MLG 032 Cartesian Similarity Metrics

Try a walking desk to stay healthy while you study or work! Show notes at ocdevel.com/mlg/32. L1/L2 norm, Manhattan, Euclidean, cosine distances, dot product Normed distances link • A norm is a function that assigns a strictly positive length to each vector in a vector space. link • Minkowski is generalized. p_root(sum(xi-yi)^p) • . "p" = ? (1, 2, ..) for below. • L1: Manhattan/city-block/taxicab. abs(x2-x1)+abs(y2-y1) • . Grid-like distance (triangle legs). Preferred for high-dim space. • L2: Euclidean. sqrt((x2-x1)^2+(y2-y1)^2 • . sqrt(dot-product) • . Straight-line distance; min distance (Pythagorean triangle edge) • Others: Mahalanobis, Chebyshev (p=inf), etc Dot product • A type of inner product.

• Outer-product: lies outside the involved planes. Inner-product: dot product lies inside the planes/axes involved link • . Dot product: inner product on a finite dimensional Euclidean space link Cosine (normalized dot)