Johnson and Lindenstrauss (1984) proved that any ﬁnite set of data in a high dimensional space can be projected into a low dimensional space with the Euclidean metric information of the set being preserved within any desired accuracy. Such dimension reduction plays a critical role in many applications with massive data. There has been extensive effort in the literature on how to ﬁnd explicit constructions of Johnson-Lindenstrauss projections. In this poster, we show how algebraic codes over ﬁnite ﬁelds can be used for fast Johnson-Lindenstrauss projections of data in high dimensional Euclidean spaces.
Knoll, Fiona, "Tighter Bounds on Johnson Lindenstrauss Transforms" (2015). Graduate Research and Discovery Symposium (GRADS). 200.