Transportation Techniques for Geometric Clustering

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This thesis introduces new techniques for clustering distributional data according to their geometric similarities. This work builds upon the optimal transportation (OT) problem that seeks global minimum cost for matching distributional data and leverages the connection between OT and power

This thesis introduces new techniques for clustering distributional data according to their geometric similarities. This work builds upon the optimal transportation (OT) problem that seeks global minimum cost for matching distributional data and leverages the connection between OT and power diagrams to solve different clustering problems. The OT formulation is based on the variational principle to differentiate hard cluster assignments, which was missing in the literature. This thesis shows multiple techniques to regularize and generalize OT to cope with various tasks including clustering, aligning, and interpolating distributional data. It also discusses the connections of the new formulation to other OT and clustering formulations to better understand their gaps and the means to close them. Finally, this thesis demonstrates the advantages of the proposed OT techniques in solving machine learning problems and their downstream applications in computer graphics, computer vision, and image processing.
Date Created
2020
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Blood Pressure Control in Aging Predicts Cerebral Atrophy Related to Small-Vessel White Matter Lesions

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Description

Cerebral small-vessel damage manifests as white matter hyperintensities and cerebral atrophy on brain MRI and is associated with aging, cognitive decline and dementia. We sought to examine the interrelationship of these imaging biomarkers and the influence of hypertension in older

Cerebral small-vessel damage manifests as white matter hyperintensities and cerebral atrophy on brain MRI and is associated with aging, cognitive decline and dementia. We sought to examine the interrelationship of these imaging biomarkers and the influence of hypertension in older individuals. We used a multivariate spatial covariance neuroimaging technique to localize the effects of white matter lesion load on regional gray matter volume and assessed the role of blood pressure control, age and education on this relationship. Using a case-control design matching for age, gender, and educational attainment we selected 64 participants with normal blood pressure, controlled hypertension or uncontrolled hypertension from the Northern Manhattan Study cohort. We applied gray matter voxel-based morphometry with the scaled subprofile model to (1) identify regional covariance patterns of gray matter volume differences associated with white matter lesion load, (2) compare this relationship across blood pressure groups, and (3) relate it to cognitive performance. In this group of participants aged 60–86 years, we identified a pattern of reduced gray matter volume associated with white matter lesion load in bilateral temporal-parietal regions with relative preservation of volume in the basal forebrain, thalami and cingulate cortex. This pattern was expressed most in the uncontrolled hypertension group and least in the normotensives, but was also more evident in older and more educated individuals. Expression of this pattern was associated with worse performance in executive function and memory. In summary, white matter lesions from small-vessel disease are associated with a regional pattern of gray matter atrophy that is mitigated by blood pressure control, exacerbated by aging, and associated with cognitive performance.

Date Created
2017-05-15
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Plasma Levels of Aβ42 and Tau Identified Probable Alzheimer’s Dementia: Findings in Two Cohorts

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Description

The utility of plasma amyloid beta (Aβ) and tau levels for the clinical diagnosis of Alzheimer’s disease (AD) dementia has been controversial. The main objective of this study was to compare Aβ42 and tau levels measured by the ultra-sensitive immunomagnetic

The utility of plasma amyloid beta (Aβ) and tau levels for the clinical diagnosis of Alzheimer’s disease (AD) dementia has been controversial. The main objective of this study was to compare Aβ42 and tau levels measured by the ultra-sensitive immunomagnetic reduction (IMR) assays in plasma samples collected at the Banner Sun Health Institute (BSHRI) (United States) with those from the National Taiwan University Hospital (NTUH) (Taiwan). Significant increase in tau levels were detected in AD subjects from both cohorts, while Aβ42 levels were increased only in the NTUH cohort. A regression model incorporating age showed that tau levels identified probable ADs with 81 and 96% accuracy in the BSHRI and NTUH cohorts, respectively, while computed products of Aβ42 and tau increased the accuracy to 84% in the BSHRI cohorts. Using 382.68 (pg/ml)2 as the cut-off value, the product achieved 92% accuracy in identifying AD in the combined cohorts. Overall findings support that plasma Aβ42 and tau assayed by IMR technology can be used to assist in the clinical diagnosis of AD.

Date Created
2017-07-24
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Separating Lexical-Semantic Access From Other Mnemonic Processes in Picture-Name Verification

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Description

We present a novel paradigm to identify shared and unique brain regions underlying non-semantic, non-phonological, abstract, audio-visual (AV) memory vs. naming using a longitudinal functional magnetic resonance imaging experiment. Participants were trained to associate novel AV stimulus pairs containing hidden

