Dimensionality Reduction mapping Q high dims P low dims (2 or 3) n points map Q->P minimize error of low-dim distances wrt high-dim dist distance measures pairwise distance matrix between points metric between points in space methods MDS (multidimensional scaling) LLE (locally linear embedding) IsoMap, charting PCA, SOM complexity naive O(n^3), many O(n^2), best O(n sqrt n) [LLE, Roweis and Saul, www.cs.toronto.edu/~roweis/papers/2323.pdf] 42