Browsing by Subject "Modularity"

Now showing 1 - 4 of 4
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    Efficient Inference and Dominant-Set Based Clustering for Functional Data
    (2024-05) Wang, Xiang; Wang, Honglang; Boukai, Benzion; Tan, Fei; Peng, Hanxiang
    This dissertation addresses three progressively fundamental problems for functional data analysis: (1) To do efficient inference for the functional mean model accounting for within-subject correlation, we propose the refined and bias-corrected empirical likelihood method. (2) To identify functional subjects potentially from different populations, we propose the dominant-set based unsupervised clustering method using the similarity matrix. (3) To learn the similarity matrix from various similarity metrics for functional data clustering, we propose the modularity guided and dominant-set based semi-supervised clustering method. In the first problem, the empirical likelihood method is utilized to do inference for the mean function of functional data by constructing the refined and bias-corrected estimating equation. The proposed estimating equation not only improves efficiency but also enables practically feasible empirical likelihood inference by properly incorporating within-subject correlation, which has not been achieved by previous studies. In the second problem, the dominant-set based unsupervised clustering method is proposed to maximize the within-cluster similarity and applied to functional data with a flexible choice of similarity measures between curves. The proposed unsupervised clustering method is a hierarchical bipartition procedure under the penalized optimization framework with the tuning parameter selected by maximizing the clustering criterion called modularity of the resulting two clusters, which is inspired by the concept of dominant set in graph theory and solved by replicator dynamics in game theory. The advantage offered by this approach is not only robust to imbalanced sizes of groups but also to outliers, which overcomes the limitation of many existing clustering methods. In the third problem, the metric-based semi-supervised clustering method is proposed with similarity metric learned by modularity maximization and followed by the above proposed dominant-set based clustering procedure. Under semi-supervised setting where some clustering memberships are known, the goal is to determine the best linear combination of candidate similarity metrics as the final metric to enhance the clustering performance. Besides the global metric-based algorithm, another algorithm is also proposed to learn individual metrics for each cluster, which permits overlapping membership for the clustering. This is innovatively different from many existing methods. This method is superiorly applicable to functional data with various similarity metrics between functional curves, while also exhibiting robustness to imbalanced sizes of groups, which are intrinsic to the dominant-set based clustering approach. In all three problems, the advantages of the proposed methods are demonstrated through extensive empirical investigations using simulations as well as real data applications.
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    Segregation of functional networks is associated with cognitive resilience in Alzheimer's disease
    (Oxford University Press, 2021) Ewers, Michael; Luan, Ying; Frontzkowski, Lukas; Neitzel, Julia; Rubinski, Anna; Dichgans, Martin; Hassenstab, Jason; Gordon, Brian A.; Chhatwal, Jasmeer P.; Levin, Johannes; Schofield, Peter; Benzinger, Tammie L.S; Morris, John C.; Goate, Alison; Karch, Celeste M.; Fagan, Anne M.; McDade, Eric; Allegri, Ricardo; Berman, Sarah; Chui, Helena; Cruchaga, Carlos; Farlow, Marty; Graff-Radford, Neill; Jucker, Mathias; Lee, Jae-Hong; Martins, Ralph N.; Mori, Hiroshi; Perrin, Richard; Xiong, Chengjie; Rossor, Martin; Fox, Nick C.; O’Connor, Antoinette; Salloway, Stephen; Danek, Adrian; Buerger, Katharina; Bateman, Randall J.; Habeck, Christian; Stern, Yaakov; Franzmeier, Nicolai; Alzheimer’s Disease Neuroimaging Initiative; Dominantly Inherited Alzheimer Network; Neurology, School of Medicine
    Cognitive resilience is an important modulating factor of cognitive decline in Alzheimer's disease, but the functional brain mechanisms that support cognitive resilience remain elusive. Given previous findings in normal ageing, we tested the hypothesis that higher segregation of the brain's connectome into distinct functional networks represents a functional mechanism underlying cognitive resilience in Alzheimer's disease. Using resting-state functional MRI, we assessed both resting-state functional MRI global system segregation, i.e. the balance of between-network to within-network connectivity, and the alternate index of modularity Q as predictors of cognitive resilience. We performed all analyses in two independent samples for validation: (i) 108 individuals with autosomal dominantly inherited Alzheimer's disease and 71 non-carrier controls; and (ii) 156 amyloid-PET-positive subjects across the spectrum of sporadic Alzheimer's disease and 184 amyloid-negative controls. In the autosomal dominant Alzheimer's disease sample, disease severity was assessed by estimated years from symptom onset. In the sporadic Alzheimer's sample, disease stage was assessed by temporal lobe tau-PET (i.e. composite across Braak stage I and III regions). In both samples, we tested whether the effect of disease severity on cognition was attenuated at higher levels of functional network segregation. For autosomal dominant Alzheimer's disease, we found higher functional MRI-assessed system segregation to be associated with an attenuated effect of estimated years from symptom onset on global cognition (P = 0.007). Similarly, for patients with sporadic Alzheimer's disease, higher functional MRI-assessed system segregation was associated with less decrement in global cognition (P = 0.001) and episodic memory (P = 0.004) per unit increase of temporal lobe tau-PET. Confirmatory analyses using the alternate index of modularity Q revealed consistent results. In conclusion, higher segregation of functional connections into distinct large-scale networks supports cognitive resilience in Alzheimer's disease.
