Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Elemental analysis and forensic comparison of soils by laser-induced breakdown spectroscopy (LIBS) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS)

The elemental analysis of soil is useful in forensic and environmental sciences. Methods were developed and optimized for two laser-based multi-element analysis techniques: laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and laser-induced breakdown spectroscopy (LIBS). This work represents the first use of a 266 nm laser for forensic soil analysis by LIBS. Sample preparation methods were developed and optimized for a variety of sample types, including pellets for large bulk soil specimens (470 mg) and sediment-laden filters (47 mg), and tape-mounting for small transfer evidence specimens (10 mg). Analytical performance for sediment filter pellets and tape-mounted soils was similar to that achieved with bulk pellets. An inter-laboratory comparison exercise was designed to evaluate the performance of the LA-ICP-MS and LIBS methods, as well as for micro X-ray fluorescence (μXRF), across multiple laboratories. Limits of detection (LODs) were 0.01-23 ppm for LA-ICP-MS, 0.25-574 ppm for LIBS, 16-4400 ppm for μXRF, and well below the levels normally seen in soils. Good intra-laboratory precision (≤ 6 % relative standard deviation (RSD) for LA-ICP-MS; ≤ 8 % for μXRF; ≤ 17 % for LIBS) and inter-laboratory precision (≤ 19 % for LA-ICP-MS; ≤ 25 % for μXRF) were achieved for most elements, which is encouraging for a first inter-laboratory exercise. While LIBS generally has higher LODs and RSDs than LA-ICP-MS, both were capable of generating good quality multi-element data sufficient for discrimination purposes. Multivariate methods using principal components analysis (PCA) and linear discriminant analysis (LDA) were developed for discriminations of soils from different sources. Specimens from different sites that were indistinguishable by color alone were discriminated by elemental analysis. Correct classification rates of 94.5 % or better were achieved in a simulated forensic discrimination of three similar sites for both LIBS and LA-ICP-MS. Results for tape-mounted specimens were nearly identical to those achieved with pellets. Methods were tested on soils from USA, Canada and Tanzania. Within-site heterogeneity was site-specific. Elemental differences were greatest for specimens separated by large distances, even within the same lithology. Elemental profiles can be used to discriminate soils from different locations and narrow down locations even when mineralogy is similar.

Elemental Analysis and Forensic Comparison of Soils by Laser-Induced Breakdown Spectroscopy (LIBS) and Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS)

The elemental analysis of soil is useful in forensic and environmental sciences. Methods were developed and optimized for two laser-based multi-element analysis techniques: laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and laser-induced breakdown spectroscopy (LIBS). This work represents the first use of a 266 nm laser for forensic soil analysis by LIBS. Sample preparation methods were developed and optimized for a variety of sample types, including pellets for large bulk soil specimens (470 mg) and sediment-laden filters (47 mg), and tape-mounting for small transfer evidence specimens (10 mg). Analytical performance for sediment filter pellets and tape-mounted soils was similar to that achieved with bulk pellets. An inter-laboratory comparison exercise was designed to evaluate the performance of the LA-ICP-MS and LIBS methods, as well as for micro X-ray fluorescence (μXRF), across multiple laboratories. Limits of detection (LODs) were 0.01-23 ppm for LA-ICP-MS, 0.25-574 ppm for LIBS, 16-4400 ppm for µXRF, and well below the levels normally seen in soils. Good intra-laboratory precision (≤ 6 % relative standard deviation (RSD) for LA-ICP-MS; ≤ 8 % for µXRF; ≤ 17 % for LIBS) and inter-laboratory precision (≤ 19 % for LA-ICP-MS; ≤ 25 % for µXRF) were achieved for most elements, which is encouraging for a first inter-laboratory exercise. While LIBS generally has higher LODs and RSDs than LA-ICP-MS, both were capable of generating good quality multi-element data sufficient for discrimination purposes. Multivariate methods using principal components analysis (PCA) and linear discriminant analysis (LDA) were developed for discriminations of soils from different sources. Specimens from different sites that were indistinguishable by color alone were discriminated by elemental analysis. Correct classification rates of 94.5 % or better were achieved in a simulated forensic discrimination of three similar sites for both LIBS and LA-ICP-MS. Results for tape-mounted specimens were nearly identical to those achieved with pellets. Methods were tested on soils from USA, Canada and Tanzania. Within-site heterogeneity was site-specific. Elemental differences were greatest for specimens separated by large distances, even within the same lithology. Elemental profiles can be used to discriminate soils from different locations and narrow down locations even when mineralogy is similar.

