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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: Smartphone-based sensing systems for data-intensive applications
Creator: Moazzami, Mohammad-Mahdi
Date: 2017
Collection: Electronic Theses & Dissertations
Description: "Supported by advanced sensing capabilities, increasing computational resources and the advances in Artificial Intelligence, smartphones have become our virtual companions in our daily life. An average modern smartphone is capable of handling a wide range of tasks including navigation, advanced image processing, speech processing, cross app data processing and etc. The key facet that is common in all of these applications is the data intensive computation. In this dissertation we have taken...
Show more"Supported by advanced sensing capabilities, increasing computational resources and the advances in Artificial Intelligence, smartphones have become our virtual companions in our daily life. An average modern smartphone is capable of handling a wide range of tasks including navigation, advanced image processing, speech processing, cross app data processing and etc. The key facet that is common in all of these applications is the data intensive computation. In this dissertation we have taken steps towards the realization of the vision that makes the smartphone truly a platform for data intensive computations by proposing frameworks, applications and algorithmic solutions. We followed a data-driven approach to the system design. To this end, several challenges must be addressed before smartphones can be used as a system platform for data-intensive applications. The major challenge addressed in this dissertation include high power consumption, high computation cost in advance machine learning algorithms, lack of real-time functionalities, lack of embedded programming support, heterogeneity in the apps, communication interfaces and lack of customized data processing libraries. The contribution of this dissertation can be summarized as follows. We present the design, implementation and evaluation of the ORBIT framework, which represents the first system that combines the design requirements of a machine learning system and sensing system together at the same time. We ported for the first time off-the-shelf machine learning algorithms for real-time sensor data processing to smartphone devices. We highlighted how machine learning on smartphones comes with severe costs that need to be mitigated in order to make smartphones capable of real-time data-intensive processing. From application perspective we present SPOT. SPOT aims to address some of the challenges discovered in mobile-based smart-home systems. These challenges prevent us from achieving the promises of smart-homes due to heterogeneity in different aspects of smart devices and the underlining systems. We face the following major heterogeneities in building smart-homes:: (i) Diverse appliance control apps (ii) Communication interface, (iii) Programming abstraction. SPOT makes the heterogeneous characteristics of smart appliances transparent, and by that it minimizes the burden of home automation application developers and the efforts of users who would otherwise have to deal with appliance-specific apps and control interfaces. From algorithmic perspective we introduce two systems in the smartphone-based deep learning area: Deep-Crowd-Label and Deep-Partition. Deep neural models are both computationally and memory intensive, making them difficult to deploy on mobile applications with limited hardware resources. On the other hand, they are the most advanced machine learning algorithms suitable for real-time sensing applications used in the wild. Deep-Partition is an optimization-based partitioning meta-algorithm featuring a tiered architecture for smartphone and the back-end cloud. Deep-Partition provides a profile-based model partitioning allowing it to intelligently execute the Deep Learning algorithms among the tiers to minimize the smartphone power consumption by minimizing the deep models feed-forward latency. Deep-Crowd-Label is prototyped for semantically labeling user's location. It is a crowd-assisted algorithm that uses crowd-sourcing in both training and inference time. It builds deep convolutional neural models using crowd-sensed images to detect the context (label) of indoor locations. It features domain adaptation and model extension via transfer learning to efficiently build deep models for image labeling. The work presented in this dissertation covers three major facets of data-driven and compute-intensive smartphone-based systems: platforms, applications and algorithms; and helps to spurs new areas of research and opens up new directions in mobile computing research."--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: Harnessing low-pass filter defects for improving wireless link performance : measurements and applications
Creator: Renani, Alireza Ameli
Date: 2018
Collection: Electronic Theses & Dissertations
Description: "The design trade-offs of transceiver hardware are crucial to the performance of wireless systems. The effect of such trade-offs on individual analog and digital components are vigorously studied, but their systemic impacts beyond component-level remain largely unexplored. In this dissertation, we present an in-depth study to characterize the surprisingly notable systemic impacts of low-pass filter design, which is a small yet indispensable component used for shaping spectrum and rejecting...
