On lipschitz embedding of finite metric spaces in Hilbert space

By Jean Bourgain. 1985

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Citations in the corpus

Auto-Keras: An Efficient Neural Architecture Search System (2018, methodology): “The new space is constructed by embedding the original metric space into a new one using Bourgain Theorem [3], which ensures the validity of the kernel.”
Position-aware Graph Neural Networks (2019, background): “Bourgain theorem (Bourgain, 1985) guarantees that only k = O(log(2) n) anchor-sets are needed to preserve the distances in the original graph with low distortion.”
Lipschitz $p$-summing operators (2009, background): “In [4], Bourgain proved that every n-point metric space can be embedded into a Hilbert space with distortion at most C log n, where C is an absolute constant.”
Techniques for Automated Machine Learning (2019, methodology): “It calculates the number of network morphism operations [12] required to transform one network to another and introduces a valid kernel function based on the Bourgain embedding algorithm [9].”
The geometry of graphs and some of its algorithmic applications (1994, background): “Bourgain [7] had shown that every n-point metric can be embedded in an O(1og n)-dimensional Euclidean space with a logarithmic distortion and our algorithm finds embeddings which are at least as good.”
Euclidean quotients of finite metric spaces (2004, methodology): “This result should be viewed in comparison to Bourgain’s embedding theorem [10], which states that for every n-point metric spaces X, c2(X) = O(log n).”
The Design of Approximation Algorithms (2011, background): “4, is essentially a result of Bourgain [55].”