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 52 for “"Matrix completion"”.
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Low rank matrix completion
We consider the problem of recovering a low rank matrix given a sampling of its entries. Such problems are of considerable interest in a diverse set of fields including control, system identification, statistics and signal processing. Although the general low rank matrix completion problem is …
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Algorithms for matrix completion
We consider collaborative filtering methods for matrix completion. A typical approach is to find a low rank matrix that matches the observed ratings. However, the corresponding problem has local optima. In this thesis, we study two approaches to remedy this issue: reference vector method and trace …
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Deterministic network coding by matrix completion
… is based on a new algorithm for maximum-rank completion of mixed matrices-taking a matrix whose entries are a mixture of numeric values and symbolic variables, and assigning values to the variables so as to maximize the resulting matrix rank. Our algorithm is faster than existing deterministic …
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Exploiting Observation Bias to Improve Matrix Completion
We consider a variant of matrix completion where entries are revealed in a biased manner, adopting a model akin to that introduced by Ma & Chen (2019) [1]. Instead of treating this observation bias as a disadvantage, as is typically the case, the goal is to exploit the shared information between …
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Theory and Applications of Matrix Completion in Genomics Datasets
… use of the novel Neural Tangent Kernel (NTK) in matrix completion. We derive the functional form of the NTK for a single-hidden-layer, infinite-width neural network with ReLU activation, and develop a framework applying the NTK to matrix completion. We explore a specific application of this …
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Blind regression : understanding collaborative filtering from matrix completion to tensor completion
… We apply our framework to the problem of matrix completion and give a nonparametric method which, similar to CF, combines the local estimates according to the distance between the neighbors. We use the sample variance of the difference in ratings between neighbors as the proximity of the …
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Matrix completion algorithms with applications in biomedicine, e-commerce and social science
This thesis investigates matrix completion algorithms with applications in biomedicine, e-commerce and social science. In general, matrix completion algorithms work well for low rank matrices. Such matrices find many applications in recommender systems and social network analysis. On the other …
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Ultraconnected and Critical Graphs
… graphs in the positive definite partial matrix completion problem. We completely characterize when the join of graphs is ultraconnected, and prove that ultraconnectivity is preserved by Cartesian products. We completely characterize when adding a vertex to an ultraconnected graph …
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Perspectives on Geometry and Optimization: from Measures to Neural Networks
This thesis explores geometrical aspects of matrix completion, interior point methods, unbalanced optimal transport, and neural network training. We use these examples to illustrate four ways in which geometry plays key yet fundamentally different roles in optimization. The first part explores the …
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Algorithms for Large-scale Data Analytics and Applications to the COVID-19 Pandemic
… 1, we consider a novel reformulation of the matrix completion problem and developed a projected stochastic gradient descent method, fastImpute, to solve matrix completion 20x faster than state-of-the-art methods while providing optimality guarantees. In Chapter 2, we introduce the …
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Low rank methods for optimizing clustering
… We utilize low rank structures in the solution matrix of the convex formulation and use a low-rank factorization of the solution matrix directly as a practical alternative. The resulting optimization problem is non-convex, but has a smaller number of solution variables, and can be locally …
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Theory of mind development and executive functioning in elementary school children
… (sentence memory, and forward digit span), matrix completion, executive functioning (backward digit span), and second-order theory of mind tasks were obtained. Partial correlations of the measures controlling for age revealed verbal ability to be significantly correlated with theory of mind …
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Blind regression : nonparametric regression for latent variable models via collaborative filtering
… blind regression, a framework motivated by matrix completion for recommender systems: given m users, n items, and a subset of user-item ratings, the goal is to predict the unobserved ratings given the data, i.e., to complete the partially observed matrix. We posit that user u and movie i …
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Challenges in recommender systems : scalability, privacy, and structured recommendations
… develop a scalable primal dual algorithm for matrix completion based on trace norm regularization. The regularization problem is solved via a constraint generation method that explicitly maintains a sparse dual and the corresponding low rank primal solution. We provide a new dual block …
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Distributed Singular Value Decomposition Through Least Squares
… value decomposition (SVD) is an essential matrix factorization technique that decomposes a matrix into singular values and corresponding singular vectors that form orthonormal bases. SVD has wide-ranging applications from principal component analysis (PCA) to matrix completion and …
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Learning to Predict End-to-End Network Performance
… performance prediction is formulated as a matrix completion problem where the matrix contains performance measures between network nodes with some of them known and the others unknown and thus to be filled. This new formulation is advantageous in that it is flexible to deal with various …
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Efficient and guaranteed algorithms for sparse inverse problems
… vectors obtained through a common sensing matrix. In a favorable situation, the unknown matrix, which consists of the jointly sparse signals, has linearly independent nonzero rows. In this case, the Multiple Signal Classification (MUSIC) algorithm, originally proposed by Schmidt for the …
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Statistical inference in high-dimensional matrix models
Matrix models are ubiquitous in modern statistics. For instance, they are used in finance to assess interdependence of assets, in genomics to impute missing data and in movie recommender systems to model the relationship between users and movie ratings. Typically such models are either …
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Low-rank completion and recovery of correlation matrices
… and partially observed matrices, the problem of matrix completion within a low-rank framework is of particular significance. This dissertation presents the methods of spectral completion and convex relaxation, which have been successfully applied to the particular problem of lowrank completion …
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Robust learning with low-dimensional structure: theory,algorithms and applications
… ?low-rank subspace model? that underlies matrix completion and Robust PCA, and ?union-of-subspace model? that arises in the problem of subspace clustering. In the upcoming chapters, we will present (i) stability of matrix factorization and its consequences in the robustness of …
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