in the area of the ratio classification literature. Also, it contributes to the use of transformation analysis as a factor comparison technique by deriving a significance test for the outputs of this analysis. Moreover, this is the only large scale study to be conducted on the classification patterns of bank financial ratios.

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) is a powerful technique for the analysis of organic surfaces and interfaces for many innovative technologies. However, despite recent developments, there are still many issues and challenges hindering the robust, validated use of ToF-SIMS for quantitative measurement. These include: the lack of metrology and fundamental understanding for the use of novel cluster primary ion beams such as C60ⁿ⁺ and Ar₂₀₀₀⁺; the need for validated and robust measurement protocols for difficult samples, such as those with significant micron scale surface topography; the lack of guidance on novel data analysis methods including multivariate analysis which have the potential to simplify many time-consuming and intensive analyses in industry; and the need to establish best practice to improve the accuracy of measurements. This thesis describes research undertaken to address the above challenges. Sample topography and field effects were evaluated experimentally using model conducting and insulating fibres and compared with computer simulations to provide recommendation to diagnose and reduce the effects. Two popular multivariate methods, principal component analysis (PCA) and multivariate curve resolution (MCR), were explored using mixed organic systems consisting of a simple polymer blend and complex hair fibres treated with a multi-component formulation to evaluate different multivariate and data preprocessing methods for the optimal identification, localisation and quantification of the chemical components. Finally, cluster ion beams C60ⁿ⁺ and Ar_500-2500⁺ were evaluated on an inorganic surface and an organic delta layer reference material respectively to elucidate the fundamental metrology of cluster ion sputtering and pave the way for their use in organic depth profiling. These studies provide the essential metrological foundation to address frontier issues in surface and nanoanalysis and extend the measurement capabilities of ToF-SIMS.

Approved for public release, distribution is unlimited / This study continues a previous face recognition investigation using uncooled infrared technology. The database developed in an earlier study is further expanded to include 50 volunteers with 30 facial images from each subject. The automatic image reduction method reduces the pixel size of each image from 160 120 to 60 45 . The study reexamines two linear classification methods: the Principal Component Analysis (PCA) and Fisher Linear Discriminant Analysis (LDA). Both PCA and LDA apply eigenvectors and eigenvalues concepts. In addition, the Singular Value Decomposition based Snapshot method is applied to decrease the computational load. The K-fold Cross Validation is applied to estimate classification performances. Results indicate that the best PCA-based method (using all eigenvectors) produces an average classification performance equal to 79.22%. Incorporated with PCA for dimension reduction, the LDA-based method achieves 94.58% accuracy in average classification performance. Additional testing on unfocused images produces no significant impact on the overall classification performance. Overall results again confirm uncooled IR imaging can be used to identify individual subjects in a constrained indoor environment. / Lieutenant, United States Navy

No description available.

Nous nous intéresserons dans cette thèse à l'étude et la caractérisation des Textures Dynamiques (TDs), avec comme application visée l'indexation dans de grandes bases de vidéos. Ce thème de recherche étant émergent, nous proposons une définition des TDs, une taxonomie de celles-ci, ainsi qu'un état de l'art. La classe de TD la plus représentative est décrite par un modèle formel qui considère les TDs comme la superposition d'ondes porteuses et de phénomènes locaux. La construction d'outils d'analyse spatio-temporelle adaptés aux TDs est notre principale contribution. D'une part, nous montrons que la transformée en curvelets 2D+T est pertinente pour la représentation de l'onde porteuse. D'autre part, dans un objectif de décomposition des séquences vidéos, nous proposons d'utiliser l'approche par Analyse en Composantes Morphologiques. Notre contribution consiste en l'apport et l'étude de nouvelles stratégies de seuillage. Ces méthodes sont testées sur plusieurs applications: segmentation spatio-temporelle, décomposition de TDs, estimation du mouvement global d'une TD, ... Nous avons de plus montré que l'Analyse en Composantes Morphologiques et les approches multi-échelles donnent des résultats significatifs pour la recherche par le contenu et l'indexation de Textures Dynamiques de la base de données DynTex. Cette thèse constitue ainsi un premier pas vers l'indexation automatique de textures dynamiques dans des séquences d'images, et ouvre la voie à de nombreux développements sur ce sujet nouveau. Enfin, le caractère générique des approches proposées permet d'envisager leurs applications dans un cadre plus large mettant en jeu par exemple des données 3D. / This report is focused on the study and the characterization of Dynamic Textures (DTs), with the aim of video indexing in large databases. This research topic being new and emerging, we propose a taxonomy, a definition of DTs and a state of the art. The most representative DT class is described by a model that considers DTs as the superposition of several wavefronts and local oscillating phenomena. The design of spatio-temporal analysis tools adapted to DT is our main contribution. We first show that the 2D+T curvelet transform is relevant for representing wavefronts. In order to analyse and better understand the DTs, we propose in a second step to adapt the Morphological Component Analysis approach using new thresholding strategies. These methods are tested on several applications: decomposition of DTs, spatio-temporal segmentation, global motion estimation of a DT, ... We have shown that Morphological Component Analysis and multi-scale approaches enable significant results for content-based retrieval applications and dynamic texture indexing on the DynTex database. This thesis constitutes a first step towards automatic indexing of DTs in image sequences and opens the way for many new developments in this topic. Moreover, the proposed approaches are generic and could be applied in a broader context, for instance the processing of 3D data.