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 9 of 9 for “"Intrinsic Dimension"”.
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Design and analysis of algorithms for similarity search based on intrinsic dimension
… assessed in terms of the representational dimension of the data involved, that is, the number of features used to represent individual data objects. It is generally the case that high representational dimension would result in a significant increase in the processing cost of similarity …
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Estimating the Intrinsic Dimension of High-Dimensional Data Sets: A Multiscale, Geometric Approach
… work deals with the problem of estimating the intrinsic dimension of noisy, high-dimensional point clouds. A general class of sets which are locally well-approximated by <italic>k</italic> dimensional planes but which are embedded in a <italic>D</italic>>><italic>k</italic> dimensional …
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Towards Learning the Geometry of Data: From Diffusion Models to Riemannian Geometry
… geometry, paving the way for learning the intrinsic geometry of data manifolds. In chapter 3, we introduce CAFLOW, a conditional normalising flow that improves image-to-image translation by hierarchically modelling image distributions across scales. In chapter 4, we introduce non-uniform …
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Worst-case Performance of Popular Approximate Nearest Neighbor Search Implementations: Guarantees and Limitations
… query time, on data sets with bounded “intrinsic” dimension. For the other data structure variants studied, including DiskANN with “fast preprocessing”, HNSW and NSG, we present a family of instances on which the empirical query time required to achieve a “reasonable” accuracy is linear …
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Statistical aspects of optimal transport
… in practice, the barycenter problem, providing dimension-free rates of statistical estimation. In the Gaussian case, we analyze first-order methods for computing barycenters, and develop global, dimension-free rates of convergence despite the non-convexity of the problem. Extending beyond the …
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Geometric Dimensionality Reduction
… has resulted in a surge of research into dimensionality reduction techniques that spans across numerous mathematical disciplines. In this thesis we establish Geometric Dimensionality Reduction, a non-linear data compression technique that utilizes low dimensional manifolds embedded in …
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Improved Tools for Local Hamiltonians
… results for spin chains to certain trees with intrinsic dimension β < 2. This condition is met for generic trees in the plane and for certain models of hyperbranched polymers in 3D. In chapter 3 we relax the conditions on the Hamiltonian and no longer require a spectral gap or geometric …
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CLASSIFICATION RESULTS FOR SEMILINEAR ELLIPTIC EQUATIONS
… energy assumptions on the solution and when the intrinsic dimension n in (3/2,5]. These results will follow as an application of the approach introduced in Chapter 1. Chapter 3 concerns two main topics. The first one is about semilinear elliptic equations with mixed boundary conditions in …
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Sparse modeling of high-dimensional data for learning and vision
… we learn the sparse representations of high-dimensional signals for various learning and vision tasks, including image classification, single image super-resolution, compressive sensing, and graph learning. Based on the bag-of-features (BoF) image representation in a spatial pyramid, we first …