Department of Mathematics

Applied Mathematics

  •  Jelani Nelson, UC Berkeley
  •  Optimal terminal dimensionality reduction in Euclidean space; zoom link @
  •  06/11/2020
  •  2:30 PM - 3:30 PM

(Part of One World MINDS seminar: \[ \] The Johnson-Lindenstrauss lemma states that for any X a subset of R^d with |X| = n and for any epsilon, there exists a map f:X-->R^m for m = O(log n / epsilon^2) such that: for all x in X, for all y in X, (1-epsilon)|x - y|_2 <= |f(x) - f(y)|_2 <= (1+epsilon)|x - y|_2. We show that this statement can be strengthened. In particular, the above claim holds true even if "for all y in X" is replaced with "for all y in R^d". Joint work with Shyam Narayanan.



Department of Mathematics
Michigan State University
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