In an unsupervised learning problem, one is given an unlabelled dataset and hopes to find some hidden structure; the prototypical example is clustering similar data. Such problems often arise in machine learning and statistics, but also in signal processing, theoretical computer science, and any number of quantitative scientific fields. The distinguishing feature of unsupervised learning is that there are no privileged variables or labels which are particularly informative, and thus the greatest challenge is often to differentiate between what is relevant or irrelevant in any particular dataset or problem. In the course of this thesis, we study a number of problems which span the breadth of unsupervised learning. We make progress in Gaussian mixtures, independent component analysis (where we solve the open problem of underdetermined ICA), and we formulate and solve a feature selection/dimension reduction model. Throughout, our goal is to give finite sample complexity bounds for our algorithms -- these are essentially the strongest type of quantitative bound that one can prove for such algorithms. Some of our algorithmic techniques turn out to be very efficient in practice as well. Our major technical tool is tensor spectral decomposition: tensors are generalisations of matrices, and often allow access to the "fine structure" of data. Thus, they are often the right tools for unravelling the hidden structure in an unsupervised learning setting. However, naive generalisations of matrix algorithms to tensors run into NP-hardness results almost immediately, and thus to solve our problems, we are obliged to develop two new tensor decompositions (with robust analyses) from scratch. Both of these decompositions are polynomial time, and can be viewed as efficient generalisations of PCA extended to tensors.

Hyperbaric pressure has been shown to affect the secondary structure of whey proteins such as beta-lactoglobulin (beta-lg). There is limited research, however, regarding the optimal conditions by which pressurization of whey proteins could lead to irreversible changes in secondary structure including the reduction of intramolecular disulfide bonds. Irreversible changes in protein conformation and breakage of disulfide bonds of whey proteins induced by high pressure might result in an increase in their digestibility and a reduction of allergenicity. Hence, the overall objective was to explore the capability of hyperbaric pressure to alter irreversibly the secondary structure of whey proteins and thereby alter their allergenic and nutritional properties. The behaviour of different genetic variants of beta-lg was studied employing variable-pressure Fourier transform infrared (FTIR) spectroscopy to establish the optimum pressures needed for their denaturation. The results showed reversible effects of pressures up to 12.0 kbar on the secondary structure of three main genetic variants of beta-lg. The individual response of the genetic variants to pressure was distinguishable despite their subtle structural differences. Pressure-induced conformational changes were studied separately in bovine serum albumin, Ca++-saturated alpha-lactalbumin and Ca ++-free alpha-lactalbumin by FTIR spectroscopy. The studies revealed that the presence of Ca++ ion and the number of disulfide bonds protects the protein molecules against pressure. As whey proteins appeared to be resistant to denaturation upon single applications of high pressure up to 1200 MPa, we developed a novel pressure processing using a combination of pulse and continuous modes at lower pressures of 400 MPa which led to irreversible denaturation of whey protein structure and disulphide bond breakage. Weanling rats fed with whey protein isolates treated by this novel low pressure processing technique showed enhanced grow

A genetic algorithm was employed to select the optimal combination of preprocessing variables, including data pretreatment, data manipulation and feature extraction procedures, for eventual clustering of a data set consisting of hyperspectral images acquired by a focal plane array Fourier transform infrared (FPA-FTIR) spectrometer. The data set consisted of infrared images of bacterial films, and the classification task investigated was the discrimination between Gram-positive and Gram-negative bacteria. The genetic algorithm evaluated combinations of variables pertaining to bacterial film thickness tolerances, baseline correction, pixel co-addition, outlier removal, smoothing, mean centering, normalization, derivatization, integration and principal component selection. Following numerous iterations of unsupervised processing, the genetic algorithm arrived at a sub-optimal solution yielding a clustering accuracy of 97.8% and a data utilization of 28.6%. The results provided insight into the co-dependencies of the pre-processing variables and their consequential effect on the selected data. The robustness of the classification model was evaluated and reinforced by the successful classification of two distinct validation sets. The overall success of the genetic algorithm suggests that it is an effective time saving resource for the optimization of pre-processing variables that does not require operator intervention.

