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Title: Assessment of functional connectivity in the human brain : multivariate and graph signal processing methods
Creator: Villafañe-Delgado, Marisel
Date: 2017
Collection: Electronic Theses & Dissertations
Description: "Advances in neurophysiological recording have provided a noninvasive way of inferring cognitive processes. Recent studies have shown that cognition relies on the functional integration or connectivity of segregated specialized regions in the brain. Functional connectivity quantifies the statistical relationships among different regions in the brain. However, current functional connectivity measures have certain limitations in the quantification of global integration and characterization of...
Show more"Advances in neurophysiological recording have provided a noninvasive way of inferring cognitive processes. Recent studies have shown that cognition relies on the functional integration or connectivity of segregated specialized regions in the brain. Functional connectivity quantifies the statistical relationships among different regions in the brain. However, current functional connectivity measures have certain limitations in the quantification of global integration and characterization of network structure. These limitations include the bivariate nature of most functional connectivity measures, the computational complexity of multivariate measures, and graph theoretic measures that are not robust to network size and degree distribution. Therefore, there is a need of computationally efficient and novel measures that can quantify the functional integration across brain regions and characterize the structure of these networks. This thesis makes contributions in three different areas for the assessment of multivariate functional connectivity. First, we present a novel multivariate phase synchrony measure for quantifying the common functional connectivity within different brain regions. This measure overcomes the drawbacks of bivariate functional connectivity measures and provides insights into the mechanisms of cognitive control not accountable by bivariate measures. Following the assessment of functional connectivity from a graph theoretic perspective, we propose a graph to signal transformation for both binary and weighted networks. This provides the means for characterizing the network structure and quantifying information in the graph by overcoming some drawbacks of traditional graph based measures. Finally, we introduce a new approach to studying dynamic functional connectivity networks through signals defined over networks. In this area, we define a dynamic graph Fourier transform in which a common subspace is found from the networks over time based on the tensor decomposition of the graph Laplacian over time."--Pages ii-iii.
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Title: Dynamic network analysis with applications to functional neural connectivity
Creator: Golibagh Mahyari, Arash
Date: 2017
Collection: Electronic Theses & Dissertations
Description: "Contemporary neuroimaging techniques provide neural activity recordings with increasing spatial and temporal resolution yielding rich multichannel datasets that can be exploited for detailed description of anatomical and functional connectivity patterns in the brain. Studies indicate that the changes in functional connectivity patterns across spatial and temporal scales play an important role in a wide range of cognitive and executive processes such as memory and attention as well as in the...
Show more"Contemporary neuroimaging techniques provide neural activity recordings with increasing spatial and temporal resolution yielding rich multichannel datasets that can be exploited for detailed description of anatomical and functional connectivity patterns in the brain. Studies indicate that the changes in functional connectivity patterns across spatial and temporal scales play an important role in a wide range of cognitive and executive processes such as memory and attention as well as in the understanding the causes of many neural diseases and psychopathologies such as epilepsy, Alzheimers, Parkinsons and schizophrenia. Early work in the area was limited to the analysis of static brain networks obtained through averaging long-term functional connectivity, thus neglecting possible time-varying connections. There is growing evidence that functional networks dynamically reorganize and coordinate on millisecond scale for the execution of mental processes. Functional networks consist of distinct network states, where each state is defined as a period of time during which the network topology is quasi-stationary. For this reason, there has been an interest in characterizing the dynamics of functional networks using high temporal resolution electroencephalogram recordings. In this thesis, dynamic functional connectivity networks are represented by multiway arrays, tensors, which are able to capture the complete topological structure of the networks. This thesis proposes new methods for both tracking the changes in these dynamic networks and characterizing or summarizing the network states. In order to achieve this goal, a Tucker decomposition based approach is introduced for detecting the change points for task-based electroencephalogram (EEG) functional connectivity networks through calculating the subspace distance between consecutive time steps. This is followed by a tensor-matrix projection based approach for summarizing multiple networks within a time interval. Tensor based summarization approaches do not necessarily result in sparse network and succinct states. Moreover, subspace based summarizations tend to capture the background brain activity more than the low energy sparse activations. For this reason, we propose utilizing the sparse common component and innovations (SCCI) model which simultaneously finds the sparse common component of multiple signals. However, as the number of signals in the model increases, this becomes computationally prohibitive. In this thesis, a hierarchical algorithm to recover the common component in the SCCI model is proposed for large number of signals. The hierarchical recovery of SCCI model solves the time and memory limitations at the expense of a slight decrease in the accuracy. This hierarchical model is used to separate the common and innovation components of functional connectivity networks across time. The innovation components are tracked over time to detect the change points, and the common component of the detected network states are used to obtain the network summarization. SCCI recovery algorithm finds the sparse representation of the common and innovation components of signals with respect to pre-determined dictionaries. However, input signals are not always well-represented by pre-determined dictionaries. In this thesis, a structured dictionary learning algorithm for SCCI model is developed. The proposed method is applied to EEG data collected during a study of error monitoring where two different types of brain responses are elicited in response to the stimulus. The learned dictionaries can discriminate between the response types and extract the error-related potentials (ERP) corresponding to the two responses."--Pages ii-iii.
