Academic literature on the topic 'Applied Multivariate Analysis'

The present Ph.D. Thesis is focused on applications and developments of chemometrics. After a short introduction about chemometrics (Chapter 1), the present work is divided in three Chapters, reflecting the research activities addressed during the three-year PhD work: • Chapter 2 concerns the application of classification tools to food traceability (Chapter 2.1), plant metabolomics (Chapter 2.2), and food-frauds detection (Chapter 2.3) problems. • Chapter 3 concerns the application of design of experiments for a bio-remediation research (Chapter 3.1) and for machine optimization (Chapter 3.2). • Chapter 4 concerns the development of the net analyte signal (NAS) procedure and its application to several analytical problems. The main aim of this research is to face the matrix-effect problem using a multivariate approach. Chemometrics is the science that extracts useful information from chemical data. The development of instruments and computers is bringing to analytical methodologies ever more sophisticated, and the consequence is that huge amounts of data are collected. In parallel with this rapid evolution, it is, therefore, important to develop chemometric methods able to handle and process the data. Moreover, the attention is also focusing on analytical techniques that do not destroy the analyzed samples. Chemometrics and its application to non-destructive analytical methods are the main topics of this research project. Several analytical techniques have been used during this project: gas-chromatography (GC), bioluminescence, atomic absorption spectroscopy (AAS), liquid chromatography (HPLC), near-infrared spectroscopy, UV-Vis spectroscopy, Raman spectroscopy, X-ray powder diffraction (XRPD), attenuated total reflectance (ATR) spectroscopy. Moreover, this research activity was carried out in collaboration with several external research groups and companies

Thesis (MComm (Mathematics))--Stellenbosch University, 2008.<br>The general purpose of this thesis is the analysis of multivariate refinement equations, with focus on the bivariate case. Since box splines are the main prototype of such equations (just like the cardinal B-splines in the univariate case), we make them our primary subject of discussion throughout. The first two chapters are indeed about the origin and definition of box splines, and try to elaborate on them in sufficient detail so as to build on them in all subsequent chapters, while providing many examples and graphical illustrations to make precise every aspect regarding box splines that will be mentioned. Multivariate refinement equations are ones that take on the form (x) =Xi2Zn pi (Mx − i), (1) where is a real-valued function, called a refinable function, on Rn, p = {pi}i2Zn is a sequence of real numbers, called a refinement mask, and M is an n × n matrix with integer entries, called a dilation matrix. It is important to note that any such equation is thus simultaneously determined by all three of , p and M — and the thesis will try and explain what role each of these plays in a refinement equation. In Chapter 3 we discuss the definition of refinement equations in more detail and elaborate on box splines as our first examples of refinable functions, also showing that one can actually use them to create even more such functions. Also observing from Chapter iii iv 2 that box splines demand yet another parameter from us, namely an initial direction matrix D, we focus on the more general instances of these in Chapter 4, while keeping the dilation matrix M fixed. Chapter 5 then in turn deals with the matrix M and tries to generalize some of the results found in Chapter 3 accordingly, keeping the initial direction matrix fixed. Having dealt with the refinement equation itself, we subsequently focus our attention on the support of a (bivariate) refinable function — that is, the part of the xy-grid on which such a function “lives” — and that of a refinement mask, in Chapter 6, and obtain a few results that are in a sense introductory to our work in the next chapter. Next, we move on to discuss one area in which refinable functions are especially applicable, namely subdivision, which is analyzed in Chapter 7. After giving the basic definitions of subdivision and subdivision convergence, and investigating the “sum rules” in Section 7.1, we prove our main subdivision convergence result in Section 7.2. The chapter is concluded with some examples in Section 7.3. The thesis is concluded, in Chapter 8, with a number of remarks on what has been done and issues that are left for future research.