We present a novel paradigm to identify shared and unique brain regions underlying non-semantic, non-phonological, abstract, audio-visual (AV) memory vs. naming using a longitudinal functional magnetic resonance imaging experiment. Participants were trained to associate novel AV stimulus pairs containing hidden linguistic content. Half of the stimulus pairs were distorted images of animals and sine-wave speech versions of the animal's name. Images and sounds were distorted in such a way as to make their linguistic content easily recognizable only after being made aware of its existence. Memory for the pairings was tested by presenting an AV pair and asking participants to verify if the two stimuli formed a learned pairing. After memory testing, the hidden linguistic content was revealed and participants were tested again on their recollection of the pairings in this linguistically informed state. Once informed, the AV verification task could be performed by naming the picture. There was substantial overlap between the regions involved in recognition of non-linguistic sensory memory and naming, suggesting a strong relation between them. Contrasts between sessions identified left angular gyrus and middle temporal gyrus as key additional players in the naming network. Left inferior frontal regions participated in both naming and non-linguistic AV memory suggesting the region is responsible for AV memory independent of phonological content contrary to previous proposals. Functional connectivity between angular gyrus and left inferior frontal gyrus and left middle temporal gyrus increased when performing the AV task as naming. The results are consistent with the hypothesis that, at the spatial resolution of fMRI, the regions that facilitate non-linguistic AV associations are a subset of those that facilitate naming though reorganized into distinct networks.

Date Created
2013-10-11
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Identifying Effective Connectivity Parameters in Simulated fMRI: A Direct Comparison of Switching Linear Dynamic System, Stochastic Dynamic Causal, and Multivariate Autoregressive Models

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Description

The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity

The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity is elusive with different methods potentially attempting to identify different aspects of connectivity. Commonalities of connectivity definitions across methods upon which base direct comparisons can be difficult to derive. Here, we explicitly define “effective connectivity” using a common set of observation and state equations that are appropriate for three connectivity methods: dynamic causal modeling (DCM), multivariate autoregressive modeling (MAR), and switching linear dynamic systems for fMRI (sLDSf). In addition while deriving this set, we show how many other popular functional and effective connectivity methods are actually simplifications of these equations. We discuss implications of these connections for the practice of using one method to simulate data for another method. After mathematically connecting the three effective connectivity methods, simulated fMRI data with varying numbers of regions and task conditions is generated from the common equation. This simulated data explicitly contains the type of the connectivity that the three models were intended to identify. Each method is applied to the simulated data sets and the accuracy of parameter identification is analyzed. All methods perform above chance levels at identifying correct connectivity parameters. The sLDSf method was superior in parameter estimation accuracy to both DCM and MAR for all types of comparisons.

Date Created
2013-05-14
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A Statistical Parametric Mapping Toolbox Used for Voxel-Wise Analysis of FDG-PET Images of Rat Brain

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Description

Purpose: PET (positron emission tomography) imaging researches of functional metabolism using fluorodeoxyglucose ([superscript 18]F-FDG) of animal brain are important in neuroscience studies. FDG-PET imaging studies are often performed on groups of rats, so it is desirable to establish an objective voxel-based

Purpose: PET (positron emission tomography) imaging researches of functional metabolism using fluorodeoxyglucose ([superscript 18]F-FDG) of animal brain are important in neuroscience studies. FDG-PET imaging studies are often performed on groups of rats, so it is desirable to establish an objective voxel-based statistical methodology for group data analysis.

Material and Methods: This study establishes a statistical parametric mapping (SPM) toolbox (plug-ins) named spmratIHEP for voxel-wise analysis of FDG-PET images of rat brain, in which an FDG-PET template and an intracranial mask image of rat brain in Paxinos & Watson space were constructed, and the default settings were modified according to features of rat brain. Compared to previous studies, our constructed rat brain template comprises not only the cerebrum and cerebellum, but also the whole olfactory bulb which made the later cognitive studies much more exhaustive. And with an intracranial mask image in the template space, the brain tissues of individuals could be extracted automatically. Moreover, an atlas space is used for anatomically labeling the functional findings in the Paxinos & Watson space. In order to standardize the template image with the atlas accurately, a synthetic FDG-PET image with six main anatomy structures is constructed from the atlas, which performs as a target image in the co-registration.

Results: The spatial normalization procedure is evaluated, by which the individual rat brain images could be standardized into the Paxinos & Watson space successfully and the intracranial tissues could also be extracted accurately. The practical usability of this toolbox is evaluated using FDG-PET functional images from rats with left side middle cerebral artery occlusion (MCAO) in comparison to normal control rats. And the two-sample t-test statistical result is almost related to the left side MCA.

Conclusion: We established a toolbox of SPM8 named spmratIHEP for voxel-wise analysis of FDG-PET images of rat brain.

Date Created
2014-09-26
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Association Between an Alzheimer’s Disease-Related Index and APOE ε4 Gene Dose

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Description

Background: We introduced a hypometabolic convergence index (HCI) to characterize in a single measurement the extent to which a person’s fluorodeoxyglucose positron emission tomogram (FDG PET) corresponds to that in Alzheimer’s disease (AD). Apolipoprotein E ε4 (APOE ε4) gene dose is

Background: We introduced a hypometabolic convergence index (HCI) to characterize in a single measurement the extent to which a person’s fluorodeoxyglucose positron emission tomogram (FDG PET) corresponds to that in Alzheimer’s disease (AD). Apolipoprotein E ε4 (APOE ε4) gene dose is associated with three levels of risk for late-onset AD. We explored the association between gene dose and HCI in cognitively normal ε4 homozygotes, heterozygotes, and non-carriers.

