# Classifier architecture and Features.1

Greg Kochanski

http://kochanski.org/gpk

February 14, 2004

To talk about close'' and far'' in a consistent manner, we need to have the concept of a distance metric. A distance metric, is a function or algorithm for calculating a distance between two things, and . It has three properties:

1. It is always positive or zero.
2. The distance from a thing2 to itself is zero.
3. It obeys the triangle inequality: For any three points, , , and , for any possible choice of . In other words, the straight line between and , which has a length , is shorter3 than any other path between and , such as a path that goes by way of .
Anything that obeys these three properties is a distance metric. Common examples are Euclidean distance in two dimensions:
 (1)

and city block metric [#!cityblock!#]:
 (2)

(The Euclidean and city-block metrics generalize to any number of dimensions in a straightforward manner.)

Greg Kochanski 2004-02-14