Module smartcore::metrics::distance

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Multitude of distance metrics are defined here

Collection of Distance Functions

Many algorithms in machine learning require a measure of distance between data points. Distance metric (or metric) is a function that defines a distance between a pair of point elements of a set. Formally, the distance can be any metric measure that is defined as \( d(x, y) \geq 0\) and follows three conditions:

  1. \( d(x, y) = 0 \) if and only \( x = y \), positive definiteness
  2. \( d(x, y) = d(y, x) \), symmetry
  3. \( d(x, y) \leq d(x, z) + d(z, y) \), subadditivity or triangle inequality

for all \(x, y, z \in Z \)

A good distance metric helps to improve the performance of classification, clustering and information retrieval algorithms significantly.

Modules

  • euclidian
    Euclidean Distance is the straight-line distance between two points in Euclidean spacere that presents the shortest distance between these points.
  • hamming
    Hamming Distance between two strings is the number of positions at which the corresponding symbols are different.
  • mahalanobis
    The Mahalanobis distance is the distance between two points in multivariate space.
  • manhattan
    Also known as rectilinear distance, city block distance, taxicab metric.
  • minkowski
    A generalization of both the Euclidean distance and the Manhattan distance.

Structs

Traits

  • Distance
    Distance metric, a function that calculates distance between two points