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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: 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: High-dimensional learning from random projections of data through regularization and diversification
Creator: Aghagolzadeh, Mohammad
Date: 2015
Collection: Electronic Theses & Dissertations
Description: Random signal measurement, in the form of random projections of signal vectors, extends the traditional point-wise and periodic schemes for signal sampling. In particular, the well-known problem of sensing sparse signals from linear measurements, also known as Compressed Sensing (CS), has promoted the utility of random projections. Meanwhile, many signal processing and learning problems that involve parametric estimation do not consist of sparsity constraints in their original forms. With the...
Show moreRandom signal measurement, in the form of random projections of signal vectors, extends the traditional point-wise and periodic schemes for signal sampling. In particular, the well-known problem of sensing sparse signals from linear measurements, also known as Compressed Sensing (CS), has promoted the utility of random projections. Meanwhile, many signal processing and learning problems that involve parametric estimation do not consist of sparsity constraints in their original forms. With the increasing popularity of random measurements, it is crucial to study the generic estimation performance under the random measurement model. In this thesis, we consider two specific learning problems (named below) and present the following two generic approaches for improving the estimation accuracy: 1) by adding relevant constraints to the parameter vectors and 2) by diversification of the random measurements to achieve fast decaying tail bounds for the empirical risk function.The first problem we consider is Dictionary Learning (DL). Dictionaries are extensions of vector bases that are specifically tailored for sparse signal representation. DL has become increasingly popular for sparse modeling of natural images as well as sound and biological signals, just to name a few. Empirical studies have shown that typical DL algorithms for imaging applications are relatively robust with respect to missing pixels in the training data. However, DL from random projections of data corresponds to an ill-posed problem and is not well-studied. Existing efforts are limited to learning structured dictionaries or dictionaries for structured sparse representations to make the problem tractable. The main motivation for considering this problem is to generate an adaptive framework for CS of signals that are not sparse in the signal domain. In fact, this problem has been referred to as 'blind CS' since the optimal basis is subject to estimation during CS recovery. Our initial approach, similar to some of the existing efforts, involves adding structural constraints on the dictionary to incorporate sparse and autoregressive models. More importantly, our results and analysis reveal that DL from random projections of data, in its unconstrained form, can still be accurate given that measurements satisfy the diversity constraints defined later.The second problem that we consider is high-dimensional signal classification. Prior efforts have shown that projecting high-dimensional and redundant signal vectors onto random low-dimensional subspaces presents an efficient alternative to traditional feature extraction tools such as the principle component analysis. Hence, aside from the CS application, random measurements present an efficient sampling method for learning classifiers, eliminating the need for recording and processing high-dimensional signals while most of the recorded data is discarded during feature extraction. We work with the Support Vector Machine (SVM) classifiers that are learned in the high-dimensional ambient signal space using random projections of the training data. Our results indicate that the classifier accuracy can be significantly improved by diversification of the random measurements.
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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: Noise-shaping stochastic optimization and online learning with applications to digitally-assisted analog circuits
Creator: Shaga, Ravi Krishna
Date: 2011
Collection: Electronic Theses & Dissertations
Description: Analog circuits that use on-chip digital-to-analog converters for calibration use DSP based algorithms for optimizing and calibrating the system parameters. However, the performance of traditional online-gradient descent based optimization and calibration algorithms suffer from artifacts due to quantization noise which adversely affects the real-time and precise convergence to the desired parameters. This thesis proposes and analyzes a novel class of on-line learning algorithms that can noise...
Show moreAnalog circuits that use on-chip digital-to-analog converters for calibration use DSP based algorithms for optimizing and calibrating the system parameters. However, the performance of traditional online-gradient descent based optimization and calibration algorithms suffer from artifacts due to quantization noise which adversely affects the real-time and precise convergence to the desired parameters. This thesis proposes and analyzes a novel class of on-line learning algorithms that can noise-shape the effect of quantization noise during the adaptation procedure and in the process achieve faster spectral convergence compared to the conventional quantized gradient-descent approach. We extend the proposed framework to higher-order noise-shaping and derive criteria for achieving optimal system performance. The thesis also explores the application of stochastic perturbative gradient descent techniques to the proposed noise-shaping online learning framework where we show the performance of the stochastic algorithm can be improved in the spectral domain. The thesis applies the proposed optimization method for online calibration of subthreshold analog circuits where artifacts like mismatch and non-linearity are more pronounced. We also show that even with non-monotonic calibration DACs, the proposed algorithm is still able to find an optimal system solution without getting trapped into local minima. Using measured results obtained from prototype fabricated in a 0.5μm CMOS process, we demonstrate the robustness of the proposed algorithm for the task of: (a) compensating and tracking of offset parameters; and (b) calibration of the center frequency of a sub-threshold gm-C biquad filter.