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Title: Higher-order data reduction through clustering, subspace analysis and compression for applications in functional connectivity brain networks
Creator: Ozdemir, Alp
Date: 2017
Collection: Electronic Theses & Dissertations
Description: "With the recent advances in information technology, collection and storage of higher-order datasets such as multidimensional data across multiple modalities or variables have become much easier and cheaper than ever before. Tensors, also known as multiway arrays, provide natural representations for higher-order datasets and provide a way to analyze them by preserving the multilinear relations in these large datasets. These higher-order datasets usually contain large amount of redundant...
Show more"With the recent advances in information technology, collection and storage of higher-order datasets such as multidimensional data across multiple modalities or variables have become much easier and cheaper than ever before. Tensors, also known as multiway arrays, provide natural representations for higher-order datasets and provide a way to analyze them by preserving the multilinear relations in these large datasets. These higher-order datasets usually contain large amount of redundant information and summarizing them in a succinct manner is essential for better inference. However, existing data reduction approaches are limited to vector-type data and cannot be applied directly to tensors without vectorizing. Developing more advanced approaches to analyze tensors effectively without corrupting their intrinsic structure is an important challenge facing Big Data applications. This thesis addresses the issue of data reduction for tensors with a particular focus on providing a better understanding of dynamic functional connectivity networks (dFCNs) of the brain. Functional connectivity describes the relationship between spatially separated neuronal groups and analysis of dFCNs plays a key role for interpreting complex brain dynamics in different cognitive and emotional processes. Recently, graph theoretic methods have been used to characterize the brain functionality where bivariate relationships between neuronal populations are represented as graphs or networks. In this thesis, the changes in these networks across time and subjects will be studied through tensor representations. In Chapter 2, we address a multi-graph clustering problem which can be thought as a tensor partitioning problem. We introduce a hierarchical consensus spectral clustering approach to identify the community structure underlying the functional connectivity brain networks across subjects. New information-theoretic criteria are introduced for selecting the optimal community structure. Effectiveness of the proposed algorithms are evaluated through a set of simulations comparing with the existing methods as well as on FCNs across subjects. In Chapter 3, we address the online tensor data reduction problem through a subspace tracking perspective. We introduce a robust low-rank+sparse structure learning algorithm for tensors to separate the low-rank community structure of connectivity networks from sparse outliers. The proposed framework is used to both identify change points, where the low-rank community structure changes significantly, and summarize this community structure within each time interval. Finally, in Chapter 4, we introduce a new multi-scale tensor decomposition technique to efficiently encode nonlinearities due to rotation or translation in tensor type data. In particular, we develop a multi-scale higher-order singular value decomposition (MS-HoSVD) approach where a given tensor is first permuted and then partitioned into several sub-tensors each of which can be represented as a low-rank tensor increasing the efficiency of the representation. We derive a theoretical error bound for the proposed approach as well as provide analysis of memory cost and computational complexity. Performance of the proposed approach is evaluated on both data reduction and classification of various higher-order datasets."--Pages ii-iii.
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Title: TENSOR LEARNING WITH STRUCTURE, GEOMETRY AND MULTI-MODALITY
Creator: Sofuoglu, Seyyid Emre
Date: 2022
Collection: Electronic Theses & Dissertations
Description: With the advances in sensing and data acquisition technology, it is now possible to collect datafrom different modalities and sources simultaneously. Most of these data are multi-dimensional in nature and can be represented by multiway arrays known as tensors. For instance, a color image is a third-order tensor defined by two indices for spatial variables and one index for color mode. Some other examples include color video, medical imaging such as EEG and fMRI, spatiotemporal data...