Show more"The design trade-offs of transceiver hardware are crucial to the performance of wireless systems. The effect of such trade-offs on individual analog and digital components are vigorously studied, but their systemic impacts beyond component-level remain largely unexplored. In this dissertation, we present an in-depth study to characterize the surprisingly notable systemic impacts of low-pass filter design, which is a small yet indispensable component used for shaping spectrum and rejecting interference. Using a bottom-up approach, we examine how signal-level distortions caused by the trade-offs of low-pass filter design propagate to the upper-layers of wireless communication, reshaping bit error patterns and degrading link performance of today's 802.11 systems. Moreover, we propose a novel unequal error protection algorithm that harnesses low-pass filter defects for improving wireless LAN throughput, particularly to be used in forward error correction, channel coding, and applications such as video streaming. Lastly, we conduct experiments to evaluate the unequal error protection algorithm in video streaming, and we present substantial enhancements of video quality in mobile environments."--Page ii.
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Title: MEASURING AND MODELING THE EFFECTS OF SEA LEVEL RISE ON NEAR-COASTAL RIVERINE REGIONS : A GEOSPATIAL COMPARISON OF THE SHATT AL-ARAB RIVER IN SOUTHERN IRAQ WITH THE MISSISSIPPI RIVER DELTA IN SOUTHERN LOUISIANA, USA.
Creator: Kadhim, Ameen Awad
Date: 2018
Collection: Electronic Theses & Dissertations
Description: There is a growing debate among scientists on how sea level rise (SLR) will impact coastal environments, particularly in countries where economic activities are sustained along these coasts. An important factor in this debate is how best to characterize coastal environmental impacts over time. This study investigates the measurement and modeling of SLR and effects on near-coastal riverine regions. The study uses a variety of data sources, including satellite imagery from 1975 to 2017, digital...
Show moreThere is a growing debate among scientists on how sea level rise (SLR) will impact coastal environments, particularly in countries where economic activities are sustained along these coasts. An important factor in this debate is how best to characterize coastal environmental impacts over time. This study investigates the measurement and modeling of SLR and effects on near-coastal riverine regions. The study uses a variety of data sources, including satellite imagery from 1975 to 2017, digital elevation data and previous studies. This research is focusing on two of these important regions: southern Iraq along the Shatt Al-Arab River (SAR) and the southern United States in Louisiana along the Mississippi River Delta (MRD). These sites are important for both their extensive low-lying land and for their significant coastal economic activities. The dissertation consists of six chapters. Chapter one introduces the topic. Chapter two compares and contrasts bothregions and evaluates escalating SLR risk. Chapter three develops a coupled human and natural system (CHANS) perspective for SARR to reveal multiple sources of environmental degradation in this region. Alfa century ago SARR was an important and productive region in Iraq that produced fruits like dates, crops, vegetables, and fish. By 1975 the environment of this region began to deteriorate, and since then, it is well-documented that SARR has suffered under human and natural problems. In this chapter, I use the CHANS perspective to identify the problems, and which ones (human or natural systems) are especially responsible for environmental degradation in SARR. I use several measures of ecological, economic, and social systems to outline the problems identified through the CHANS framework. SARR has experienced extreme weather changes from 1975 to 2017 resulting in lower precipitation (-17mm) and humidity (-5.6%), higher temperatures (1.6 C), and sea level rise, which are affecting the salinity of groundwater and Shatt Al Arab river water. At the same time, human systems in SARR experienced many problems including eight years of war between Iraq and Iran, the first Gulf War, UN Security Council imposed sanctions against Iraq, and the second Gulf War. I modeled and analyzed the regions land cover between 1975 and 2017 to understand how the environment has been affected, and found that climate change is responsible for what happened in this region based on other factors. Chapter four constructs and applies an error propagation model to elevation data in the Mississippi River Delta region (MRDR). This modeling both reduces and accounts for the effects of digital elevation model (DEM) error on a bathtub inundation model used to predict the SLR risk in the region. Digital elevation data is essential to estimate coastal vulnerability to flooding due to sea level rise. Shuttle Radar Topography Mission (SRTM) 1 Arc-Second Global is considered the best free global digital elevation data available. However, inundation estimates from SRTM are subject to uncertainty due to inaccuracies in the elevation data. Small systematic errors in low, flat areas can generate large errors in inundation models, and SRTM is subject to positive bias in the presence of vegetation canopy, such as along channels and within marshes. In this study, I conduct an error assessment and develop statistical error modeling for SRTM to improve the quality of elevation data in these at-risk regions. Chapter five applies MRDR-based model from chapter four to enhance the SRTM 1 Arc-Second Global DEM data in SARR. As such, it is the first study to account for data uncertainty in the evaluation of SLR risk in this sensitive region. This study transfers an error propagation model from MRDR to the Shatt al-Arab river region to understand the impact of DEM error on an inundation model in this sensitive region. The error propagation model involves three stages. First, a multiple regression model, parameterized from MRDR, is used to generate an expected DEM error surface for SARR. This surface is subtracted from the SRTM DEM for SARR to adjust it. Second, residuals from this model are simulated for SARR: these are mean-zero and spatially autocorrelated with a Gaussian covariance model matching that observed in MRDR by convolution filtering of random noise. More than 50 realizations of error were simulated to make sure a stable result was realized. These realizations were subtracted from the adjusted SRTM to produce DEM realizations capturing potential variation. Third, the DEM realizations are each used in bathtub modeling to estimate flooding area in the region with 1 m of sea level rise. The distribution of flooding estimates shows the impact of DEM error on uncertainty in inundation likelihood, and on the magnitude of total flooding. Using the adjusted DEM realizations 47 ± 2 percent of the region is predicted to flood, while using the raw SRTM DEM only 28% of the region is predicted to flood.