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Title: Data analysis and selection for statistical machine translation
Creator: Eetemadi, Sauleh
Date: 2016
Collection: Electronic Theses & Dissertations
Description: Statistical Machine Translation has received significant attention from the academic community over the past decade which has led to significant improvements in machine translation quality. As a result it is widely adopted in the industry (Google, Microsoft, Twitter, Facebook, ... etc.) as well as the government (http://nist.gov). The biggest factor in this improvement has been the availability of ever increasing sources of training data as digital multilingual communication and information...
Show moreStatistical Machine Translation has received significant attention from the academic community over the past decade which has led to significant improvements in machine translation quality. As a result it is widely adopted in the industry (Google, Microsoft, Twitter, Facebook, ... etc.) as well as the government (http://nist.gov). The biggest factor in this improvement has been the availability of ever increasing sources of training data as digital multilingual communication and information dissemination become ubiquitous. Relatively little research has been done on training data analysis and selection, despite training data being the main contributor of machine translation quality.In this work, we first examine fundamental properties of translated and authored text. We introduce a new linguistically motivated feature (Part of Speech Tag Minimal Translation Units) that outperforms prior work in sentence level translation direction detection. Next, we develop a cross-domain data matrix that enables comparison between different features in the translation direction detection task. We extend our previously introduced feature for translation direction detection to use statistically trained brown clusters instead of part of speech tags. This new feature outperforms all prior work in all cross-domain data matrix combinations.Data selection in machine translation is performed in different scenarios with different objectives including: reducing training resource consumption, domain adaptation, improving quality or reducing deployment size. We develop an efficient (computational complexity and memory consumption is linear in training data size) framework for training data selection and compression called Vocabulary Saturation Filter (VSF). In our experiments we show the machine translation system trained on data selected using VSF is comparable to prior data selection methods with quadratic computational complexity. However, VSF is sensitive to data order. Therefore we experiment with different orderings of the data and compare the results.Finally, we develop a highly scalable and flexible data selection framework where arbitrary sentence level features can be used for data selection. In addition, a variable threshold function can be used to incorporate any scoring function that is constant throughout the selection process. After introducing this framework, inspired by the features we introduced for detecting translation direction, we use joint models of source and target using Minimal Translation Units (MTU) in addition to source side context using brown clusters to compare various features and threshold functions within this framework. We run end-to-end experiments using data selected by various methods and compare the statistical translation models using various test sets and phrase table comparison metrics.
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Title: Tracking single-units in chronic neural recordings for brain machine interface applications
Creator: Eleryan, Ahmed Ibrahim
Date: 2013
Collection: Electronic Theses & Dissertations
Description: Ensemble recording of multiple single-unit activity has been used to study the mechanisms of neural population coding over prolonged periods of time, and to perform reliable neural decoding in neuroprosthetic motor control applications. However, there are still many challenges towards achieving reliable stable single-units recordings. One primary challenge is the variability in spike waveform features and firing characteristics of single units recorded using chronically implanted...
Show moreEnsemble recording of multiple single-unit activity has been used to study the mechanisms of neural population coding over prolonged periods of time, and to perform reliable neural decoding in neuroprosthetic motor control applications. However, there are still many challenges towards achieving reliable stable single-units recordings. One primary challenge is the variability in spike waveform features and firing characteristics of single units recorded using chronically implanted microelectrodes, making it challenging to ascertain the identity of the recorded neurons across days. In this study, I present a fast and efficient algorithm that tracks multiple single-units recorded in non-human primates performing brain control of a robotic limb, based on features extracted from units' average waveforms and interspike intervals histograms. The algorithm requires a relatively short recording duration to perform the analysis and can be applied at the start of each recording session without requiring the subject to be engaged in a behavioral task. The algorithm achieves a classification accuracy of up to 90% compared to manual tracking. I also explore using the algorithm to develop an automated technique for unit selection to perform reliable decoding of movement parameters from neural activity.
