Advanced Data Analytics Using Python by Sayan Mukhopadhyay

Author:Sayan Mukhopadhyay
Language: eng
Format: epub
Publisher: Apress, Berkeley, CA

Properties

The distances are measures that satisfy the following properties:dist(x, y) = 0 if and only if x=y.

dist(x, y) > 0 when x ≠ y.

dist(x, y) = dist(x, y).

dist(x,y) + dist(y,z) >= d(z,x) for all x, y, and z.

General and Euclidean Distance

The distance between the points p and q is the length of the geometrical line between them: (. This is called Euclidean distance .

According to Cartesian coordinates, if p = (p1, p2,…, p n ) and q = (q1, q2,…, q n ) are the two points in Euclidean n-space, then the distance (d) from q to p or from p to q is derived from the Pythagorean theorem, as shown here:

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