Johnson-Lindenstrauss projection of high dimensional data

摘要: Johnson and Lindenstrauss (1984) proved that any finite set of data in a high dimensional space can be projected into low with the Euclidean metric information being preserved within desired accuracy. Such dimension reduction plays critical role many applications massive data. There has been extensive effort literature on how to find explicit constructions Johnson-Lindenstrauss projections. In this poster, we show algebraic codes over fields used for fast projections spaces. Transform Problem Given space, want project so pairwise distances are probability. Lemma •Let n positive integer, 0 ǫ] < δ. –A transformation matrix A property is called Transformation.