Technology
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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)