Extensions of Lipschitz Mappings into a Hilbert Space¶
Johnson, W. B., & Lindenstrauss, J. (1982). Extensions of Lipschitz Mappings into a Hilbert Space. Conference in Modern Analysis and Probability, 26, 189-206.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Dimension
- Johnson and Lindenstrauss's 1984 lemma
This sourceProves that n points in any high-dimensional Euclidean space embed in O(log n / ε²) dimensions with all pairwise distances preserved to factor (1 ± ε).
- Johnson and Lindenstrauss's 1984 lemma
- Embedding
- And watch for distortion: approximate embeddings, which is what most practical machine-learning embeddings are, introduce distortion that must be quantified (Johnson–Lindenstrauss bounds, distortion measures) and checked against the downstream conclusions.
This sourceProves the distortion bound for embedding points into a lower-dimensional Euclidean space, the basis for quantifying approximate-embedding distortion.
- And watch for distortion: approximate embeddings, which is what most practical machine-learning embeddings are, introduce distortion that must be quantified (Johnson–Lindenstrauss bounds, distortion measures) and checked against the downstream conclusions.
Verification¶
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