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 15 of 15 for “"Tensor decompositions"”.
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Algorithms and software for efficient tensor decompositions
Tensors, which generalize vectors and matrices to higher dimensions, provide a powerful framework for representing and analyzing multi-way data arising in science and engineering. Their ability to capture complex, multi-relational structures makes them invaluable in applications ranging from …
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Asymptotic staticity and tensor decompositions with fast decay conditions
… lack of surjectivity of a certain operator. Some tensor decompositions in asymptotically flat manifolds exhibit some of the difficulties encountered above. The Helmholtz decomposition, which plays a role in the preparation of initial data for the Maxwell equations, is discussed as a model problem. …
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ON THE EFFICIENCY OF ALGORITHMS FOR TENSOR DECOMPOSITIONS AND THEIR APPLICATIONS
Multi-dimensional arrays, or tensors, are fundamental objects in computational science for their ability to store multi-dimensional data and to encode bilinear forms. We will consider algorithms and applications of the CP and Tucker tensor decompositions, focusing our efforts on optimizing …
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Towards efficient algorithms and systems for tensor decompositions and tensor networks
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-03-01 without embargo terms
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Continuous low-rank tensor decompositions, with applications to stochastic optimal control and data assimilation
… framework tightly integrates two emerging areas: tensor decompositions and continuous computation. Tensor decompositions are able to effectively compress and operate with low-rank multidimensional arrays. Continuous computation is a paradigm for computing with functions instead of arrays, and it …
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Parallel Algorithms for and Applications of the Dense Canonical Polyadic Decomposition
Tensor decompositions have gained popularity in various research communities as a means of analyzing high dimensional, complex data.
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Understanding Deep Learning via Analyzing Training Dynamics
… analysis techniques of training dynamics in tensor decompositions and then showcase the explanation of two phenomena by analyzing gradient descent dynamics. </p><p>In the first part, we analyze the gradient descent dynamics in over-parameterized tensor decompositions. For non-orthogonal …
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CONVERGENGE ANALYSIS ON SVD-BASED ALGORITHMS FOR TENSOR LOW RANK APPROXIMATIONS
This thesis is to study a few problems on tensor decompositions and approximations in real space. Among other things, we revisit the classical problem of finding the best rank-R CANDECOMP/PARAFAC(CP) approximation with diff erent cases R > 1 and R = 1 respectively. Unlike the rank-1 approximation …
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Tensor Methods for Signal Reconstruction and Network Embedding
… principled alternatives, such as multi-linear tensor methods, that are also effective and oftentimes significantly outperform neural network approaches. In the era of data deluge, multi-dimensional data, also known as tensors, are ubiquitous in a number of engineering tasks and data analytics. …
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Multivariate Rational Approximation in Action: From Data-driven Modeling to Nonlinear Eigenvalue Problems
… improves scalability by incorporating low-rank tensor decompositions into the framework. Second, we generalize p-AAA to arbitrary data sets by deriving novel formulations of least-squares problems that incorporate interpolation constraints on scattered data sets. Several numerical experiments …
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Portfolio Optimization Using Financial Chaos Index and Time-Homogeneous Top-K Ranking
… of asset prices. This new index relies on a tensor-based embedding of the stock market information, which in turn frees it from the restrictive value- or capitalization-weighting assumptions that commonly underlie other various popular indexes. We show that our index is a robust estimator of …
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Parallel Gauss-Newton method for CP decomposition
… we leverage a formulation that employs tensor contractions for implicit matrix-vector products within the conjugate gradient method. The use of tensor contractions enables us to employ the Cyclops library for distributed-memory tensor computations to parallelize the Gauss-Newton approach …
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Optimization Algorithms for Structured Machine Learning and Image Processing Problems
… lasso), unsupervised learning (e.g., robust tensor decompositions), and total-variation image denoising. These algorithms are of wide interest to the optimization, machine learning, and image processing communities. Specifically, (i) we present two algorithms to solve the Group Lasso problem. …
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Relative waring rank of binary forms
This Dissertation was approved for publication on 2017-07-05 at 08:54.
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Uncertainty quantification for integrated circuits and microelectrornechanical systems
… At the high-level, a fast algorithm based on tensor decompositions is proposed to compute the basis functions and Gauss quadrature points. Our algorithm is verified by some MEMS/IC co-design examples with both low-dimensional and high-dimensional (up to 184) random parameters, showing about …