L’analisi e il monitoraggio di processo sono diventati di fondamentale importanza per garantire le prestazioni del processo e mantenere la qualità del prodotto. A tal scopo, la spettroscopia rappresenta uno strumento innovativo che permette di superare le problematiche che si incontrano con le tecniche analitiche convenzionali (per esempio, la gas cromatografia), poichè è veloce e non distruttiva e può fornire informazioni sullo stato chimico del processo in tempo reale. Tuttavia, a causa della grande quantità di informazioni presenti nelle misure raccolte, l’interpretazione e l’estrazione di informazione non è un compito semplice. A tal proposito, le tecniche multivariate agevolano significativamente il trattamento dei dati e permettono di inferire informazioni sul sistema analizzato. In questa tesi, quattro sistemi sono indagati mediante misure spettroscopiche per mostrare la varietà di problemi che possono sorgere quando si trattano dati complessi e altamente informativi provenienti da differenti tecniche spettroscopiche. Per questo motivo, sono state esplorate differenti tecniche multivariate e sono mostrate le loro potenzialità e limitazioni: (i) si suggeriscono strategie basate sulla Principal Component Analysis e Partial Least Squares Regression per un migliore e più robusto monitoraggio di qualità dei detergenti commerciali liquidi; (ii) la Moving Window Principal Component Analysis è proposta per il monitoraggio di processi che si evolvono come la cristallizzazione di un Ingrediente Farmaceutico Attivo per identificare la nucleazione; (iii) la Time Window Statistical Total Correlation Spectroscopy insieme alla Multivariate Curve Resolution sono proposte per indagare la reazione di formazione di un materiale cementizio; (iv) la Multivariate Curve Resolution è utilizzata per ottenere informazioni sulla dissoluzione nello spazio e nel tempo di una pasta costituita da tensioattivi a partire da dati iperspettrali . Perciò, le tecniche multivariate applicate a dati spettroscopici si dimostrano capaci di raggiungere i seguenti risultati: a) Nel caso di detergenti commerciali, le osservazioni che non rispecchiano le condizioni di riferimento sono classificate correttamente. Inoltre, l’approccio proposto identifica quando la stima della concentrazione dei composti non può essere considerata accurata; b) Riguardo la cristallizzazione dell’ingrediente farmaceutico, la nucleazione è stata individuata in modo accurato; c) Gli spettri e la concentrazione dei composti coinvolti nella reazione di presa di un materiale cementizio sono stati stimati e l’evoluzione temporale del processo può essere seguita; d) La velocità di dissoluzione dei tensioattivi presenti nella pasta è stata valutata. Di conseguenza, i metodi multivariati implementati su misure spettroscopiche si rivelano essenziali per trattare i dati e agevolare la comprensione e il monitoraggio di processo.<br>Process analysis and monitoring has become essential in industry to ensure improvement of the process performances and to maintain a specific product quality. To this aim, spectroscopy represents an innovative tool that allows to overcome the issues encountered with conventional analytical techniques (e.g. gas chromatography), since it is fast and non-destructive and can give information about the chemical state of the process in real time. Nevertheless, due to the huge amount of information present in the collected data, the interpretation and information extraction is not a straightforward task. For this purpose, multivariate techniques significantly aid the treatment of the data and allow to infer information about the system analyzed. In this thesis, four systems are investigated by means of spectroscopy to show the variety of problems that may arise when dealing with complex and highly informative data coming from different spectroscopic techniques. To this aim, different multivariate techniques are explored and their potentialities and limitations are shown: (i) Strategies based on Principal Component Analysis and Partial Least Squares Regression are suggested for an improved and more robust quality monitoring of liquid commercial detergents; (ii) Moving Window Principal Component Analysis is proposed for the monitoring of an evolving process like the crystallization of an Active Pharmaceutical Ingredient in order to detect the nucleation; (iii) Time Window Statistical Total Correlation Spectroscopy combined with Multivariate Curve Resolution are proposed to investigate the setting reaction of a cementing material; (iv) Multivariate Curve Resolution is employed to infer information from hyperspectral data about the dissolution of a surfactants paste. Therefore, multivariate techniques applied to spectroscopic data demonstrate capable of achieving the following results: a) in case of commercial detergents, they correctly classify observations that do not agree with the reference conditions. Moreover, the approach proposed is able to assess when the estimation of the compounds concentration cannot be considered accurate, this scenario may occur when the deviations of one compound is not taken into account during model calibration; b) for the crystallization of the pharmaceutical ingredient, the nucleation is accurately detected; c) spectra and concentration of the compounds involved in the setting reaction of a cementing material are estimated and time evolution of the process can be tracked; d) the dissolution rate of the surfactants present in the paste is estimated. As a result, multivariate methods applied to spectroscopic data reveal essential to treat data and aid process understanding and monitoring.