Show moreWith the advances in sensing and data acquisition technology, it is now possible to collect datafrom different modalities and sources simultaneously. Most of these data are multi-dimensional in nature and can be represented by multiway arrays known as tensors. For instance, a color image is a third-order tensor defined by two indices for spatial variables and one index for color mode. Some other examples include color video, medical imaging such as EEG and fMRI, spatiotemporal data encountered in urban traffic monitoring, etc.In the past two decades, tensors have become ubiquitous in signal processing, statistics andcomputer science. Traditional unsupervised and supervised learning methods developed for one- dimensional signals do not translate well to higher order data structures as they get computationally prohibitive with increasing dimensionalities. Vectorizing high dimensional inputs creates problems in nearly all machine learning tasks due to exponentially increasing dimensionality, distortion of data structure and the difficulty of obtaining sufficiently large training sample size.In this thesis, we develop tensor-based approaches to various machine learning tasks. Existingtensor based unsupervised and supervised learning algorithms extend many well-known algorithms, e.g. 2-D component analysis, support vector machines and linear discriminant analysis, with better performance and lower computational and memory costs. Most of these methods rely on Tucker decomposition which has exponential storage complexity requirements; CANDECOMP-PARAFAC (CP) based methods which might not have a solution; or Tensor Train (TT) based solutions which suffer from exponentially increasing ranks. Many tensor based methods have quadratic (w.r.t the size of data), or higher computational complexity, and similarly, high memory complexity. Moreover, existing tensor based methods are not always designed with the particular structure of the data in mind. Many of the existing methods use purely algebraic measures as their objective which might not capture the local relations within data. Thus, there is a necessity to develop new models with better computational and memory efficiency, with the particular structure of the data and problem in mind. Finally, as tensors represent the data with more faithfulness to the original structure compared to the vectorization, they also allow coupling of heterogeneous data sources where the underlying physical relationship is known. Still, most of the current work on coupled tensor decompositions does not explore supervised problems.In order to address the issues around computational and storage complexity of tensor basedmachine learning, in Chapter 2, we propose a new tensor train decomposition structure, which is a hybrid between Tucker and Tensor Train decompositions. The proposed structure is used to imple- ment Tensor Train based supervised and unsupervised learning frameworks: linear discriminant analysis (LDA) and graph regularized subspace learning. The algorithm is designed to solve ex- tremal eigenvalue-eigenvector pair computation problems, which can be generalized to many other methods. The supervised framework, Tensor Train Discriminant Analysis (TTDA), is evaluated in a classification task with varying storage complexities with respect to classification accuracy and training time on four different datasets. The unsupervised approach, Graph Regularized TT, is evaluated on a clustering task with respect to clustering quality and training time on various storage complexities. Both frameworks are compared to discriminant analysis algorithms with similar objectives based on Tucker and TT decompositions.In Chapter 3, we present an unsupervised anomaly detection algorithm for spatiotemporaltensor data. The algorithm models the anomaly detection problem as a low-rank plus sparse tensor decomposition problem, where the normal activity is assumed to be low-rank and the anomalies are assumed to be sparse and temporally continuous. We present an extension of this algorithm, where we utilize a graph regularization term in our objective function to preserve the underlying geometry of the original data. Finally, we propose a computationally efficient implementation of this framework by approximating the nuclear norm using graph total variation minimization. The proposed approach is evaluated for both simulated data with varying levels of anomaly strength, length and number of missing entries in the observed tensor as well as urban traffic data. In Chapter 4, we propose a geometric tensor learning framework using product graph structures for tensor completion problem. Instead of purely algebraic measures such as rank, we use graph smoothness constraints that utilize geometric or topological relations within data. We prove the equivalence of a Cartesian graph structure to TT-based graph structure under some conditions. We show empirically, that introducing such relaxations due to the conditions do not deteriorate the recovery performance. We also outline a fully geometric learning method on product graphs for data completion.In Chapter 5, we introduce a supervised learning method for heterogeneous data sources suchas simultaneous EEG and fMRI. The proposed two-stage method first extracts features taking the coupling across modalities into account and then introduces kernelized support tensor machines for classification. We illustrate the advantages of the proposed method on simulated and real classification tasks with small number of training data with high dimensionality.
