Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 31 for “"Low-rank approximation"”.
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Dynamic speech imaging with low-rank approximation
… However, conventional MRI suffers from low spatiotemporal resolution, which limits its applica-tion in dynamic speech imaging. This thesis presents a novel model-based dynamic MR imaging method to capture speech dynamics in high spatiotemporal resolution. Specifically, high …
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Bounds and Low-Rank Approximation for Controlled Markov Processes
… shed light on fundamental limits, allowing us to distinguish situations where intrinsic noise masks poor decisions from situations where any attempt of improvement is futile. We connect infinite-dimensional linear programming over cones of occupation measures to techniques for …
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Applications of low-rank approximation: complex networks and inverse problems
The use of low-rank approximation is crucial when one is interested in solving problems of large dimension. In this case, the matrix with reduced rank can be obtained starting from the singular value decomposition considering only the largest components. This thesis describes how the use of the …
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Large scale urban patterns in NYC: traffic prediction and analysis via clustering and low rank approximation
… prediction and analysis via clustering and low rank approximation. Our work consists of several dependent, large-scale optimization problems in order to estimate the number of taxi passengers who travel from a certain origin node to a certain destination node at any given time of day. A …
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Real-Time Detection of GPS Spoofing Attack with Hankel Matrix and Unwrapped Phase Angle Data
… two attacks. Previous researchers exploited low-rank approximation of Hankel Matrix to differentiate between FDIA and physical events. We have demonstrated that, together with angle unwrapping algorithm, low-rank approximation of Hankel Matrix can help us separating GPS-spoofing attack with …
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Analytical and Numerical Study of Lindblad Equations
… more explicit scaling for parameters when the approximations are made. Moreover, we derive a classical master equation based on the Lindbladian formalism.</p><p>In Chp. 3, we consider numerical aspects of Lindblad equations. Motivated by the dynamical low-rank approximation method for matrix …
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The power of randomized algorithms : from numerical linear algebra to biological systems
… algebra. In particular, we give a randomized low-rank approximation algorithm for positive semidefinite matrices that runs in sublinear time, significantly improving upon what is possible with traditional deterministic methods. We also discuss lower bounds on low-rank approximation and …
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High-order retractions for reduced-order modeling and uncertainty quantification
… to efficiently evolve the dynamics of a system's low-rank approximation. Through the study of differential geometry, we are able to analyze the error incurred at each time step. A novel, explicit, computationally inexpensive set of algorithms, which we call perturbative retractions, are proposed …
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Faster linear algebra for data analysis and machine learning
… include singular value decomposition and low-rank approximation, several varieties of linear regression, data clustering, and nonlinear kernel methods. To scale these problems to massive datasets, we design new algorithms based on random sampling and iterative refinement, tools that have …
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Complex data analytics via sparse, low-rank matrix approximation
… Specifically, we have achieved the following: 1) we develop Exemplar-based low-rank sparse Matrix Decomposition (EMD), a novel method for fast clustering large-scale data by incorporating low-rank approximations into matrix decomposition-based clustering; 2) we propose ECKF, a general …
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Dimensionality reduction for sparse and structured matrices
… discuss connections and possible extensions to low-rank approximation, k-means clustering, and several other ubiquitous matrix problems.
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Model-Architecture Co-design of Deep Neural Networks for Embedded Systems
… I first developed a lossy three-stage low-rank approximation scheme that can reduce the computational complexity of a pre-trained model by 3-5x and up to 8-9x for individual convolutional layers. This scheme requires restructuring of the convolutional layers and generally suits the …
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Nearly tight oblivious subspace embeddings by trace inequalities
… problems such as as least squares regression and low-rank approximation. This new method is based on elementary tail bounds combined with matrix trace inequalities (Golden-Thompson or Lieb's theorem), and does not require combinatorics, unlike the Nelson-Nguyen approach. There are also variants of …
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New directions in streaming algorithms
… algorithms of the frequency estimation and low-rank approximation problems with machine learning oracles in order to improve their space-accuracy tradeoffs. The new algorithms combine the benefits of machine learning with the formal guarantees available through algorithm design theory.
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Novel Fast Algorithms For Low Rank Matrix Approximation
<p>Recent advances in matrix approximation have seen an emphasis on randomization techniques in which the goal was to create a sketch of an input matrix. This sketch, a random submatrix of an input matrix, having much fewer rows or columns, still preserves its relevant features. In one of such …
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Sampling-based algorithms for dimension reduction
Can one compute a low-dimensional representation of any given data by looking only at its small sample, chosen cleverly on the fly? Motivated by the above question, we consider the problem of low-rank matrix approximation: given a matrix A..., one wants to compute a rank-k matrix (where k << min{m, …
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Solution of large scale elastic problems with the boundary element method : applications to infrasound and micro-seismicity generated by wind turbines
… regions. Such a problem is the estimation of low-frequency noise and soil waves generated by a wind turbine (WT) because of its structural dynamic behavior. However, due to the size of that problem, the BEM becomes insufficient requiring very time consuming computations and almost forbidden …
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Geostatistical methods for disease prevalence mapping
Geostatistical methods are increasingly used in low-resource settings where disease registries are either non-existent or geographically incomplete. In this thesis, which is comprised of four papers, we address some of the common issues that arise from analysing disease prevalence data. In the …
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Scalable Bayesian Matrix and Tensor Factorization for Discrete Data
… of scalable Bayesian factorization models for low rank approximation of massive matrix or tensors with binary and count-valued observations. The proposed models enjoy the following properties: (1) The inference complexity scales linearly in the number of non-zeros in the data; (2) The …
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Krylov subspace estimation
… path of a given Gaussian random process and a low-rank approximation to the covariance matrix of a given process. The algorithm is compared to existing algorithms for realization in terms of an analytical estimate of computational cost and an experimental characterization of overall …
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