Indiana University-Purdue University Indianapolis (IUPUI) / This research performs a comparative study of techniques for combining spatial data and multivariate statistical methods for characterizing water quality conditions in a river basin. The study has been performed on the White River basin in central Indiana, and uses sixteen physical and chemical water quality parameters collected from 44 different monitoring sites, along with various spatial data related to land use – land cover, soil characteristics, terrain characteristics, eco-regions, etc. Various parameters related to the spatial data were analyzed using ArcHydro tools and were included in the multivariate analysis methods for the purpose of creating classification equations that relate spatial and spatio-temporal attributes of the watershed to water quality data at monitoring stations. The study compares the use of various statistical estimates (mean, geometric mean, trimmed mean, and median) of monitored water quality variables to represent annual and seasonal water quality conditions. The relationship between these estimates and the spatial data is then modeled via linear and non-linear multivariate methods. The linear statistical multivariate method uses a combination of principal component analysis, cluster analysis, and discriminant analysis, whereas the non-linear multivariate method uses a combination of Kohonen Self-Organizing Maps, Cluster Analysis, and Support Vector Machines. The final models were tested with recent and independent data collected from stations in the Eagle Creek watershed, within the White River basin. In 6 out of 20 models the Support Vector Machine more accurately classified the Eagle Creek stations, and in 2 out of 20 models the Linear Discriminant Analysis model achieved better results. Neither the linear or non-linear models had an apparent advantage for the remaining 12 models. This research provides an insight into the variability and uncertainty in the interpretation of the various statistical estimates and statistical models, when water quality monitoring data is combined with spatial data for characterizing general spatial and spatio-temporal trends.

Indiana University-Purdue University Indianapolis (IUPUI) / The aim of this study was to use multivariate statistical techniques to: (1) determine the reproducibility of fiber evidence analyzed by MSP, (2) determine whether XRF is an appropriate technique for forensic tape analysis, and (3) determine if DART/MS is an appropriate technique for forensic tape analysis. This was achieved by employing several multivariate statistical techniques including agglomerative hierarchical clustering, principal component analysis, discriminant analysis, and analysis of variance. First, twelve dyed textile fibers were analyzed by UV-Visible MSP. This analysis included an inter-laboratory study, external validations, differing preprocessing techniques, and color coordinates. The inter-laboratory study showed no statistically significant difference between the different instruments. The external validations had overall acceptable results. Using first derivatives as a preprocessing technique and color coordinates to define color did not result in any additional information. Next, the tape backings of thirty-three brands were analyzed by XRF. After chemometric analysis it was concluded that the 3M tapes with black adhesive can be classified by brand except for Super 33+ (Cold Weather) and Super 88. The colorless adhesive tapes were separated into two large groups which were correlated with the presence of aluminosilicate filler. Overall, no additional discrimination was seen by using XRF compared to the traditional instrumentation for tape analysis previously published. Lastly, the backings of eighty-nine brands of tape were analyzed by DART/MS. The analysis of the black adhesive tapes showed that again discrimination between brands is possible except for Super 33+ and Super 88. However, now Tartan and Temflex have become indistinguishable. The colorless adhesive tapes again were more or less indistinguishable from one another with the exception of Tuff Hand Tool, Qualpack, and a roll of 3M Tartan, which were found to be unique. It cannot be determined if additional discrimination was achieved with DART/MS because the multivariate statistical techniques have not been applied to the other instrumental techniques used during tape analysis.