Statistical analysis and meta-analysis of microarray data

The microarray technology provides a high-throughput technique to study gene expression. Microarrays can help us diagnose different types of cancers, understand biological processes, assess host responses to drugs and pathogens, find markers for specific diseases, and much more. Microarray experiments generate large amounts of data. Thus, effective data processing and analysis are critical for making reliable inferences from the data. ^ The first part of dissertation addresses the problem of finding an optimal set of genes (biomarkers) to classify a set of samples as diseased or normal. Three statistical gene selection methods (GS, GS-NR, and GS-PCA) were developed to identify a set of genes that best differentiate between samples. A comparative study on different classification tools was performed and the best combinations of gene selection and classifiers for multi-class cancer classification were identified. For most of the benchmarking cancer data sets, the gene selection method proposed in this dissertation, GS, outperformed other gene selection methods. The classifiers based on Random Forests, neural network ensembles, and K-nearest neighbor (KNN) showed consistently god performance. A striking commonality among these classifiers is that they all use a committee-based approach, suggesting that ensemble classification methods are superior. ^ The same biological problem may be studied at different research labs and/or performed using different lab protocols or samples. In such situations, it is important to combine results from these efforts. The second part of the dissertation addresses the problem of pooling the results from different independent experiments to obtain improved results. Four statistical pooling techniques (Fisher inverse chi-square method, Logit method. Stouffer's Z transform method, and Liptak-Stouffer weighted Z-method) were investigated in this dissertation. These pooling techniques were applied to the problem of identifying cell cycle-regulated genes in two different yeast species. As a result, improved sets of cell cycle-regulated genes were identified. The last part of dissertation explores the effectiveness of wavelet data transforms for the task of clustering. Discrete wavelet transforms, with an appropriate choice of wavelet bases, were shown to be effective in producing clusters that were biologically more meaningful. ^

Principal component analysis and assessment of language network activation patterns in pediatric epilepsy

This dissertation establishes a novel data-driven method to identify language network activation patterns in pediatric epilepsy through the use of the Principal Component Analysis (PCA) on functional magnetic resonance imaging (fMRI). A total of 122 subjects’ data sets from five different hospitals were included in the study through a web-based repository site designed here at FIU. Research was conducted to evaluate different classification and clustering techniques in identifying hidden activation patterns and their associations with meaningful clinical variables. The results were assessed through agreement analysis with the conventional methods of lateralization index (LI) and visual rating. What is unique in this approach is the new mechanism designed for projecting language network patterns in the PCA-based decisional space. Synthetic activation maps were randomly generated from real data sets to uniquely establish nonlinear decision functions (NDF) which are then used to classify any new fMRI activation map into typical or atypical. The best nonlinear classifier was obtained on a 4D space with a complexity (nonlinearity) degree of 7. Based on the significant association of language dominance and intensities with the top eigenvectors of the PCA decisional space, a new algorithm was deployed to delineate primary cluster members without intensity normalization. In this case, three distinct activations patterns (groups) were identified (averaged kappa with rating 0.65, with LI 0.76) and were characterized by the regions of: (1) the left inferior frontal Gyrus (IFG) and left superior temporal gyrus (STG), considered typical for the language task; (2) the IFG, left mesial frontal lobe, right cerebellum regions, representing a variant left dominant pattern by higher activation; and (3) the right homologues of the first pattern in Broca's and Wernicke's language areas. Interestingly, group 2 was found to reflect a different language compensation mechanism than reorganization. Its high intensity activation suggests a possible remote effect on the right hemisphere focus on traditionally left-lateralized functions. In retrospect, this data-driven method provides new insights into mechanisms for brain compensation/reorganization and neural plasticity in pediatric epilepsy.