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Title: LIDAR AND CAMERA CALIBRATION USING A MOUNTED SPHERE
Creator: Li, Jiajia
Date: 2020
Collection: Electronic Theses & Dissertations
Description: Extrinsic calibration between lidar and camera sensors is needed for multi-modal sensor data fusion. However, obtaining precise extrinsic calibration can be tedious, computationally expensive, or involve elaborate apparatus. This thesis proposes a simple, fast, and robust method performing extrinsic calibration between a camera and lidar. The only required calibration target is a hand-held colored sphere mounted on a whiteboard. The convolutional neural networks are developed to automatically...
Show moreExtrinsic calibration between lidar and camera sensors is needed for multi-modal sensor data fusion. However, obtaining precise extrinsic calibration can be tedious, computationally expensive, or involve elaborate apparatus. This thesis proposes a simple, fast, and robust method performing extrinsic calibration between a camera and lidar. The only required calibration target is a hand-held colored sphere mounted on a whiteboard. The convolutional neural networks are developed to automatically localize the sphere relative to the camera and the lidar. Then using the localization covariance models, the relative pose between the camera and lidar is derived. To evaluate the accuracy of our method, we record image and lidar data of a sphere at a set of known grid positions by using two rails mounted on a wall. The accurate calibration results are demonstrated by projecting the grid centers into the camera image plane and finding the error between these points and the hand-labeled sphere centers.
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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: Signal Processing Based Distortion Mitigation in Interferometric Radar Angular Velocity Estimation
Creator: Klinefelter, Eric
Date: 2021
Collection: Electronic Theses & Dissertations
Description: Interferometric angular velocity estimation is a relatively recent radar technique which uses a pair of widely spaced antenna elements and a correlation receiver to directly measure the angular velocity of a target. Traditional radar systems measure range, radial velocity (Doppler), and angle, while angular velocity is typically derived as the time-rate change of the angle measurements. The noise associated with the derived angular velocity estimate is statistically correlated with the angle...
Show moreInterferometric angular velocity estimation is a relatively recent radar technique which uses a pair of widely spaced antenna elements and a correlation receiver to directly measure the angular velocity of a target. Traditional radar systems measure range, radial velocity (Doppler), and angle, while angular velocity is typically derived as the time-rate change of the angle measurements. The noise associated with the derived angular velocity estimate is statistically correlated with the angle measurements, and thus provides no additional information to traditional state space trackers. Interferometric angular velocity estimation, on the other hand, provides an independent measurement, thus forming a basis in R2 for both position and velocity.While promising results have been presented for single target interferometric angular velocity estimation, there is a known issue which arises when multiple targets are present. The ideal interferometric response with multiple targets would contain only the mixing product between like targets across the antenna responses, yet instead, the mixing product between all targets is generated, resulting in unwanted `cross-terms' or intermodulation distortion. To date, various hardware based methods have been presented, which are effective, though they tend to require an increased number of antenna elements, a larger physical system baseline, or signals with wide bandwidths. Presented here are novel methods for signal processing based interferometric angular velocity estimation distortion mitigation, which can be performed with only a single antenna pair and traditional continuous-wave or frequency-modulated continuous wave signals.In this work, two classes of distortion mitigation methods are described: model-based and response decomposition. Model-based methods use a learned or analytic model with traditional non-linear optimization techniques to arrive at angular velocity estimates based on the complete interferometric signal response. Response decomposition methods, on the other hand, aim to decompose the individual antenna responses into separate responses pertaining to each target, then associate like targets between antenna responses. By performing the correlation in this manner, the cross-terms, which typically corrupt the interferometric response, are mitigated. It was found that due to the quadratic scaling of distortion terms, model-based methods become exceedingly difficult as the number of targets grows large. Thus, the method of response decomposition is selected and results on measured radar signals are presented. For this, a custom single-board millimeter-wave interferometric radar was developed, and angular velocity measurements were performed in an enclosed environment consisting of two robotic targets. A set of experiments was designed to highlight easy, medium, and difficult cases for the response decomposition algorithm, and results are presented herein.