Methods: An algorithm was used to characterize and compare AD-related HCIs in cognitively normal individuals, including 36 ε4 homozygotes, 46 heterozygotes, and 78 non-carriers.

Results: These three groups differed significantly in their HCIs (ANOVA, p = 0.004), and there was a significant association between HCIs and gene dose (linear trend, p = 0.001).

Conclusions: The HCI is associated with three levels of genetic risk for late-onset AD. This supports the possibility of using a single FDG PET measurement to help in the preclinical detection and tracking of AD.

Date Created
2013-06-26
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Peripheral apoE Isoform Levels in Cognitively Normal APOE ε3/ε4 Individuals Are Associated With Regional Gray Matter Volume and Cerebral Glucose Metabolism

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Description

Background: Carriers of the APOE ε4 allele are at increased risk of developing Alzheimer’s disease (AD), and have been shown to have reduced cerebral metabolic rate of glucose (CMRgl) in the same brain areas frequently affected in AD. These individuals also

Background: Carriers of the APOE ε4 allele are at increased risk of developing Alzheimer’s disease (AD), and have been shown to have reduced cerebral metabolic rate of glucose (CMRgl) in the same brain areas frequently affected in AD. These individuals also exhibit reduced plasma levels of apolipoprotein E (apoE) attributed to a specific decrease in the apoE4 isoform as determined by quantification of individual apoE isoforms in APOE ε4 heterozygotes. Whether low plasma apoE levels are associated with structural and functional brain measurements and cognitive performance remains to be investigated.

Methods: Using quantitative mass spectrometry we quantified the plasma levels of total apoE and the individual apoE3 and apoE4 isoforms in 128 cognitively normal APOE ε3/ε4 individuals included in the Arizona APOE cohort. All included individuals had undergone extensive neuropsychological testing and 25 had in addition undergone FDG-PET and MRI to determine CMRgl and regional gray matter volume (GMV).

Results: Our results demonstrated higher apoE4 levels in females versus males and an age-dependent increase in the apoE3 isoform levels in females only. Importantly, a higher relative ratio of apoE4 over apoE3 was associated with GMV loss in the right posterior cingulate and with reduced CMRgl bilaterally in the anterior cingulate and in the right hippocampal area. Additional exploratory analysis revealed several negative associations between total plasma apoE, individual apoE isoform levels, GMV and CMRgl predominantly in the frontal, occipital and temporal areas. Finally, our results indicated only weak associations between apoE plasma levels and cognitive performance which further appear to be affected by sex.

Conclusions: Our study proposes a sex-dependent and age-dependent variation in plasma apoE isoform levels and concludes that peripheral apoE levels are associated with GMV, CMRgl and possibly cognitive performance in cognitively healthy individuals with a genetic predisposition to AD.

Date Created
2016-12-21
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Studying Ventricular Abnormalities in Mild Cognitive Impairment With Hyperbolic Ricci Flow and Tensor-Based Morphometry

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Description

Mild Cognitive Impairment (MCI) is a transitional stage between normal aging and dementia and people with MCI are at high risk of progression to dementia. MCI is attracting increasing attention, as it offers an opportunity to target the disease process

Mild Cognitive Impairment (MCI) is a transitional stage between normal aging and dementia and people with MCI are at high risk of progression to dementia. MCI is attracting increasing attention, as it offers an opportunity to target the disease process during an early symptomatic stage. Structural magnetic resonance imaging (MRI) measures have been the mainstay of Alzheimer's disease (AD) imaging research, however, ventricular morphometry analysis remains challenging because of its complicated topological structure. Here we describe a novel ventricular morphometry system based on the hyperbolic Ricci flow method and tensor-based morphometry (TBM) statistics. Unlike prior ventricular surface parameterization methods, hyperbolic conformal parameterization is angle-preserving and does not have any singularities. Our system generates a one-to-one diffeomorphic mapping between ventricular surfaces with consistent boundary matching conditions. The TBM statistics encode a great deal of surface deformation information that could be inaccessible or overlooked by other methods. We applied our system to the baseline MRI scans of a set of MCI subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI: 71 MCI converters vs. 62 MCI stable). Although the combined ventricular area and volume features did not differ between the two groups, our fine-grained surface analysis revealed significant differences in the ventricular regions close to the temporal lobe and posterior cingulate, structures that are affected early in AD. Significant correlations were also detected between ventricular morphometry, neuropsychological measures, and a previously described imaging index based on fluorodeoxyglucose positron emission tomography (FDG-PET) scans. This novel ventricular morphometry method may offer a new and more sensitive approach to study preclinical and early symptomatic stage AD.

Date Created
2015-01-01
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