Lipid oxidation has important consequences in the edible oil industry, producing compounds with sensory impact and thus reducing the economic value of the products. This work focused on the development of two Fourier transform infrared (FTIR) spectroscopy methods for the measurement of peroxide value (PV) and anisidine value (AV), representing the primary and secondary oxidation products of edible oils. / The infrared method developed for PV determination was based on a mathematical treatment by the partial least squares method of the information contained in the spectral region between 3750 and 3150 cm$ sp{-1}$. / The second method developed considered aldehyde content and anisidine value, a measure of secondary oxidation products. / The two methods developed are rapid ($ sim$2 min/sample) and have the advantage of being automatable. An infrared system coupled to a computer can collect the spectrum of an oil, analyze it and present a report without the need for personnel trained in FTIR spectroscopy. The cost of such a system would rapidly be absorbed through savings on personnel cost, time and chemical reagents required for conventional chemical methods and as such provides a useful advance in quality control methodology for the edible oils sector. (Abstract shortened by UMI.)

The Fast Fourier Transform (FFT) has been used in many scientific and engineering applications. The use of FFT for financial derivatives has been gaining momentum in the recent past. In this thesis, i) we have improved a recently proposed model of FFT for pricing financial derivatives to help design an efficient parallel algorithm. The improved mathematical model put forth in our research bridges a gap between quantitative approaches for the option pricing problem and practical implementation of such approaches on modern computer architectures. The thesis goes further by proving that the improved model of fast Fourier transform for option pricing produces accurate option values. ii) We have developed a parallel algorithm for the FFT using the classical Cooley-Tukey algorithm and improved this algorithm by introducing a data swapping technique that brings data closer to the respective processors and hence reduces the communication overhead to a large extent leading to better performance of the parallel algorithm. We have tested the new algorithm on a 20 node SunFire 6800 high performance computing system and compared the new algorithm with the traditional Cooley-Tukey algorithm. Option values are calculated for various strike prices with a proper selection of strike-price spacing to ensure fine-grid integration for FFT computation as well as to maximize the number of strikes lying in the desired region of the stock price. Compared to the traditional Cooley-Tukey algorithm, the current algorithm with data swapping performs better by more than 15% for large data sizes. In the rapidly changing market place, these improvements could mean a lot for an investor or financial institution because obtaining faster results offers a competitive advantages.

In this thesis, it is demonstrated that the two-dimensional Windowed Fourier Transform (WFT) can be effectively used to analyze the local spectral characteristics of electromagnetic scattering signals in the two-dimensional spatial frequency domain. The WFT is the extension of the Short Time Fourier Transform (STFT), which was originally derived to analyze the local spectral characteristics of one dimensional time functions. Since the WFT focuses on the local spectral behavior of the scattered field, the signal localization maps produced in the spectral domain by the WFT can be used to identify the contributions of the rays, at a given location in space, arising from various scattering mechanisms in high frequency applications.

Lignin, a byproduct of the chemical pulping can be gasified to produce fuel gas and value-added products. Two lignins, MeadWestvaco (MWV) lignin and Sigma Aldrich (SA) lignin, were studied using two different reactors. A laminar entrained flow reactor (LEFR) was used initially to determine the effect of lignin type, temperature and residence time on char yield and fixed carbon conversion during pyrolysis and gasification. During both pyrolysis and gasification, the maximum decrease in char yield took place in the initial stage of the reaction and there was little change at longer residence times. There was not much difference between pyrolysis and gasification in the residence times obtained in the LEFR. Furthermore, a thermogravimetric analyzer (TGA) was used to study the effect of lignin type on pyrolysis and gasification. The reaction rates and char yields were affected by the lignin composition. Lignin pyrolysis showed similar behavior until 600°C but only the high-ash SA lignin showed secondary pyrolysis reactions above 600°C. Carbon gasification reactions were delayed in SA lignin. Na2CO3 addition made the primary pyrolysis reaction occur at a lower rate and enhanced the rate for secondary pyrolysis reactions. Fourier Transform Infrared (FTIR) Spectroscopy results showed that the significant loss of spectral detail started at different temperatures for MWV lignin and SA lignin. Kinetic parameters obtained using differential and Coats - Redfern integral method were comparable at lower temperatures but varied at high temperatures. Na2CO3 addition decreased the activation energy of primary pyrolysis.