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Title: ASSESSMENT OF CROSS-FREQUENCY PHASE-AMPLITUDE COUPLING IN NEURONAL OSCILLATIONS
Creator: Munia, Tamanna Tabassum Khan
Date: 2021
Collection: Electronic Theses & Dissertations
Description: Oscillatory activity in the brain has been associated with a wide variety of cognitive processes including decision making, feedback processing, and working memory control. The high temporal resolution provided by electroencephalography (EEG) enables the study of variation of oscillatory power and coupling across time. Various forms of neural synchrony across frequency bands have been suggested as the mechanism underlying neural binding. Recently, a considerable amount of work has focused on...
Show moreOscillatory activity in the brain has been associated with a wide variety of cognitive processes including decision making, feedback processing, and working memory control. The high temporal resolution provided by electroencephalography (EEG) enables the study of variation of oscillatory power and coupling across time. Various forms of neural synchrony across frequency bands have been suggested as the mechanism underlying neural binding. Recently, a considerable amount of work has focused on phase-amplitude coupling (PAC)– a form of cross-frequency coupling where the amplitude of a high-frequency signal is modulated by the phase of low-frequency oscillations.The existing methods for assessing PAC have certain limitations which can influence the final PAC estimates and the subsequent neuroscientific findings. These limitations include low frequency resolution, narrowband assumption, and inherent requirement of bandpass filtering. These methods are also limited to quantifying univariate PAC and cannot capture inter-areal cross frequency coupling between different brain regions. Given the availability of multi-channel recordings, a multivariate analysis of phase-amplitude coupling is needed to accurately quantify the coupling across multiple frequencies and brain regions. Moreover, the existing PAC measures are usually stationary in nature, focusing on phase-amplitude modulations within a particular time window or over arbitrary sliding short time windows. Therefore, there is a need for computationally efficient measures that can quantify PAC with a high-frequency resolution, track the variation of PAC with time, both in bivariate and multivariate settings and provide a better insight into the spatially distributed dynamic brain networks across different frequency bands.In this thesis, we introduce a PAC computation technique that aims to overcome some of these drawbacks and extend it to multi-channel settings for quantifying dynamic cross-frequency coupling in the brain. The main contributions of the thesis are threefold. First, we present a novel time frequency based PAC (t-f PAC) measure based on a high-resolution complex time-frequency distribution, known as the Reduced Interference Distribution (RID)-Rihaczek. This t-f PAC measure overcomes the drawbacks associated with filtering by extracting instantaneous phase and amplitude components directly from the t-f distribution and thus provides high resolution PAC estimates. Following the introduction of a complex time-frequency-based high resolution PAC measure, we extend this measure to multi-channel settings to quantify the inter-areal PAC across multiple frequency bands and brain regions. We propose a tensor-based representation of multi-channel PAC based on Higher Order Robust PCA (HoRPCA). The proposed method can identify the significantly coupled brain regions along with the frequency bands that are involved in the observed couplings while accurately discarding the non-significant or spurious couplings. Finally, we introduce a matching pursuit based dynamic PAC (MP-dPAC) measure that allows us to compute PAC from time and frequency localized atoms that best describe the signal and thus capture the temporal variation of PAC using a data-driven approach. We evaluate the performance of the proposed methods on both synthesized and real EEG data collected during a cognitive control-related error processing study. Based on our results, we posit that the proposed multivariate and dynamic PAC measures provide a better insight into understanding the spatial, spectral, and temporal dynamics of cross-frequency phase-amplitude coupling in the brain.
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Title: A multivariate time-frequency based phase synchrony measure and applications to dynamic brain network analysis
Creator: Mutlu, Ali Yener
Date: 2012
Collection: Electronic Theses & Dissertations
Description: Irregular, non-stationary, and noisy multichannel data are abound in many fields of research. Observations of multichannel data in nature include changes in weather, the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology and the dynamics of the action potentials in neurons.One particular application of interest is the functional integration of neuronal networks in the human brain. Human brain is known to be...
