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. ^

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.

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.

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.

Thermal imaging as a biometrics approach to facial signature authentication

This dissertation develops an image processing framework with unique feature extraction and similarity measurements for human face recognition in the thermal mid-wave infrared portion of the electromagnetic spectrum. The goals of this research is to design specialized algorithms that would extract facial vasculature information, create a thermal facial signature and identify the individual. The objective is to use such findings in support of a biometrics system for human identification with a high degree of accuracy and a high degree of reliability. This last assertion is due to the minimal to no risk for potential alteration of the intrinsic physiological characteristics seen through thermal infrared imaging. The proposed thermal facial signature recognition is fully integrated and consolidates the main and critical steps of feature extraction, registration, matching through similarity measures, and validation through testing our algorithm on a database, referred to as C-X1, provided by the Computer Vision Research Laboratory at the University of Notre Dame. Feature extraction was accomplished by first registering the infrared images to a reference image using the functional MRI of the Brain’s (FMRIB’s) Linear Image Registration Tool (FLIRT) modified to suit thermal infrared images. This was followed by segmentation of the facial region using an advanced localized contouring algorithm applied on anisotropically diffused thermal images. Thermal feature extraction from facial images was attained by performing morphological operations such as opening and top-hat segmentation to yield thermal signatures for each subject. Four thermal images taken over a period of six months were used to generate thermal signatures and a thermal template for each subject, the thermal template contains only the most prevalent and consistent features. Finally a similarity measure technique was used to match signatures to templates and the Principal Component Analysis (PCA) was used to validate the results of the matching process. Thirteen subjects were used for testing the developed technique on an in-house thermal imaging system. The matching using an Euclidean-based similarity measure showed 88% accuracy in the case of skeletonized signatures and templates, we obtained 90% accuracy for anisotropically diffused signatures and templates. We also employed the Manhattan-based similarity measure and obtained an accuracy of 90.39% for skeletonized and diffused templates and signatures. It was found that an average 18.9% improvement in the similarity measure was obtained when using diffused templates. The Euclidean- and Manhattan-based similarity measure was also applied to skeletonized signatures and templates of 25 subjects in the C-X1 database. The highly accurate results obtained in the matching process along with the generalized design process clearly demonstrate the ability of the thermal infrared system to be used on other thermal imaging based systems and related databases. A novel user-initialization registration of thermal facial images has been successfully implemented. Furthermore, the novel approach at developing a thermal signature template using four images taken at various times ensured that unforeseen changes in the vasculature did not affect the biometric matching process as it relied on consistent thermal features.

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.

Solar radiation–enhanced dissolution of particulate organic matter from coastal marine sediments

We investigated the influence of solar radiation on the transfer of organic matter from the particulate to dissolved phase during resuspension of coastal sediments collected from seven sites across Florida Bay (organic carbon values ranged from 2% to 9% by weight). Sediments were resuspended in oligotrophic seawater for 48 h in 1-liter quartz flasks in the dark and under simulated solar radiation (SunTest XLS+) at wet weight concentrations of 100 mg L21 and 1 g L21 (dry weights ranged from 27 to 630 mg L21). There were little to no dissolved organic carbon (DOC) increases in dark resuspensions, but substantial DOC increases occurred in irradiated resuspensions. DOC levels increased 4 mg C L21 in an irradiated 1 g L21 suspension (dry weight 400 mg L21) of an organic-rich (7% organic carbon) sediment. At a particle load commonly found in coastal waters (dry weight 40 mg L21), an irradiated suspension of the same organic-rich sediment produced 1 mg C L21. DOC increases in irradiated resuspensions were well-correlated with particulate organic carbon (POC) added. Photodissolution of POC ranged from 6% to 15% at high sediment levels and 10% to 33% at low sediment levels. Parallel factor analysis modeling of excitation-emission matrix fluorescence data (EEM PARAFAC) suggested the dissolved organic matter (DOM) produced during photodissolution included primarily humic-like components and a less important input of protein-like components. Principal component analysis (PCA) of EEM data revealed a marked similarity in the humic character of photodissolved DOM from organic-rich sediments and the humic character of Florida Bay waters.

A novel signal processing method for intraoperative neurophysiological monitoring in spinal surgeries

Intraoperative neurophysiologic monitoring is an integral part of spinal surgeries and involves the recording of somatosensory evoked potentials (SSEP). However, clinical application of IONM still requires anywhere between 200 to 2000 trials to obtain an SSEP signal, which is excessive and introduces a significant delay during surgery to detect a possible neurological damage. The aim of this study is to develop a means to obtain the SSEP using a much less, twelve number of recordings. The preliminary step involved was to distinguish the SSEP with the ongoing brain activity. We first establish that the brain activity is indeed quasi-stationary whereas an SSEP is expected to be identical every time a trial is recorded. An algorithm was developed using Chebychev time windowing for preconditioning of SSEP trials to retain the morphological characteristics of somatosensory evoked potentials (SSEP). This preconditioning was followed by the application of a principal component analysis (PCA)-based algorithm utilizing quasi-stationarity of EEG on 12 preconditioned trials. A unique Walsh transform operation was then used to identify the position of the SSEP event. An alarm is raised when there is a 10% time in latency deviation and/or 50% peak-to-peak amplitude deviation, as per the clinical requirements. The algorithm shows consistency in the results in monitoring SSEP in up to 6-hour surgical procedures even under this significantly reduced number of trials. In this study, the analysis was performed on the data recorded in 29 patients undergoing surgery during which the posterior tibial nerve was stimulated and SSEP response was recorded from scalp. This method is shown empirically to be more clinically viable than present day approaches. In all 29 cases, the algorithm takes 4sec to extract an SSEP signal, as compared to conventional methods, which take several minutes. The monitoring process using the algorithm was successful and proved conclusive under the clinical constraints throughout the different surgical procedures with an accuracy of 91.5%. Higher accuracy and faster execution time, observed in the present study, in determining the SSEP signals provide a much improved and effective neurophysiological monitoring process.

Evaluating the Distribution of Terrestrial Dissolved Organic Matter in a Complex Coastal Ecosystem Using Fluorescence Spectroscopy

The coastal zone of the Florida Keys features the only living coral reef in the continental United States and as such represents a unique regional environmental resource. Anthropogenic pressures combined with climate disturbances such as hurricanes can affect the biogeochemistry of the region and threaten the health of this unique ecosystem. As such, water quality monitoring has historically been implemented in the Florida Keys, and six spatially distinct zones have been identified. In these studies however, dissolved organic matter (DOM) has only been studied as a quantitative parameter, and DOM composition can be a valuable biogeochemical parameter in assessing environmental change in coastal regions. Here we report the first data of its kind on the application of optical properties of DOM, in particular excitation emission matrix fluorescence with parallel factor analysis (EEM-PARAFAC), throughout these six Florida Keys regions in an attempt to assess spatial differences in DOM sources. Our data suggests that while DOM in the Florida Keys can be influenced by distant terrestrial environments such as the Everglades, spatial differences in DOM distribution were also controlled in part by local surface runoff/fringe mangroves, contributions from seasgrass communities, as well as the reefs and waters from the Florida Current. Application of principal component analysis (PCA) of the relative abundance of EEM-PARAFAC components allowed for a clear distinction between the sources of DOM (allochthonous vs. autochthonous), between different autochthonous sources and/or the diagenetic status of DOM, and further clarified contribution of terrestrial DOM in zones where levels of DOM were low in abundance. The combination between EEM-PARAFAC and PCA proved to be ideally suited to discern DOM composition and source differences in coastal zones with complex hydrology and multiple DOM sources.

Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

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.