Comparison of medical and forensic profiling potential of volatile biomarkers from different biological specimens from individuals and across populations

There is limited scientific knowledge on the composition of human odor from different biological specimens and the effect that physiological and psychological health conditions could have on them. There is currently no direct comparison of the volatile organic compounds (VOCs) emanating from different biological specimens collected from healthy individuals as well as individuals with certain diagnosed medical conditions. Therefore the question of matching VOCs present in human odor across various biological samples and across health statuses remains unanswered. The main purpose of this study was to use analytical instrumental methods to compare the VOCs from different biological specimens from the same individual and to compare the populations evaluated in this project. The goals of this study were to utilize headspace solid-phase microextraction gas chromatography mass spectrometry (HS-SPME-GC/MS) to evaluate its potential for profiling VOCs from specimens collected using standard forensic and medical methods over three different populations: healthy group with no diagnosed medical or psychological condition, one group with diagnosed type 2 diabetes, and one group with diagnosed major depressive disorder. The pre-treatment methods of collection materials developed for the study allowed for the removal of targeted VOCs from the sampling kits prior to sampling, extraction and analysis. Optimized SPME-GC/MS conditions has been demonstrated to be capable of sampling, identifying and differentiating the VOCs present in the five biological specimens collected from different subjects and yielded excellent detection limits for the VOCs from buccal swab, breath, blood, and urine with average limits of detection of 8.3 ng. Visual, Spearman rank correlation, and PCA comparisons of the most abundant and frequent VOCs from each specimen demonstrated that each specimen has characteristic VOCs that allow them to be differentiated for both healthy and diseased individuals. Preliminary comparisons of VOC profiles of healthy individuals, patients with type 2 diabetes, and patients with major depressive disorder revealed compounds that could be used as potential biomarkers to differentiate between healthy and diseased individuals. Finally, a human biological specimen compound database has been created compiling the volatile compounds present in the emanations of human hand odor, oral fluids, breath, blood, and urine.

An incremental multilinear system for human face learning and recognition

This dissertation establishes a novel system for human face learning and recognition based on incremental multilinear Principal Component Analysis (PCA). Most of the existing face recognition systems need training data during the learning process. The system as proposed in this dissertation utilizes an unsupervised or weakly supervised learning approach, in which the learning phase requires a minimal amount of training data. It also overcomes the inability of traditional systems to adapt to the testing phase as the decision process for the newly acquired images continues to rely on that same old training data set. Consequently when a new training set is to be used, the traditional approach will require that the entire eigensystem will have to be generated again. However, as a means to speed up this computational process, the proposed method uses the eigensystem generated from the old training set together with the new images to generate more effectively the new eigensystem in a so-called incremental learning process. In the empirical evaluation phase, there are two key factors that are essential in evaluating the performance of the proposed method: (1) recognition accuracy and (2) computational complexity. In order to establish the most suitable algorithm for this research, a comparative analysis of the best performing methods has been carried out first. The results of the comparative analysis advocated for the initial utilization of the multilinear PCA in our research. As for the consideration of the issue of computational complexity for the subspace update procedure, a novel incremental algorithm, which combines the traditional sequential Karhunen-Loeve (SKL) algorithm with the newly developed incremental modified fast PCA algorithm, was established. In order to utilize the multilinear PCA in the incremental process, a new unfolding method was developed to affix the newly added data at the end of the previous data. The results of the incremental process based on these two methods were obtained to bear out these new theoretical improvements. Some object tracking results using video images are also provided as another challenging task to prove the soundness of this incremental multilinear learning method.