Show moreIrregular, non-stationary, and noisy multichannel data are abound in many fields of research. Observations of multichannel data in nature include changes in weather, the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology and the dynamics of the action potentials in neurons.One particular application of interest is the functional integration of neuronal networks in the human brain. Human brain is known to be one of the most complex biological systems and quantifying functional neural coordination in the brain is a fundamental problem. It has been recently proposed that networks of highly nonlinear and non-stationary reciprocal interactions are the key features of functional integration. Among many linear and nonlinear measures of dependency, time-varying phase synchrony has been proposed as a promising measure of connectivity. Current state-of-the-art in time-varying phase estimation uses either the Hilbert transform or the complex wavelet transform of the signals. Both of these methods have some major drawbacks such as the assumption that the signals are narrowband for the Hilbert transform and the non-uniform time-frequency resolution inherent to the wavelet analysis. Furthermore, the current phase synchrony measures are limited to quantifying bivariate relationships and do not reveal any information about multivariate synchronization patterns which are important for understanding the underlying oscillatory networks.In this dissertation, a new phase estimation method based on the Rihaczek distribution and Reduced Interference Rihaczek distribution belonging to Cohen's class is proposed. These distributions offer phase estimates with uniformly high time-frequency resolution which can be used for defining time and frequency dependent phase synchrony within the same frequency band as well as across different frequency bands. Properties of the phase estimator and the corresponding phase synchrony measure are evaluated both analytically and through simulations showing the effectiveness of the new measures compared to existing ones. The proposed distribution is then extended to quantify the cross-frequency phase synchronization between two signals across different frequencies. In addition, a cross frequency-spectral lag distribution is introducedto quantify the amount of amplitude modulation between signals. Furthermore, the notion of bivariate synchrony is extended to multivariate synchronization to quantify the relationships within and across groups of signals. Measures of multiple correlation and complexity are used as well as a more direct multivariate synchronization measure, `Hyperspherical Phase Synchrony', is proposed. This new measure is based on computing pairwise phase differences to create a multidimensional phase difference vector and mapping this vector to a high dimensional space. Hyperspherical phase synchrony offers lower computational complexity and is more robust to noise compared to the existing measures.Finally, a subspace analysis framework is proposed for studying time-varying evolution of functional brain connectivity. The proposed approach identifies event intervals accounting for the underlying neurophysiological events and extracts key graphs for describing the particular intervals with minimal redundancy. Results from the application to EEG data indicate the effectiveness of the proposed framework in determining the event intervals and summarizing brain activity with a few number of representative graphs.
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Title: Directed information for complex network analysis from multivariate time series
Creator: Liu, Ying
Date: 2012
Collection: Electronic Theses & Dissertations
Description: Complex networks, ranging from gene regulatory networks in biology to social networks in sociology, havereceived growing attention from the scientific community. The analysis of complex networks employs techniquesfrom graph theory, machine learning and signal processing. In recent years, complex network analysis tools havebeen applied to neuroscience and neuroimaging studies to have a better understanding of the human brain. In thisthesis, we focus on inferring and analyzing the complex...
Show moreComplex networks, ranging from gene regulatory networks in biology to social networks in sociology, havereceived growing attention from the scientific community. The analysis of complex networks employs techniquesfrom graph theory, machine learning and signal processing. In recent years, complex network analysis tools havebeen applied to neuroscience and neuroimaging studies to have a better understanding of the human brain. In thisthesis, we focus on inferring and analyzing the complex functional brain networks underlying multichannelelectroencephalogram (EEG) recordings. Understanding this complex network requires the development of a measureto quantify the relationship between multivariate time series, algorithms to reconstruct the network based on thepairwise relationships, and identification of functional modules within the network.Functional and effective connectivity are two widely studiedapproaches to quantify the connectivity between two recordings.Unlike functional connectivity which only quantifies the statisticaldependencies between two processes by measures such as crosscorrelation, phase synchrony, and mutual information (MI), effectiveconnectivity quantifies the influence one node exerts on anothernode. Directed information (DI) measure is one of the approachesthat has been recently proposed to capture the causal relationshipsbetween two time series. Two major challenges remain with theapplication of DI to multivariate data, which include thecomputational complexity of computing DI with increasing signallength and the accuracy of estimation from limited realizations ofthe data. Expressions that can simplify the computation of theoriginal definition of DI while still quantifying the causalityrelationship are needed. In addition, the advantage of DI overconventionally causality measures such as Granger causality has notbeen fully investigated. In this thesis, we propose time-laggeddirected information and modified directed information to addressthe issue of computational complexity, and compare the performanceof this model free measure with model based measures (e.g. Grangercausality) for different realistic signal models.Once the pairwise DI between two random processes is computed,another problem is to infer the underlying structure of the complexnetwork with minimal false positive detection. We propose to useconditional directed information (CDI) proposed by Kramer to addressthis issue, and introduce the time-lagged conditional directedinformation and modified conditional directed information to lowerthe computational complexity of CDI. Three network inferencealgorithms are presented to infer directed acyclic networks whichcan quantify the causality and also detect the indirect couplingssimultaneously from multivariate data.One last challenge in the study of complex networks, specifically in neuroscience applications, is to identifythe functional modules from multichannel, multiple subject recordings. Most research on community detection inthis area so far has focused on finding the association matrix based on functional connectivity, instead ofeffective connectivity, thus not capturing the causality in the network. In addition, in order to find a modularstructure that best describes all of the subjects in a group, a group analysis strategy is needed. In thisthesis, we propose a multi-subject hierarchical community detection algorithm suitable for a group of weightedand asymmetric (directed) networks representing effective connectivity, and apply the algorithm to multichannelelectroencephalogram (EEG) data.