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Title: Neural mechanisms of goal-directed action selection by prefrontal cortex : implications for brain-machine interfaces
Creator: Mohebi, Ali
Date: 2014
Collection: Electronic Theses & Dissertations
Description: Initiating a movement goal and maintaining that goal throughout the planning and execution of a goal-directed action is an essential element of all goal-directed behavior. In thecontext of Brain Machine Interfaces (BMIs), a direct communication pathway between thebrain and a man-made computing device, continuous access to movement goals is essential,so as to guide the control of neuroprosthetic limbs that provide neurologically impaired subjects with an alternative to their lost motor...
Show moreInitiating a movement goal and maintaining that goal throughout the planning and execution of a goal-directed action is an essential element of all goal-directed behavior. In thecontext of Brain Machine Interfaces (BMIs), a direct communication pathway between thebrain and a man-made computing device, continuous access to movement goals is essential,so as to guide the control of neuroprosthetic limbs that provide neurologically impaired subjects with an alternative to their lost motor function. The Prefrontal cortex (PFC) has beensuggested as an executive control area of the brain that bridges the temporal gap betweenincoming sensory information and ensuing motor actions. The mechanisms underlying thedynamics of PFC neural activity, however, remain poorly understood. The main objectiveof this dissertation is to elucidate the role of PFC neurons in mediating goal initiation andmaintenance during goal-directed behavior.Using a combination of electrophysiological recordings, optogenetic and pharmacological manipulation of population activity and behavioral assays in awake behaving subjects,we demonstrate that the PFC plays a critical role in the planning and execution of a twoalternative forced choice task. In particular, PFC neurons were mostly goal selective duringthe choice epoch of the task when subjects had to select the action with the highest utility while suppressing all other unrewarded actions. Decoding PFC neural activity usingadvanced machine learning algorithms showed robust single trial prediction of motor goals,suggesting that PFC may be a candidate site for inferring volitional motor intent. In addition, results from inactivation experiments demonstrate a lateralized performance declinewith respect to the inactivation site, further confirming the critical role of the PFC in mediating the motor- but not the sensory- information during the execution of goal-directedbehavior. Taken together, our results suggest that the design of next generation BMIs couldbe further improved by incorporating goal information from cognitive control areas of thebrain, thereby augmenting the capability of current designs that only rely on decoding themoment-by-moment kinematics of intended limb movements from motor areas of the brain.
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Title: Statistical signal processing tools for analyzing large-scale neural ensembles
Creator: Aghagolzadeh, Mehdi
Date: 2012
Collection: Electronic Theses & Dissertations
Description: Understanding how a neuron processes information and communicates with other neurons is key to unravel the brain's mechanisms underlying perception, learning and motor processing. Key to characterize neurons acting in concert is the ability to simultaneously measure their firing patterns in awake behaving subjects. Microelectrode arrays (MEAs) implanted in the brain allow simultaneous monitoring of the activity of large ensembles of cells while subjects carry out specific tasks. Isolating the...
Show moreUnderstanding how a neuron processes information and communicates with other neurons is key to unravel the brain's mechanisms underlying perception, learning and motor processing. Key to characterize neurons acting in concert is the ability to simultaneously measure their firing patterns in awake behaving subjects. Microelectrode arrays (MEAs) implanted in the brain allow simultaneous monitoring of the activity of large ensembles of cells while subjects carry out specific tasks. Isolating the spike pattern characterizing each cell's signature firing requires sophisticated signal processing algorithms, particularly to track the nonstationary behavior of these waveforms over extended periods of time. In this thesis, we introduce a compressive spike sorting technique that discriminates spike patterns from individual neurons using a sparse representation of the ensemble raw data. An iterative learning algorithm is introduced to estimate and adapt a set of optimal thresholds that maximize the separability between spike classes while minimizing the average waveform reconstruction error. Once derived, spike trains are then used to infer functional connectivity patterns among the recorded neural ensemble constituents. We introduce two information-theoretic approaches within the realm of graphical models that capture the spatiotemporal dependency between neurons' spiking patterns. Specifically, the class of spatiotemporal maximum entropy models is shown to incorporate higher-order interactions. We demonstrate the richness of these techniques in improving our understanding of neural function and dysfunction at the millisecond and micron resolutions, and their potential to be applied in emerging applications of brain machine interface technology to help improve the lifestyle of people with severe disabilities.