Thesis (M.S. in Applied Science (Operations Research) )--Naval Postgraduate School, June 2007.<br>Thesis Advisor(s): Ronald D. Fricker. "June 2007." Includes bibliographical references (p. 71-72). Also available in print.

Biological terrorism is a threat to the security and well-being of the United States. It is critical to detect the presence of these attacks in a timely manner, in order to provide sufficient and effective responses to minimize or contain the damage inflicted. Syndromic surveillance is the process of monitoring public health-related data and applying statistical tests to determine the potential presence of a disease outbreak in the observed system. Our research involved a comparative analysis of two multivariate statistical methods, the multivariate CUSUM (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA), both modified to look only for increases in disease incidence. While neither of these methods is currently in use in a biosurveillance system, they are among the most promising multivariate methods for this application. Our analysis was based on a series of simulations using synthetic syndromic surveillance data that mimics various types of background disease incidence and outbreaks. We found that, similar to results for the univariate CUSUM and EWMA, the directionally-sensitive MCUSUM and MEWMA perform very similarly.

Thesis (MscEng)--Stellenbosch University, 2003.<br>ENGLISH ABSTRACT: Outliers may be defined as observations that are sufficiently aberrant to arouse the suspicion of the analyst as to their origin. They could be the result of human error, in which case they should be corrected, but they may also be an interesting exception, and this would deserve further investigation. Identification of outliers typically consists of an informal inspection of a plot of the data, but this is unreliable for dimensions greater than two. A formal procedure for detecting outliers allows for consistency when classifying observations. It also enables one to automate the detection of outliers by using computers. The special case of univariate data is treated separately to introduce essential concepts, and also because it may well be of interest in its own right. We then consider techniques used for detecting multiple outliers in a multivariate normal sample, and go on to explain how these may be generalized to include cluster analysis. Multivariate outlier detection is based on the Minimum Covariance Determinant (MCD) subset, and is therefore treated in detail. Exact bivariate algorithms were refined and implemented, and the solutions were used to establish the performance of the commonly used heuristic, Fast–MCD.<br>AFRIKAANSE OPSOMMING: Uitskieters word gedefinieer as waarnemings wat tot s´o ’n mate afwyk van die verwagte gedrag dat die analis wantrouig is oor die oorsprong daarvan. Hierdie waarnemings mag die resultaat wees van menslike foute, in welke geval dit reggestel moet word. Dit mag egter ook ’n interressante verskynsel wees wat verdere ondersoek benodig. Die identifikasie van uitskieters word tipies informeel deur inspeksie vanaf ’n grafiese voorstelling van die data uitgevoer, maar hierdie benadering is onbetroubaar vir dimensies groter as twee. ’n Formele prosedure vir die bepaling van uitskieters sal meer konsekwente klassifisering van steekproefdata tot gevolg hˆe. Dit gee ook geleentheid vir effektiewe rekenaar implementering van die tegnieke. Aanvanklik word die spesiale geval van eenveranderlike data behandel om noodsaaklike begrippe bekend te stel, maar ook aangesien dit in eie reg ’n area van groot belang is. Verder word tegnieke vir die identifikasie van verskeie uitskieters in meerveranderlike, normaal verspreide data beskou. Daar word ook ondersoek hoe hierdie idees veralgemeen kan word om tros analise in te sluit. Die sogenaamde Minimum Covariance Determinant (MCD) subversameling is fundamenteel vir die identifikasie van meerveranderlike uitskieters, en word daarom in detail ondersoek. Deterministiese tweeveranderlike algoritmes is verfyn en ge¨ımplementeer, en gebruik om die effektiwiteit van die algemeen gebruikte heuristiese algoritme, Fast–MCD, te ondersoek.