Fire debris analysis currently relies on visual pattern recognition of the total ion chromatograms, extracted ion profiles, and target compound chromatograms to identify the presence of an ignitable liquid. This procedure is described in the ASTM International E1618-10 standard method. For large data sets, this methodology can be time consuming and is a subjective method, the accuracy of which is dependent upon the skill and experience of the analyst. This research aimed to develop an automated classification method for large data sets and investigated the use of the total ion spectrum (TIS). The TIS is calculated by taking an average mass spectrum across the entire chromatographic range and has been shown to contain sufficient information content for the identification of ignitable liquids. The TIS of ignitable liquids and substrates were compiled into model data sets. Substrates are defined as common building materials and household furnishings that are typically found at the scene of a fire and are, therefore, present in fire debris samples. Fire debris samples were also used which were obtained from laboratory-scale and large-scale burns. An automated classification method was developed using computational software that was written in-house. Within this method, a multi-step classification scheme was used to detect ignitable liquid residues in fire debris samples and assign these to the classes defined in ASTM E1618-10. Classifications were made using linear discriminant analysis, quadratic discriminant analysis (QDA), and soft independent modeling of class analogy (SIMCA). The model data sets iv were tested by cross-validation and used to classify fire debris samples. Correct classification rates were calculated for each data set. Classifier performance metrics were also calculated for the first step of the classification scheme which included false positive rates, true positive rates, and the precision of the method. The first step, which determines a sample to be positive or negative for ignitable liquid residue, is arguably the most important in the forensic application. Overall, the highest correct classification rates were achieved using QDA for the first step of the scheme and SIMCA for the remaining steps. In the first step of the classification scheme, correct classification rates of 95.3% and 89.2% were obtained using QDA to classify the crossvalidation test set and fire debris samples, respectively. For this step, the cross-validation test set resulted in a true positive rate of 96.2%, a false positive rate of 9.3%, and a precision of 98.2%. The fire debris data set had a true positive rate of 82.9%, a false positive rate of 1.3%, and a precision of 99.0%. Correct classifications rates of 100% were achieved for both data sets in the majority of the remaining steps which used SIMCA for classification. The lowest correct classification rate, 69.2%, was obtained for the fire debris samples in one of the final steps in the classification scheme. In this research, the first statistically valid error rates for fire debris analysis have been developed through cross-validation of large data sets. The fire debris analyst can use the automated method as a tool for detecting and classifying ignitable liquid residues in fire debris samples. The error rates reduce the subjectivity associated with the current methods and provide a level of confidence in sample classification that does not currently exist in forensic fire debris analysis.

This thesis focuses on statistical and machine learning methods designed for sequential and repeated measurement data. We start off by considering the classic general linear model (MANOVA) followed by its generalization, the growth curve model (GMANOVA), designed for analysis of repeated measurement data. By considering a binary classification problem of normal data together with the corresponding maximum likelihood estimators for the growth curve model, we demonstrate how a classification rule based on linear discriminant analysis can be derived which can be used for repeated measurement data in a meaningful way. We proceed to the topics of neural networks which serve as our second method of classification. The reader is introduced to classic neural networks and relevant subtopics are discussed. We present a generalization of the classic neural network model to the recurrent neural network model and the LSTM model which are designed for sequential data. Lastly, we present three types of data sets with an total of eight cases where the discussed classification methods are tested. / Den här uppsatsen introducerar klassificeringsmetoder skapade för data av typen upprepade mätningar och sekventiell data. Den klassiska MANOVA modellen introduceras först som en grund för den mer allmäna tillväxtkurvemodellen(GMANOVA), som i sin tur används för att modellera upprepade mätningar på ett meningsfullt sätt. Under antagandet av normalfördelad data så härleds en binär klassificeringsmetod baserad på linjär diskriminantanalys, som tillsammans med maximum likelihood-skattningar från tillväxtkurvemodellen ger en binär klassificeringsregel för data av typen upprepade mätningarn. Vi fortsätter med att introducera läsaren för klassiska neurala nätverk och relevanta ämnen diskuteras. Vi generaliserar teorin kring neurala nätverk till typen "recurrent" neurala nätverk och LSTM som är designade för sekventiell data. Avslutningsvis så testas klassificeringsmetoderna på tre typer av data i totalt åtta olika fall.

