Johnson–Lindenstrauss lemma

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• ID : Q6268577

말뭉치

1. The Johnson-Lindenstrauss Lemma (JL lemma) tells us that we need dimension , and that the mapping is a (random) linear mapping.
2. A variant of the Johnson–Lindenstrauss lemma for circulant matrices.
3. A simple short proof of the Johnson-Lindenstrauss lemma (concerning nearly isometric embeddings of finite point sets in lower-dimensional spaces) is given.
4. Earlier versions of the Johnson-Lindenstrauss lemma used a slightly different function .
5. It turns out that the Johnson-Lindenstrauss lemma is almost optimal.
6. Then, if we map the ‘s to points in while preserving distances up to a factor , then the dimension must be at least , which is nearly what the Johnson-Lindenstrauss lemma would give.
7. The Johnson-Lindenstrauss lemma very strongly depends on properties of the Euclidean norm.

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위키데이터

• ID : Q6268577