A novel analytical method is developed to examine the chemical composition of plant oils by electrospray ionisation high-resolution Fourier transform ion cyclotron resonance mass spectrometry in both positive- and negative-ion modes. To date, this is the first reported application of this technique for the study of macadamia nut oil. Samples of macadamia nut oil from the Macadamia Integrifolia- Proteaceae family (smooth shell) are examined. The fatty acid profile of the oil is obtained by this mass spectrometric examination of the transesterified and hydrolysed oil samples. The Fourier transform ion-cyclotron resonance mass spectrometry results are compared to those obtained from similar samples using gas chromatography-mass spectrometry techniques. High performance liquid chromatography and Fourier transform ion cyclotron resonance mass spectrometry are used to separate and assign the isomers present in the methanol extract of the oils in separate experiments. Significant results in this study include: - The first observation and identity of a number of oxidised triacylglycerols in macadamia oil samples. - The first observation of oxidised and free fatty acids, measured directly in hydrolysed oil and in the methanol extract of macadamia oil. - High resolution Fourier transform ion cyclotron resonance mass spectrometry in broadband mode which enables isobars to be observed. - Esterified oil Fourier transform ion cyclotron resonance mass spectrometry results are consistent with our gas chromatography-mass spectrometry results and with the results of similar studies on macadamia oil in the literature. - A number of fatty acids with odd number of carbon atoms are observed in the oil. - In electrospray ionisation Fourier transform ion cyclotron resonance mass spectrometry of oils, the sample preparation is straightforward. The sample is dissolved in methanol or acetonitrile and the solution is introduced to the electrospray source directly. Introducing oil samples to the gas chromatograph-mass spectrometer needs the oils to be esterified prior to the analysis. - In this work, state-of-the-art mass spectrometry demonstrates distinct advantages in comparison to gas chromatography measurements such as direct identification of free fatty acids in oil samples, whereas this is not possible in gas chromatography-mass spectrometry due to the required esterification step prior to the analysis. - High performance liquid chromatography fraction collection is combined with Fourier transform ion cyclotron resonance mass spectrometry in off-line mode and found to improve the sensitivity, selectivity and signal to noise levels due to the lower number of compounds in each high performance liquid chromatography fraction compared to the methanol extract of macadamia oil sample. Also isomers of monoacylglycerols have been resolved using the high performance liquid chromatography technique.

Geopolymer chemistry governs the formation of an X-ray amorphous aluminosilicate cement material. Binders form at ambient temperatures from a variety of different raw material sources, including industrial wastes. Early research in this field was based around investigating binder material properties; however, more recently, geopolymer formation chemistry has been intensively studied. Better understanding of the chemical processes governing geopolymer curing reactions will allow a wider variety of waste materials to be utilised and also the tailoring of binder properties for specific applications. (For complete abstract open document).

Cleaning validation of pharmaceutical manufacturing equipment is required by legislation. Generally, wet chemical techniques are employed using swabbing and/or rinse sampling methods. These are generally either selective and time consuming, or less selective and give results in a shorter period. The infrared reflection absorption spectroscopy (IRRAS) technique explored here attempts to deliver accurate, selective surface contamination information in real time to complement current methods and reduce down-time. The IRRAS instrument used in this research is a Fourier transform infrared (FTIR) spectrometer coupled by an IR fibre-optic cable to a grazing-angle sampling head with a fixed incidence angle of 80°. The introduced flexibility permits collection of in situ spectra from contaminated surfaces. Calibration models are developed using the multivariate, linear partial least squares (PLS) statistical method. The research focuses on sodium dodecyl sulfate (SDS), a model cleaning agent, on metal (aluminium and stainless steel) and dielectric (glass, EPDM and silicone) surfaces. The effects of surface finish are investigated for SDS on stainless steel. Calibrations for SDS and paracetamol in the presence of each other on glass surfaces are examined, as well as a common industrial cleaner (P3 cosa® PUR80) on polished stainless steel. For the calibration sets in this thesis, RMSECV values were < 0.41 µg cm⁻², corresponding to conservative surface residues detection limits of better than ~0.86 µg cm⁻². However, RMSECV values depend on the calibration loading range, and the detection limits were typically ~0.2 µg cm⁻² for loading ranges 0-2.5 µg cm⁻². These are below visual detection limits, generally taken to be 1-4 µg cm⁻², depending on the analyte and substrate. This shows that IRRAS is a viable method for the real-time detection and quantification of surface contamination by surfactants and active pharmaceutical ingredients on metals and dielectrics.