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Title: Safe Control Design for Uncertain Systems
Creator: Marvi, Zahra
Date: 2021
Collection: Electronic Theses & Dissertations
Description: This dissertation investigates the problem of safe control design for systems under model and environmental uncertainty. Reinforcement learning (RL) provides an interactive learning framework in which the optimal controller is sequentially derived based on instantaneous reward. Although powerful, safety consideration is a barrier to the wide deployment of RL algorithms in practice. To overcome this problem, we proposed an iterative safe off-policy RL algorithm. The cost function that encodes...
Show moreThis dissertation investigates the problem of safe control design for systems under model and environmental uncertainty. Reinforcement learning (RL) provides an interactive learning framework in which the optimal controller is sequentially derived based on instantaneous reward. Although powerful, safety consideration is a barrier to the wide deployment of RL algorithms in practice. To overcome this problem, we proposed an iterative safe off-policy RL algorithm. The cost function that encodes the designer's objectives is augmented with a control barrier function (CBF) to ensure safety and optimality. The proposed formulation provides a look-ahead and proactive safety planning, in which the safety is planned and optimized along with the performance to minimize the intervention with the optimal controller. Extensive safety and stability analysis is provided and the proposed method is implemented using the off-policy algorithm without requiring complete knowledge about the system dynamics. This line of research is then further extended to have a safety and stability guarantee even during the data collection and exploration phases in which random noisy inputs are applied to the system. However, satisfying the safety of actions when little is known about the system dynamics is a daunting challenge. We present a novel RL scheme that ensures the safety and stability of the linear systems during the exploration and exploitation phases. This is obtained by having a concurrent model learning and control, in which an efficient learning scheme is employed to prescribe the learning behavior. This characteristic is then employed to apply only safe and stabilizing controllers to the system. First, the prescribed errors are employed in a novel adaptive robustified control barrier function (AR-CBF) which guarantees that the states of the system remain in the safe set even when the learning is incomplete. Therefore, the noisy input in the exploratory data collection phase and the optimal controller in the exploitation phase are minimally altered such that the AR-CBF criterion is satisfied and, therefore, safety is guaranteed in both phases. It is shown that under the proposed prescribed RL framework, the model learning error is a vanishing perturbation to the original system. Therefore, a stability guarantee is also provided even in the exploration when noisy random inputs are applied to the system. A learning-enabled barrier-certified safe controllers for systems that operate in a shared and uncertain environment is then presented. A safety-aware loss function is defined and minimized to learn the uncertain and unknown behavior of external agents that affect the safety of the system. The loss function is defined based on safe set error, instead of the system model error, and is minimized for both current samples as well as past samples stored in the memory to assure a fast and generalizable learning algorithm for approximating the safe set. The proposed model learning and CBF are then integrated together to form a learning-enabled zeroing CBF (L-ZCBF), which employs the approximated trajectory information of the external agents provided by the learned model but shrinks the safety boundary in case of an imminent safety violation using instantaneous sensory observations. It is shown that the proposed L-ZCBF assures the safety guarantees during learning and even in the face of inaccurate or simplified approximation of external agents, which is crucial in highly interactive environments. Finally, the cooperative capability of agents in a multi-agent environment is investigated for the sake of safety guarantee. CBFs and information-gap theory are integrated to have robust safe controllers for multi-agent systems with different levels of measurement accuracy. A cooperative framework for the construction of CBFs for every two agents is employed to maximize the horizon of uncertainty under which the safety of the overall system is satisfied. The information-gap theory is leveraged to determine the contribution and share of each agent in the construction of CBFs. This results in the highest possible robustness against measurement uncertainty. By employing the proposed approach in constructing CBF, a higher horizon of uncertainty can be safely tolerated and even the failure of one agent in gathering accurate local data can be compensated by cooperation between agents. The effectiveness of the proposed methods is extensively examined in simulation results.
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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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