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Title: Discriminative sparse representations for image classification
Creator: Cardona-Romero, Suhaily
Date: 2012
Collection: Electronic Theses & Dissertations
Description: ABSTRACTDISCRIMINATIVE SPARSE REPRESENTATIONS FOR IMAGE CLASSIFICATIONBySuhaily Cardona-Romero Sparse representations and compressed sensing (CS) are two methods that have drawn the attention of the signal processing community due to their ability to reduce the dimensionality of signals while preserving enough information for signal representation. However, these compact representations do not necessarily preserve the most discriminative aspects of the signal. This thesis addresses this issue...
Show moreABSTRACTDISCRIMINATIVE SPARSE REPRESENTATIONS FOR IMAGE CLASSIFICATIONBySuhaily Cardona-Romero Sparse representations and compressed sensing (CS) are two methods that have drawn the attention of the signal processing community due to their ability to reduce the dimensionality of signals while preserving enough information for signal representation. However, these compact representations do not necessarily preserve the most discriminative aspects of the signal. This thesis addresses this issue by developing a new discriminative framework to obtain a compact representation with high discriminative information for image classification applications. The first part of this thesis presents a greedy algorithm inspired by CoSaMP with the inclusion of a new cost function that quantifies the tradeoff between discrimination power and sparsity. The inclusion of this cost function helps to select a small number of atoms from an overcomplete dictionary that produces discriminative sparse representations of images from different classes. Through experiments, it was shown that such representations can be used as features to classify new sample images even under noisy environments or missing pixels. The second part of this thesis proposes a method to obtain discriminative measurements from CS and is motivated by the fact that the presence of irrelevant features may reduce the classification accuracy. To address this issue, a feature selection step was added to CS to eliminate irrelevant features from the measurements. As a result of the elimination of such features, an improvement in the classification accuracy is observed. In conclusion, it was demonstrated that a subset of incoherent projections with high discrimination power performs better than the whole set of CS measurements for classification purposes.
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Title: Fault prognosis of bearings in electrical drives and motors
Creator: Singleton, Rodney K., II
Date: 2016
Collection: Electronic Theses & Dissertations
Description: "In recent years, there has been a growing interest in diagnosis and prognosis of motors and electrical drives. Effective and accurate diagnosis and prognosis of systems will eventually lead to condition based maintenance, which will decrease maintenance costs and system downtime, improving the reliability of electrical drives. More than 50% of motor failures are due to ball bearings. As such, the area of bearing fault diagnosis and prognosis has attracted a lot of attention in recent years....
