Results 81 to 90 of about 201,485 (174)
, 2010 Mathematical formulation of certain natural phenomena exhibits group structure on topological spaces that resemble the Euclidean space only on a small enough scale, which prevents incorporation of conventional inference methods that require global vector norms.
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Augmentation invariant manifold learning
Journal of the Royal Statistical Society Series B: Statistical MethodologyAbstract Data augmentation is a widely used technique and an essential ingredient in the recent advance in self-supervised representation learning. By preserving the similarity between augmented data, the resulting data representation can improve various downstream analyses and achieve state-of-the-art performance in many applications ...
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Manifold learning for parameter reduction
Journal of Computational Physics, 2019 Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral aspects of otherwise intractable models.
Holiday, Alexander +5 more
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Non-parametric manifold learning
Electronic Journal of StatisticsWe introduce an estimator for distances in a compact Riemannian manifold based on graph Laplacian estimates of the Laplace-Beltrami operator. We upper bound the error in the estimate of manifold distances, or more precisely an estimate of a spectrally truncated variant of manifold distance of interest in non-commutative geometry (cf.
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Communications ChemistryMolecular representation is critical in chemical machine learning. It governs the complexity of model development and the fulfillment of training data to avoid either over- or under-fitting. As electronic structures and associated attributes are the root
Tonglei Li +3 more
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On Manifold Learning in Plato's Cave: Remarks on Manifold Learning and Physical Phenomena. [PDF]
Int Conf Sampl Theory Appl SampTA, 2023 Lederman RR, Toader B.
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eLifeManifold-learning is particularly useful to resolve the complex cellular state space from single-cell RNA sequences. While current manifold-learning methods provide insights into cell fate by inferring graph-based trajectory at cell level, challenges ...
Jun Ren +8 more
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Estimation of smooth vector fields on manifolds by optimization on Stiefel group
Учёные записки Казанского университета: Серия Физико-математические науки, 2018 Real data are usually characterized by high dimensionality. However, real data obtained from real sources, due to the presence of various dependencies between data points and limitations on their possible values, form, as a rule, form a small part of the
E.N. Abramov, Yu.A. Yanovich
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Manifold learning for fMRI time-varying functional connectivity. [PDF]
Front Hum Neurosci, 2023 Gonzalez-Castillo J +5 more
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Discovering conservation laws using optimal transport and manifold learning. [PDF]
Nat Commun, 2023 Lu PY, Dangovski R, Soljačić M.
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