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)

]]>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)

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