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    Statistical methods for high-dimensional data with complex correlation structure applied to the brain dynamic functional connectivity studyDY
    (2017-01-06) Kudela, Maria Aleksandra; Harezlak, Jaroslaw; Dzemidzic, Mario; Li, Shanshan; He, Chunyan; Yiannoutsos, Constantin
    A popular non-invasive brain activity measurement method is based on the functional magnetic resonance imaging (fMRI). Such data are frequently used to study functional connectivity (FC) defined as statistical association among two or more anatomically distinct fMRI signals (Friston, 1994). FC has emerged in recent years as a valuable tool for providing a deeper understanding of neurodegenerative diseases and neuropsychiatric disorders, such as Alzheimer's disease and autism. Information about complex association structure in high-dimensional fMRI data is often discarded by a calculating an average across complex spatiotemporal processes without providing an uncertainty measure around it. First, we propose a non-parametric approach to estimate the uncertainty of dynamic FC (dFC) estimates. Our method is based on three components: an extension of a boot strapping method for multivariate time series, recently introduced by Jentsch and Politis (2015); sliding window correlation estimation; and kernel smoothing. Second, we propose a two-step approach to analyze and summarize dFC estimates from a task-based fMRI study of social-to-heavy alcohol drinkers during stimulation with avors. In the first step, we apply our method from the first paper to estimate dFC for each region subject combination. In the second step, we use semiparametric additive mixed models to account for complex correlation structure and model dFC on a population level following the study's experimental design. Third, we propose to utilize the estimated dFC to study the system's modularity defined as the mutually exclusive division of brain regions into blocks with intra-connectivity greater than the one obtained by chance. As a result, we obtain brain partition suggesting the existence of common functionally-based brain organization. The main contribution of our work stems from the combination of the methods from the fields of statistics, machine learning and network theory to provide statistical tools for studying brain connectivity from a holistic, multi-disciplinary perspective.
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    Temporal stability of the ventral attention network and general cognition along the Alzheimer’s disease spectrum
    (Elsevier, 2021) Chumin, Evgeny J.; Risacher, Shannon L.; West, John D.; Apostolova, Liana G.; Farlow, Martin R.; McDonald, Brenna C.; Wu, Yu-Chien; Saykin, Andrew J.; Sporns, Olaf; Radiology and Imaging Sciences, School of Medicine
    Understanding the interrelationships of clinical manifestations of Alzheimer’s disease (AD) and functional connectivity (FC) as the disease progresses is necessary for use of FC as a potential neuroimaging biomarker. Degradation of resting-state networks in AD has been observed when FC is estimated over the entire scan, however, the temporal dynamics of these networks are less studied. We implemented a novel approach to investigate the modular structure of static (sFC) and time-varying (tvFC) connectivity along the AD spectrum in a two-sample Discovery/Validation design (n = 80 and 81, respectively). Cortical FC networks were estimated across 4 diagnostic groups (cognitively normal, subjective cognitive decline, mild cognitive impairment, and AD) for whole scan (sFC) and with sliding window correlation (tvFC). Modularity quality (across a range of spatial scales) did not differ in either sFC or tvFC. For tvFC, group differences in temporal stability within and between multiple resting state networks were observed; however, these differences were not consistent between samples. Correlation analyses identified a relationship between global cognition and temporal stability of the ventral attention network, which was reproduced in both samples. While the ventral attention system has been predominantly studied in task-evoked designs, the relationship between its intrinsic dynamics at-rest and general cognition along the AD spectrum highlights its relevance regarding clinical manifestation of the disease.