Shifting N and P limitation along a north-south gradient of mangrove estuaries in South Florida

A multivariate statistical analysis was applied to a 10 year, multiparameter data set in an effort to describe the spatial dependence and inherent variation of water quality patterns in the mangrove estuaries of Ten Thousand Islands – Whitewater Bay area. Principal component analysis (PCA) of 16 water quality parameters collected monthly resulted in five groupings, which explained 72.5% of the variance of the original variables. The “Organic” component (PCI) was composed of alkaline phosphatase activity, total organic nitrogen, and total organic carbon; the “Dissolved Inorganic N” component (PCII) contained NO 3 − , NO 2 − , and NH 4 + ; the “Phytoplankton” component (PCIII) was made up of total phosphorus, chlorophyll a, and turbidity; dissolved oxygen and temperature were inversely related (PCIV); and salinity and soluble reactive phosphorus made up PCV. A cluster analysis of the mean and SD of PC scores resulted in the spatial aggregation of the 47 fixed stations into six classes having similar water quality, which we defined as: Mangrove Rivers, Whitewater Bay, Gulf Islands, Coot Bay, Blackwater River, and Inland Waterway. Marked differences in physical, chemical, and biological characteristics among classes were illustrated by this technique. Comparison of medians and variability of parameters among classes allowed large scale generalizations as to underlying differences in water quality in these regions. A strong south to north gradient in estuaries from high N - low P to low N - high P was ascribed to marked differences in landuse, freshwater input, geomorphology, and sedimentary geology along this tract. The ecological significance of this gradient discussed along with potential effects of future restoration plans.

Sediment and soil organic matter source assessment as revealed by the molecular distribution and carbon isotopic composition of n-alkanes

The assessment of organic matter (OM) sources in sediments and soils is a key to better understand the biogeochemical cycling of carbon in aquatic environments. While traditional molecular marker-based methods have provided such information for typical two end member (allochthonous/terrestrial vs. autochthonous/microbial)-dominated systems, more detailed, biomass-specific assessments are needed for ecosystems with complex OM inputs such as tropical and sub-tropical wetlands and estuaries where aquatic macrophytes and macroalgae may play an important role as OM sources. The aim of this study was to assess the utility of a combined approach using compound specific stable carbon isotope analysis and an n-alkane based proxy (Paq) to differentiate submerged and emergent/terrestrial vegetation OM inputs to soils/sediments from a sub-tropical wetland and estuarine system, the Florida Coastal Everglades. Results show that Paq values (0.13–0.51) for the emergent/terrestrial plants were generally lower than those for freshwater/marine submerged vegetation (0.45–1.00) and that compound specific δ13C values for the n-alkanes (C23 to C31) were distinctively different for terrestrial/emergent and freshwater/marine submerged plants. While crossplots of the Paq and n-alkane stable isotope values for the C23n-alkane suggest that OM inputs are controlled by vegetation changes along the freshwater to marine transect, further resolution regarding OM input changes along this landscape was obtained through principal component analysis (PCA), successfully grouping the study sites according to the OM source strengths. The data show the potential for this n-alkane based multi-proxy approach as a means of assessing OM inputs to complex ecosystems.

Relationships Between Hydrology and Soils Describe Vegetation Patterns in Seasonally Flooded Tree Islands of the Southern Everglades, Florida