Includes bibliography.<br>The purpose of the procedures described is to assign “objects” or "observations" in some optimum fashion to one of two or more populations. In routine banking a bank manager may wish to classify clients who wish to make loans as low or high credit risks on the basis of the elements of certain accounting statements. In such a case there are two definite distinct classes. Another investigation may be initiated to determine whether buying habits are different with respect to the categories: urban, sub-urban and rural clients. Note that in the first example the classes are determined before any sample of observations is investigated, i.e. the sample results do not influence the choice of groups. In the latter case one is trespassing on the terrain of cluster analysis.In the first case we have two types of problems, namely that of devising a classification rule from samples of already classified objects and that of imposing the classification scheme on the objects. The term "discrimination" refers to the process of deriving classification rules from samples of classified objects and the term "classification" refers to applying the rules to knew objects of unknown class. Although it is possible to convert raw data into more easily grasped forms like cartoon faces (Chernoff, 1973) this still represents the problem that any grouping or classification based on these diagrams is subjective.

El objetivo de esta tesis ha sido estudiar y desarrollar metodologias analíticas<br/>usando un sistema de inyección secuencial (SIA) con un espectrofotómetro de diodos en<br/>fila para obtener datos de segundo orden. Para tratar estos datos, las herramientas<br/>quimiométricas usadas han sido; resolución de curvas multivariante mediante mínimos<br/>cuadrados alternados (MCR-ALS) y otras técnicas relacionadas a ésta como el análisis<br/>de componentes principales (PCA) y SIMPLISMA. Además se han aplicado estrategias<br/>de diseño de experimentos para obtener las condiciones experimentales óptimas. Esta<br/>metodología se aplicó a la determinación de amoxicilina y ácido clavulánico en<br/>medicamentos.<br/>El primer capítulo de la tesis contiene una descripción de la amoxicilina y del ácido<br/>clavulánico, una explicación de los fundamentos teóricos tanto del sistema instrumental<br/>como de las herramientas quimiométricas usadas y por último, se describen los diseños<br/>de experimentos usados y la función de deseabilidad.<br/>En los dos siguientes capítulos, se muestran en forma de artículos científicos los<br/>trabajos experimentales realizados. En un primer artículo, se realizó una clasificación de<br/>los medicamentos dependiendo si se tenían interferentes o no, para posteriormente<br/>proponer el tipo de calibrado. Un paso previo a la diferenciación de los medicamentos,<br/>fue buscar una secuencia analítica que permitiera obtener un sistema en evolución. Esta<br/>etapa se llevó a cabo mediante un diseño de experimentos.<br/>En el segundo artículo, se determinó la cantidad de amoxicilina en los<br/>medicamentos que tenían interferentes y además no tenían zonas selectivas. Para llevar<br/>a cabo de forma correcta la etapa de calibración se realizó un estudio de una serie de<br/>parámetros asociados a MCR-ALS. En un tercer artículo se realizó la determinación<br/>simultánea del ácido clavulánico y de la amoxicilina que poseían unas características<br/>ácido-base y una sensibilidad espectral similar. Por tal de determinar simultáneamente<br/>ambos analitos se rediseñó todo el experimental. En el cuarto artículo se hizo una<br/>revisión bibliográfica de ambas técnicas a partir del año 2004 y se discutió el potencial de<br/>usar un sistema de inyección secuencial para generar datos de segundo orden.<br/>Con la experimentación realizada se comprobó que el paso clave en estas<br/>metodologias era obtener una buen sistema en evolución, es decir diseñar una buena<br/>secuencia analítica. Por lo que se profundizó en estrategias basadas en diseños de<br/>experimentos. En el quinto artículo, se estudiaron qué factores podían afectar a la<br/>secuencia analítica. También se propusieron respuestas que representaran de una forma<br/>cuantitativa una buena resolución. Se realizó un diseño Plackett-Burman con el objetivo<br/>de eliminar los factores no relevantes, para posteriormente modelar una superficie de<br/>respuesta a partir de los factores relevantes que permite visualizar las condiciones<br/>óptimas de la secuencia analítica.