Click here to Skip to main content
11,482,103 members (66,818 online)
Click here to Skip to main content

Quantitative Variable Distances

, 6 Jan 2009 CPOL 27.1K 6
Rate this:
Please Sign up or sign in to vote.
An overview of different distances under the Minkowski distance.

Introduction

In this article, I discuss and implement the following:

  • Minkowski Distance
  • Euclidean Distance
  • Manhattan Distance
  • Chebyshev Distance

The general metric for distance is the Minkowski distance. When lambda is equal to 1, it becomes the city block distance, and when lambda is equal to 2, it becomes the Euclidean distance. The special case is when lambda is equal to infinity (taking a limit), where it is considered as the Chebyshev distance.

MinkowskiDistance.gif

public static double MinkowskiDistance(double[] X, double[] Y, int order)
{
    int count = 0;
    double distance = 0.0;
    double sum = 0.0;
    if (X.GetUpperBound(0) != Y.GetUpperBound(0))
    {
        throw new System.ArgumentException("the number of elements" + 
                  " in X must match the number of elements in Y");
    }
    else
    {
        count = X.Length;
    }
    for (int i = 0; i < count; i++)
    {
        sum = sum + Math.Pow(Math.Abs(X[i] - Y[i]), order);
    }
    distance = Math.Pow(sum,(1/order));
    return distance;
}

Euclidean distance is the most common use of distance. When people talk about distance, this is what they are referring to. Euclidean distance, or simply 'distance', examines the root of square differences between the coordinates of a pair of objects. This is most generally known as the Pythagorean theorem.

EuclideanDistance.gif

public static double EuclideanDistance(double [] X, double []Y)
{
    int count = 0;
    double distance = 0.0;
    double sum = 0.0;
    if(X.GetUpperBound(0) != Y.GetUpperBound(0))
    {
        throw new System.ArgumentException("the number of elements" + 
                  " in X must match the number of elements in Y");
    }
    else
    {
        count = X.Length;
    }
    for (int i = 0; i < count; i++)
    {
        sum = sum + Math.Pow(Math.Abs(X[i] - Y[i]),2);
    }
    distance = Math.Sqrt(sum);
    return distance;
}

The taxicab metric is also known as rectilinear distance, L1 distance or L1 norm, city block distance, Manhattan distance, or Manhattan length, with the corresponding variations in the name of the geometry. It represents the distance between points in a city road grid. It examines the absolute differences between the coordinates of a pair of objects.

CityBlockDistance.gif

public static double ManhattanDistance(double [] X, double []Y)
{
    int count = 0;
    double distance = 0.0;
    double sum = 0.0;
    if(X.GetUpperBound(0) != Y.GetUpperBound(0))
    {
        throw new System.ArgumentException("the number of elements" + 
                  " in X must match the number of elements in Y");
    }
    else
    {
        count = X.Length;
    }
    for (int i = 0; i < count; i++)
    {
        sum = sum + Math.Abs(X[i] - Y[i]);
    }
    distance = sum;
    return distance;
}

Chebyshev distance is also called the Maximum value distance, defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. In other words, it examines the absolute magnitude of the differences between the coordinates of a pair of objects.

ChebyshevDistance.gif

public static double ChebyshevDistance(double[] X, double[] Y)
{
    int count = 0;
    if (X.GetUpperBound(0) != Y.GetUpperBound(0))
    {
        throw new System.ArgumentException("the number of elements" + 
                  " in X must match the number of elements in Y");
    }
    else
    {
        count = X.Length;
    }
    double[] newData = new double[count];
    for (int i = 0; i < count; i++)
    {
        newData[i] = Math.Abs(X[i] - Y[i]);
    }
    double max = double.MinValue;
    foreach (double num in newData)
    {
        if (num > max)
        {
            max = num;
        }
    }
    return max;
}

Sources

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

Share

About the Author

saharkiz
Web Developer
Philippines Philippines
My name : Aresh Saharkhiz.
Origin: Unknown

Education : BS Computer Science
MS Computer Science
Interests : Genetic Programming
Neural Networks
Game AI
Programming: (language == statementEnd(semicolon)


http://sites.google.com/site/docaresh

Skill:
Flash
Carrara 3D
PHP,ASP,ASP.NET
J2SE

Comments and Discussions

 
GeneralMy vote of 2 Pin
ARon_6-Jan-09 10:47
memberARon_6-Jan-09 10:47 
GeneralRe: My vote of 2 Pin
aresguya6-Jan-09 20:12
memberaresguya6-Jan-09 20:12 
Generaldouble max = double.MinValue; Pin
axelriet6-Jan-09 7:58
memberaxelriet6-Jan-09 7:58 

General General    News News    Suggestion Suggestion    Question Question    Bug Bug    Answer Answer    Joke Joke    Rant Rant    Admin Admin   

Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages.

| Advertise | Privacy | Terms of Use | Mobile
Web03 | 2.8.150520.1 | Last Updated 6 Jan 2009
Article Copyright 2009 by saharkiz
Everything else Copyright © CodeProject, 1999-2015
Layout: fixed | fluid