Tree island ecosystems are important and distinct features of Florida Everglades wetlands. We described the inter-relationships among abiotic factors describing seasonally flooded tree islands and characterized plant–soil relationships in tree islands occurring in a relatively unimpacted area of the Everglades. We used Principal Components Analysis (PCA) to reduce our multi-factor dataset, quantified forest structure and vegetation nutrient dynamics, and related these vegetation parameters to PCA summary variables using linear regression analyses. We found that, of the 21 abiotic parameters used to characterize the ecosystem structure of seasonally flooded tree islands, 13 parameters were significantly correlated with four principal components, and they described 78% of the variance among the study islands. Most variation was described by factors related to soil oxidation and hydrology, exemplifying the sensitivity of tree island structure to hydrologic conditions. PCA summary variables describing tree island structure were related to variability in Chrysobalanus icaco (L.) canopy cover, Ilex cassine (L.) and Salix caroliniana (Michx.) canopy cover, Myrica cerifera (L.) plot frequency, litter turnover, % phosphorus resorption of co-dominant species, and nitrogen nutrient-use efficiency. This study supported findings that vegetation characteristics can be sensitive indicators of variability in tree island ecosystem structure. This study produced valuable, information which was used to recommend ecological targets (i.e. restoration performance measures) for seasonally flooded tree islands in more impacted regions of the Everglades landscape.

Developing a process to create and validate an instrument assessing student attainment of competencies at an intercultural university in Mexico

This study took place at one of the intercultural universities (IUs) of Mexico that serve primarily indigenous students. The IUs are pioneers in higher education despite their numerous challenges (Bertely, 1998; Dietz, 2008; Pineda & Landorf, 2010; Schmelkes, 2009). To overcome educational inequalities among their students (Ahuja, Berumen, Casillas, Crispín, Delgado et al., 2004; Schmelkes, 2009), the IUs have embraced performance-based assessment (PBA; Casillas & Santini, 2006). PBA allows a shared model of power and control related to learning and evaluation (Anderson, 1998). While conducting a review on PBA strategies of the IUs, the researcher did not find a PBA instrument with valid and reliable estimates. The purpose of this study was to develop a process to create a PBA instrument, an analytic general rubric, with acceptable validity and reliability estimates to assess students' attainment of competencies in one of the IU's majors, Intercultural Development Management. The Human Capabilities Approach (HCA) was the theoretical framework and a sequential mixed method (Creswell, 2003; Teddlie & Tashakkori, 2009) was the research design. IU participants created a rubric during two focus groups, and seven Spanish-speaking professors in Mexico and the US piloted using students' research projects. The evidence that demonstrates the attainment of competencies at the IU is a complex set of actual, potential and/or desired performances or achievements, also conceptualized as "functional capabilities" (FCs; Walker, 2008), that can be used to develop a rubric. Results indicate that the rubric's validity and reliability estimates reached acceptable estimates of 80% agreement, surpassing minimum requirements (Newman, Newman, & Newman, 2011). Implications for practice involve the use of PBA within a formative assessment framework, and dynamic inclusion of constituencies. Recommendations for further research include introducing this study's instrument-development process to other IUs, conducting parallel mixed design studies exploring the intersection between HCA and assessment, and conducting a case study exploring assessment in intercultural settings. Education articulated through the HCA empowers students (Unterhalter & Brighouse, 2007; Walker, 2008). This study aimed to contribute to the quality of student learning assessment at the IUs by providing a participatory process to develop a PBA instrument.

Principal Component Analysis and Assessment of Language Network Activation Patterns in Pediatric Epilepsy

This dissertation establishes a novel data-driven method to identify language network activation patterns in pediatric epilepsy through the use of the Principal Component Analysis (PCA) on functional magnetic resonance imaging (fMRI). A total of 122 subjects’ data sets from five different hospitals were included in the study through a web-based repository site designed here at FIU. Research was conducted to evaluate different classification and clustering techniques in identifying hidden activation patterns and their associations with meaningful clinical variables. The results were assessed through agreement analysis with the conventional methods of lateralization index (LI) and visual rating. What is unique in this approach is the new mechanism designed for projecting language network patterns in the PCA-based decisional space. Synthetic activation maps were randomly generated from real data sets to uniquely establish nonlinear decision functions (NDF) which are then used to classify any new fMRI activation map into typical or atypical. The best nonlinear classifier was obtained on a 4D space with a complexity (nonlinearity) degree of 7. Based on the significant association of language dominance and intensities with the top eigenvectors of the PCA decisional space, a new algorithm was deployed to delineate primary cluster members without intensity normalization. In this case, three distinct activations patterns (groups) were identified (averaged kappa with rating 0.65, with LI 0.76) and were characterized by the regions of: 1) the left inferior frontal Gyrus (IFG) and left superior temporal gyrus (STG), considered typical for the language task; 2) the IFG, left mesial frontal lobe, right cerebellum regions, representing a variant left dominant pattern by higher activation; and 3) the right homologues of the first pattern in Broca's and Wernicke's language areas. Interestingly, group 2 was found to reflect a different language compensation mechanism than reorganization. Its high intensity activation suggests a possible remote effect on the right hemisphere focus on traditionally left-lateralized functions. In retrospect, this data-driven method provides new insights into mechanisms for brain compensation/reorganization and neural plasticity in pediatric epilepsy.

