The Johnson-Lindenstrauss Lemma Is Optimal for Linear Dimensionality Reduction
نویسندگان
چکیده
For any n > 1 and 0 < ε < 1/2, we show the existence of an n-point subset X of R such that any linear map from (X, `2) to ` m 2 with distortion at most 1 + ε must have m = Ω(min{n, ε−2 logn}). Our lower bound matches the upper bounds provided by the identity matrix and the Johnson-Lindenstrauss lemma [JL84], improving the previous lower bound of Alon [Alo03] by a log(1/ε) factor.
منابع مشابه
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