In this dissertation, level set methods are employed to segment masses in digital mammographic images and to classify land cover classes in hyperspectral data. For the mammography computer aided diagnosis (CAD) application, level set-based segmentation methods are designed and validated for mass periphery segmentation, spiculation segmentation, and core segmentation. The proposed periphery segmentation uses the narrowband level set method in conjunction with an adaptive speed function based on a measure of the boundary complexity in the polar domain. The boundary complexity term is shown to be beneficial for delineating challenging masses with ill-defined and irregularly shaped borders. The proposed method is shown to outperform periphery segmentation methods currently reported in the literature. The proposed mass spiculation segmentation uses a generalized form of the Dixon and Taylor Line Operator along with narrowband level sets using a customized speed function. The resulting spiculation features are shown to be very beneficial for classifying the mass as benign or malignant. For example, when using patient age and texture features combined with a maximum likelihood (ML) classifier, the spiculation segmentation method increases the overall accuracy to 92% with 2 false negatives as compared to 87% with 4 false negatives when using periphery segmentation approaches. The proposed mass core segmentation uses the Chan-Vese level set method with a minimal variance criterion. The resulting core features are shown to be effective and comparable to periphery features, and are shown to reduce the number of false negatives in some cases. Most mammographic CAD systems use only a periphery segmentation, so those systems could potentially benefit from core features.

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The prediction of a company's financial health is of critical importance to a variety of stakeholders ranging from auditors, creditors, customers, employees, financial institutions and investors through to management. There has been considerable research in this field, ranging from the univariate dichotomous approach of Beaver (1966) to the multivariate multi-state approaches of Lau (1987) and Ward (1994). All of the South African studies namely, Strebel and Andrews (1977), Daya (1977), De La Rey (1981), Clarke et al (1991) and Court et al (1999), and even, Lukhwareni's (2005) four separate models, were dichotomous in nature providing either a "Healthy" or a "Failed" state; or a "Winner" or "Loser" as in the latter case. Notwithstanding, all of these models would be classified as first stage, initial screening models. This study has focused on following a two stage approach to identifying (first stage) and analysing (second stage) the States of Health in a company. It has not adopted the rigid "Healthy" or "Failed" dichotomous methodology. For the first stage, three-state models were developed classifying a company as Healthy, Intermittent or Distressed. Both three year and five year Profit after Tax (PAT) averages for Real Earnings Growth (REG) calculations were used to determine the superior definition for the Intermittent state; with the latter coming out as superior. Models were developed for the current year (Yn), one (Yn-1), two (Yn-2) and three years (Yn-3) forward using a Test sample of twenty companies and their predictive accuracy determined by using a Holdout sample of twenty-two companies and all their data points or years of information. The statistical methods employed were a Naïve model using the simple Shareholder Value Added (SVA) ratio, CHAID and MDA, with the latter providing very disappointing results - for the Yn year (five year average), the Test sample results were 100%, 95% and 95%, respectively; with the Holdout sample results being 81.3%, 83.8% and 52.5%, respectively. The Yn-1 to Yn-3 models produced very good results for the Test sample but somewhat disappointing Holdout sample results. The best two Yn models namely, the Naïve and the CHAID models, were modified so as to enable a comparison with the notable, dichotomous De La Rey (1981) model. As such, three different approaches were adopted and in all cases, both the modified Naïve (100%, 81.3%, 100%) and the modified CHAID (100%, 85.9%, 98%) produced superior results to the De La Rey model (84.8%, 62.6%, 75.3%). For the second stage, a Financial Risk Analysis Model (FRAM) using ratios in the categories of Growth, Performance Analysis, Investment Analysis and Financial Status were used to provide underlying information or clues, independent of the first stage model, so as to enable the stakeholder to establish a more meaningful picture of the company. This would pave the way for the appropriate strategy and course of action to be followed, to take the company to the next level; whether it be taking the company out of a Distressed State (D) or further improving on its Healthy status (H). / Business Management / D. BL.

Researchers perform multivariate techniques MANOVA, discriminant analysis and factor analysis. The most common applications in social science are to identify and test the effects from the analysis. The use of this multivariate technique is uncommon in investigating the effects of power usage and Province in South Africa on the amounts of the five power modes. This dissertation discusses this issue, the methodology and practical problems of the three multivariate techniques. The author examines the applications of each technique in social public research and comparisons are made between the three multivariate techniques. This dissertation concludes with a discussion of both the concepts of the present multivariate techniques and the results found on the use of the three multivariate techniques in the energy household consumption. The author recommends focusing on the hypotheses of the study or typical questions surrounding of each technique to guide the researcher in choosing the appropriate analysis in the social research, as each technique has some strengths and limitations. / Statistics / M. Sc. (Statistics)