Developing a Process to Create and Validate an Instrument Assessing Student Attainment of Competencies at an Intercultural University in Mexico

This study took place at one of the intercultural universities (IUs) of Mexico that serve primarily indigenous students. The IUs are pioneers in higher education despite their numerous challenges (Bertely, 1998; Dietz, 2008; Pineda & Landorf, 2010; Schmelkes, 2009). To overcome educational inequalities among their students (Ahuja, Berumen, Casillas, Crispín, Delgado et al., 2004; Schmelkes, 2009), the IUs have embraced performance-based assessment (PBA; Casillas & Santini, 2006). PBA allows a shared model of power and control related to learning and evaluation (Anderson, 1998). While conducting a review on PBA strategies of the IUs, the researcher did not find a PBA instrument with valid and reliable estimates. The purpose of this study was to develop a process to create a PBA instrument, an analytic general rubric, with acceptable validity and reliability estimates to assess students’ attainment of competencies in one of the IU’s majors, Intercultural Development Management. The Human Capabilities Approach (HCA) was the theoretical framework and a sequential mixed method (Creswell, 2003; Teddlie & Tashakkori, 2009) was the research design. IU participants created a rubric during two focus groups, and seven Spanish-speaking professors in Mexico and the US piloted using students’ research projects. The evidence that demonstrates the attainment of competencies at the IU is a complex set of actual, potential and/or desired performances or achievements, also conceptualized as “functional capabilities” (FCs; Walker, 2008), that can be used to develop a rubric. Results indicate that the rubric’s validity and reliability estimates reached acceptable estimates of 80% agreement, surpassing minimum requirements (Newman, Newman, & Newman, 2011). Implications for practice involve the use of PBA within a formative assessment framework, and dynamic inclusion of constituencies. Recommendations for further research include introducing this study’s instrument-development process to other IUs, conducting parallel mixed design studies exploring the intersection between HCA and assessment, and conducting a case study exploring assessment in intercultural settings. Education articulated through the HCA empowers students (Unterhalter & Brighouse, 2007; Walker, 2008). This study aimed to contribute to the quality of student learning assessment at the IUs by providing a participatory process to develop a PBA instrument.

Climate, Land Use and Hydrologic Sensitivities of Stormwater Quantity and Quality in Complex Coastal Urban Watersheds

The study analyzed hydro-climatic and land use sensitivities of stormwater runoff and quality in the complex coastal urban watershed of Miami River Basin, Florida by developing a Storm Water Management Model (EPA SWMM 5). Regression-based empirical models were also developed to explain stream water quality in relation to internal (land uses and hydrology) and external (upstream contribution, seawater) sources and drivers in six highly urbanized canal basins of Southeast Florida. Stormwater runoff and quality were most sensitive to rainfall, imperviousness, and conversion of open lands/parks to residential, commercial and industrial areas. In-stream dissolved oxygen and total phosphorus in the watersheds were dictated by internal stressors while external stressors were dominant for total nitrogen and specific conductance. The research findings and tools will be useful for proactive monitoring and management of storm runoff and urban stream water quality under the changing climate and environment in South Florida and around the world.