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HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems
Web Search and Data Mining, 2018This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius gyrovector spaces where
Lucas Vinh Tran +4 more
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An Introduction to Functional Analysis, 2020
As calculus developed, eventually turning into analysis, concepts first explored on the real line (e.g., a limit of a sequence of real numbers) eventually extended to other spaces (e.g., a limit of a sequence of vectors or of functions), and in the early
Christian Clason
semanticscholar +1 more source
As calculus developed, eventually turning into analysis, concepts first explored on the real line (e.g., a limit of a sequence of real numbers) eventually extended to other spaces (e.g., a limit of a sequence of vectors or of functions), and in the early
Christian Clason
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Approximation of Metric Spaces by Partial Metric Spaces
Applied Categorical Structures, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematical programming, 2015
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability ...
Peyman Mohajerin Esfahani, D. Kuhn
semanticscholar +1 more source
We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability ...
Peyman Mohajerin Esfahani, D. Kuhn
semanticscholar +1 more source
On metric spaces induced by fuzzy metric spaces [PDF]
Iranian Journal of Fuzzy Systems, 2016 The authors introduce a family of extended pseudo-metrics for a class of fuzzy metric spaces. It enables to construct a metric on fuzzy metric spaces and the induced metric space shares many properties with the given fuzzy metric space. For example the same topology is generated and the spaces have the same completeness. The authors present some simple
H Li, Dong Qiu, R Dong
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The Clone Space as a Metric Space
Acta Applicandae Mathematica, 1998Let \(O_k\), \(k\in\mathbb{N}\), be the set of all functions \(E^n_k\to E_k\) for some \(n\in\mathbb{N}\), where \(E_k=\{0,1,\dots,k-1\}\). Any subset \(C\) of \(O_k\) which contains all projections, i.e. functions defined by \(\text{pr}^n_i(x_1,x_2,\dots,x_n)=x_i\), \(1\leq i\leq n\), \(n\in\mathbb{N}\), and closed under superpositions is called a ...
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Pivot selection for metric-space indexing
International Journal of Machine Learning and Cybernetics, 2016Rui Mao +4 more
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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