Show more"In recent years, there has been a growing interest in diagnosis and prognosis of motors and electrical drives. Effective and accurate diagnosis and prognosis of systems will eventually lead to condition based maintenance, which will decrease maintenance costs and system downtime, improving the reliability of electrical drives. More than 50% of motor failures are due to ball bearings. As such, the area of bearing fault diagnosis and prognosis has attracted a lot of attention in recent years. Although many techniques have been successfully applied for bearing fault diagnosis, prognosis of faults and especially predicting the remaining useful life (RUL) of bearings is a remaining challenge. The main reasons for this are a lack of accurate physical degradation models, limited labeled training data, and the lack of a priori knowledge of the different health states of bearings. There are several factors that contribute to bearing failure, including the mechanical stress of a load and the electrical stress of bearing currents. Due to the intrinsic properties of motors driven by pulse-width modulation (PWM) operation, there are current paths that form from the motor shaft through the races of the bearing and back to ground. These current paths are caused by voltage division interaction with the common mode voltage and stray capacitances within the motor. One type of bearing current, electric discharge machining (EDM) current, causes a significant amount of damage to bearings. The presence of EDM currents causes pitting in the rotating elements of the bearing and ultimately leads to bearing failure. Although this relationship is well known and studied, little work has been done to relate bearing current discharge events to bearing vibrations for failure prognosis. In this work, we propose both computational and experimental approaches for RUL estimation of bearings. In Chapter 2, we present two platforms which were used to accelerate the aging process of bearings. The first, the PRONOSTIA Platform, accelerated bearing degradation via excessive loads, while collecting vibration and temperature data over the course of a run. The second platform is a new test bed we constructed to better understand the relationship between bearing currents, vibrations and failure. This test bed applies an electrical stress on test bearings to induce accelerated aging. Over the course of the experiments, we collect multiple sensor data including current, temperature, and vibration from start to failure in order to correlate current data as well as vibration data to bearing failure. In Chapter 3, we introduce an approach for learning the hidden health states of a bearing from vibration signals. This proposed approach is based on extracting multiple features from sensor signals and identifying change points in the state of the system based on these features. We also propose a framework based on temporal Hidden Markov Model for unsupervised clustering of bearing vibration data in order to identify hidden health states in the data. In Chapter 4, we introduce a data-driven methodology, which relies on both time and time-frequency domain features to track the evolution of bearing faults based on vibration signals. An extended Kalman filter is applied to these features to predict the remaining useful life and to provide a confidence interval to the RUL estimates. Performance of the proposed methods are evaluated on the PRONOSTIA experimental test bed data. In Chapter 5, we propose a computational framework that relates the current discharge events with the evolution of vibration data for a more accurate RUL estimation. We use a current discharge influx event as a trigger to perform RUL estimation on bearings using vibration data, resulting in higher accuracy and efficiency."--Pages ii-iii.
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Title: Signal processing inspired graph theoretic methods for understanding functional connectivity of the brain
Creator: Bolaños, Marcos Efren
Date: 2012
Collection: Electronic Theses & Dissertations
Description: Functional brain networks underlying cognitive control processes have been of central interest in neuroscience. A great deal of empirical and theoretical work now suggests that frontal networks in particular the medial prefrontal cortex (mPFC) and lateral prefrontal cortex (lPFC) are involved in cognitive control. The most common way to study functional brain networks has been through measures of connectivity such as coherence, synchrony and mutual information. However, it has been noted that...
Show moreFunctional brain networks underlying cognitive control processes have been of central interest in neuroscience. A great deal of empirical and theoretical work now suggests that frontal networks in particular the medial prefrontal cortex (mPFC) and lateral prefrontal cortex (lPFC) are involved in cognitive control. The most common way to study functional brain networks has been through measures of connectivity such as coherence, synchrony and mutual information. However, it has been noted that functional connectivity measures are limited to quantifying pairwise relationships between brain regions and do not describe the overall organization of the brain network. Recently, researchers have adapted tools from graph theory to address this issue. Graph theory can model a network by a set of vertices and edges upon which complex network analysis may be applied. With respect to the functional brain network, the vertices represent the individual neural assemblies and the edges are weighted by their pair-wise phase synchrony. Most graph theoretic measures, however, are limited to sparsely connected unweighted graphs. Therefore, some of the existing graph measures cannot be directly applied to the fully connected weighted graphs.In this thesis, existing graph measures and graph theoretic approaches are modified specifically for the analysis of the functional brain network. First, new weighted clustering coefficient and path length measures are introduced for quantifying the local weighted `small-world' index of the brain. These measures are based on modeling the edge weights as probabilities which represent the reliability of information flowing across these edges. These measures differ from conventional measures by considering all possible connections with varying strengths of connectivity and do notrequire arbitrary thresholding of the weighted connectivity matrix, i.e. they can be applied directly to a fully connected weighted graph. Next, concepts from signal processing are adapted to graphs to identify central vertices and anomalies within a network. These measures include new graph energy and entropy measures for graphs. The proposed graph energy measure outperforms existing definitions of graph energy for local anomaly detection because it is computed from the most relevant spectral content extracted from the graph's Laplacian matrix. A new definition of entropy rate based on modeling the adjacency matrix of a graph as a Markov process is introduced to quantify the local complexity of a weighted graph. Finally, we introduce a hierarchical consensus clustering algorithm that uses the well-known Fiedler vector to reveal a hierarchical structure of the brain network across various modular resolutions.The proposed methods are applied to error-related negativity (ERN) data, a response-locked negative deflection of the brain event-related potential observed following errors in performance tasks. Previous research shows that the primary neural generator of the ERN is the anterior cin- gulate cortex (ACC) and there is significant difference in connectivity patterns between mPFC and lPFC for error and correct responses. The proposed graph theoretic approaches give a succinct representation of the functional networks involved during action-monitoring and cognitive control and provide insight into the reorganization of the neural networks during error processing. The `small-world' measures reveal there is increased local functional segregation and integration among electrodes in the mPFC and lPFC during error responses compared to correct responses. Also, the mPFC region of the brain network demonstrated increased energy and complexity indi- cating the presence of an anomalous perturbation located around the FCz. Finally, the hierarchical consensus clustering algorithm revealed an increase in modularity across the mPFC during error responses indicating a reorganization of the underlying functional network.