<br/>El inconveniente de utilizar la metodología de superficie de respuesta es que en<br/>los casos donde el número de factores relevantes sea superior a 3 o 4, el número de<br/>experiencias aumenta considerablemente. En estos casos, una técnica alternativa es<br/>simplex que dio lugar a un sexto artículo.<br/>El último capítulo de la tesis contiene las conclusiones. Como una conclusión<br/>general, se puede decir que la combinación de un sistema de inyección secuencial (SIA)<br/>y una herramienta quimiométrica como la resolución de curvas multivariante mediante<br/>mínimos cuadrados alternados (MCR-ALS) puede ser usado tanto para realizar un<br/>análisis cualitativo y cuantitativo ya que proporciona información de los perfiles de<br/>concentración y perfiles espectrales de las diferentes especies a estudio.<br>The objective of this thesis is to study and develop analytical methods to determine<br/>amoxicillin and clavulanic acid in pharmaceuticals using sequential injection analysis (SIA)<br/>with a diode-array spectrophotometric detector to obtain second-order data. To treat these<br/>data, the chemometric tool used was; multivariate curve resolution with alternating least<br/>squares (MCR-ALS) and the techniques involved in the resolution process are: principal<br/>analysis components (PCA) and simple-to-use interactive self-modelling mixture analysis<br/>(SIMPLISMA).<br/>The first chapter contains a brief description of the theoretical backgrounds that<br/>have been used during this thesis. We explain the characteristics and properties of<br/>amoxicillin and clavulanic acid, we describes the instrumental and the chemometric tools<br/>used and at the end, we introduce the experimental designs used and the desirability<br/>function.<br/>In the next two chapters contain the bulk of the work carried out for this thesis and<br/>incorporate papers published in journals. In the first paper, the pharmaceuticals were<br/>classified according to their selective zones in order to propose the type of calibration. In a<br/>previous step, the experimental work was conducted to find an analytical sequence that<br/>allows us to obtain an evolving system. This step was carried out using experimental<br/>design. In the second paper, the quantity of amoxicillin in the pharmaceuticals with<br/>interferents or without selective zones was determined. To carry out correctly the<br/>calibration step, we studied different conditions related to the MCR-ALS process.<br/>In the third paper, we propose the simultaneous determination of amoxicillin and<br/>clavulanic acid which they have the acid-base characteristics and spectral profile similar.<br/>To determine both analytes, a new analytical sequence was redesigned. In the fourth<br/>paper, we describe the state of the art of sequential injection analysis (SIA) and<br/>multivariate curve resolution with alternating least squares (MCR-ALS) by reviewing the<br/>bibliography since 2004. We discuss the potential of SIA for generating second-order<br/>data.<br/>In previous papers, we found that the most critical step in the development of<br/>analytical methods based on SIA and MCR-ALS was to obtain an analytical sequence that<br/>provides an evolving system. To resolve so, we developed the method of experimental<br/>design to obtain the optimal analytical sequence.<br/>In the forth paper, we studied all the factors and analysed how they affect to the<br/>analytical sequence. We also proposed responses to quantitatively represent a good<br/>resolution. Once these factors and responses were proposed, we used a Plackett-Burman<br/>design to remove the non-relevant factors and then modelled a response surface. In the<br/>maximum of response surface, the optimum conditions for the analytical sequence could<br/>be visualised. To transform several responses into a single response, we used the overall<br/>desirability function. In the sixth paper, we applied an alternative optimisation method<br/>knows as the simplex approach. We aimed to determine amoxicillin and clavulanic acid<br/>simultaneously when the number of factors and responses was higher than in the<br/>previous paper.<br/>The last chapter contains the conclusions of the thesis. In general, we conclude<br/>that a combined sequential injection analysis (SIA) with a multivariate detector (i.e. diode<br/>array spectrophotometer) and multivariate curve resolution with alternating least squares<br/>(MCR-ALS) can be used for both qualitative and quantitative analyses since, it provides<br/>concentration and spectra profiles for the different species of the sample.