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Title: Sparse and redundant models for data mining and consumer video summarization
Creator: Dang, Chinh Trung
Date: 2015
Collection: Electronic Theses & Dissertations
Description: This dissertation develops new data mining and representative selection techniques for consumervideo data using sparse and redundant models. Extracting key frames1 and key excerptsfrom video has important roles in many applications, such as to facilitate browsing a large videocollection, to support automatic video retrieval, video search, video compression, etc. In addition,a set of key frames or video summarization in general helps users to quickly access importantsections (in semantic...
Show moreThis dissertation develops new data mining and representative selection techniques for consumervideo data using sparse and redundant models. Extracting key frames1 and key excerptsfrom video has important roles in many applications, such as to facilitate browsing a large videocollection, to support automatic video retrieval, video search, video compression, etc. In addition,a set of key frames or video summarization in general helps users to quickly access importantsections (in semantic meaning) in a video sequence, and hence enable rapid viewing.The current literature on video summarization has focused mainly on certain types of videosthat conform to well-defined structures and characteristics that facilitates key frame extraction.Some of these typical types of videos include sports, news, TV drama, movie dialog, documentaryvideos, and medical video. The prior techniques on well-defined structured/professional videoscannot be applied into consumer (or personal generated) videos acquired from digital cameras.Meanwhile, consumer video is increasing rapidly due to the popularity of handheld consumerdevices, on-line social networks and multimedia sharing websites.Consumer video has no particular structure or well-defined theme. The mixed sound trackcoming from multiple sound sources, along with severe noise make it difficult to identify semanticallymeaningful audio segments for key frames. In addition, consumer videos typically have onelong shot with low quality visuals due to various factors such as camera shake and poor lightingalong with no fixed features (subtitles, text captions) that could be exploited for further information to evaluate the importance of frames or segments. For many of these reasons, consumer-videosummarization is still a very challenging problem area.In this dissertation, we present new frameworks based on sparse and redundant models of imageand video dataset toward solving the consumer video summarization problem. In particular, in thisdissertation, we investigate three different models of image and video data for summarization.1. Sparse representation of video framesWe exploit the self-expressiveness property to create `1 norm sparse graph, which is applicablefor huge high dimensional dataset. A spectral clustering algorithm has been appliedinto the sparse graph for the selection of a set of clusters. Our work analyzes each cluster asone point in a Grassmann manifold and then selects an optimal set of clusters. The final representativeis evaluated using a graph centrality technique for the sub-graph correspondingwith each selected cluster.2. Sparse and low rank model for video framesA novel key frame extraction framework based on Robust Principal Component Analysis isproposed to automatically select a set of maximally informative frames from an input video.The framework is developed from a novel perspective of low rank and sparse components,in which the low rank component of a video frame reveals the relationship of that frameto the whole video sequence, and the sparse component indicates the distinct informationof particular frames. A set of key frames are identified by solving an `1 norm based nonconvexoptimization problem where the solution minimizes the reconstruction errors of thewhole dataset for a given set of selected key frames and maximizes the sum of distinctinformation. Moreover, the algorithm provides a mechanism for adapting new observations,and consequently, updating new set of key frames.3. Sparse/redundant representation for a single video frameWe propose a new patch-based image/video analysis approach. Using the new model, wecreate a new feature that we refer to as the heterogeneity image patch (HIP) index of an imageor a video frame. The HIP index, which is evaluated using patch-based image/video analysis,provides a measure for the level of heterogeneity (and hence the amount of redundancy) thatexists among patches of an image/video frame. We apply the proposed HIP frameworkto solve both of the video summarization problem areas: key frame extraction and videoskimming.
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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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