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Title: Community detection in temporal multi-layer networks
Creator: Al-sharoa, Esraa Mustafa
Date: 2019
Collection: Electronic Theses & Dissertations
Description: "Many real world systems and relational data can be modeled as networks or graphs. With the availability of large amounts of network data, it is important to be able to reduce the network's dimensionality and extract useful information from it. A key approach to network data reduction is community detection. The objective of community detection is to summarize the network by a set of modules, where the similarity within the modules is maximized while the similarity between different modules...
Show more"Many real world systems and relational data can be modeled as networks or graphs. With the availability of large amounts of network data, it is important to be able to reduce the network's dimensionality and extract useful information from it. A key approach to network data reduction is community detection. The objective of community detection is to summarize the network by a set of modules, where the similarity within the modules is maximized while the similarity between different modules is minimized. Early work in graph based community detection methods focused on static or single layer networks. This type of networks is usually considered as an oversimplification of many real world complex systems, such as social networks where there may be different types of relationships that evolve with time. Consequently, there is a need for a meaningful representation of such complex systems. Recently, multi-layer networks have been used to model complex systems where the objects may interact through different mechanisms. However, there is limited amount of work in community detection methods for dynamic and multi-layer networks. In this thesis, we focus on detecting and tracking the community structure in dynamic and multi-layer networks. Two particular applications of interest are considered including temporal social networks and dynamic functional connectivity networks (dFCNs) of the brain. In order to detect the community structure in dynamic single-layer and multi-layer networks, we have developed methods that capture the structure of these complex networks. In Chapter 2, a low-rank + sparse estimation based evolutionary spectral clustering approach is proposed to detect and track the community structure in temporal networks. The proposed method tries to decompose the network into low-rank and sparse parts and obtain smooth cluster assignments by minimizing the subspace distance between consecutive time points, simultaneously. Effectiveness of the proposed approach is evaluated on several synthetic and real social temporal networks and compared to the existing state-of-the-art algorithms. As the method developed in Chapter 2 is limited to dynamic single-layer networks and can only take limited amount of historic information into account, a tensor-based approach is developed in Chapter 3 to detect the community structure in dynamic single-layer and multi-layer networks. The proposed framework is used to track the change points as well as identify the community structure across time and multiple subjects of dFCNs constructed from resting state functional magnetic resonance imaging (rs-fMRI) data. The dFCNs are summarized into a set of FC states that are consistent over time and subjects. The detected community structures are evaluated using a consistency measure. In Chapter 4, an information-theoretic approach is introduced to aggregate the dynamic networks and identify the time points that are topologically similar to combine them into a tensor. The community structure of the reduced network is then detected using a tensor based approach similar to the one described in Chapter 3. In Chapter 5, a temporal block spectral clustering framework is introduced to detect and track the community structure of multi-layer temporal networks. A set of intra- and inter-adjacency matrices is constructed and combined to create a set of temporal supra-adjacency matrices. In particular, both the connections between nodes of the network within a time window, i.e. intra-layer adjacency, as well as the connections between nodes across different time windows, i.e. inter-layer adjacency are taken into account. The community structure is then detected by applying spectral clustering to these supra-adjacency matrices. The proposed approach is evaluated on dFCNs constructed from rs-fMRI across time and subjects revealing dynamic connectivity patterns between the resting state networks (RSNs)."--Pages ii-iii.
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