Distance Metric - Euclidean Distance
The java program finds distance between two points by Euclidean distance metric and the points can be a scalar (single element) or a vector (more than one element).
The Euclidean distance between two points is measured based on Pythagoras theorem on right angle triangle.
AC2 = AB2 + BC2
AC2 - area of hypotenous
AB2 – area of base
BC2 – area of perpendicular
Euclidean distance= AC = sqrt( AB^2 +BC^2)
Euclidean distance - on 1-D
The points x and y are scalar on 1-dimension and each point has one element. It is consider that the points on a measuring scale in case of 1-Dimension. The distance between these two points are measured by the following formula.
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| ID-Euclidean |
Euclidean distance - on 2-D
The points x and y are vector on 2-dimension and each point has two elements.It is consider that the points on a Cartesian 2-D coordinate graph in case of 2-Dimension. The distance between these two points are measured by the following formula.
 |
| 2D-Euclidean |
Euclidean distance -Example on 2-D
A and B are two points on 2-D Cartesian coordinates and find distance between these two points A and B using euclidean distance equation.
int A[] = { 2,3 }; // 2D vector A
int B[] = { 2,1 }; // 2D vector B
||A-B|| = sqrt ( (A[0]-B[0])^2 + (A[1]-B[1])^2 )
= sqrt ( (2-2)^2 + (3-1)^2 );
= sqrt ( 0^2 + 2^2 );
= sqrt ( 0 + 4 );
= sqrt ( 4 );
||A-B|| = 2
Distance between vectors A=[2,3] and B=[2,1] is 2
Euclidean distance - on N-D
The points x and y are vector on N-dimension and each point has N number of elements. It is consider that the points on a Cartesian 2-D coordinate graph in case of 2-Dimension. The distance between these two points are measured by the following one of the equation.
 |
| N-Dimensional Euclidean |
 |
| N-Dimensional Euclidean |
Euclidean Distance - Java program
public class Euclidean {
public static double distance(double x, double y) {
return Math.sqrt( Math.pow(x-y,2.0) );
}
public static double distance(int x, int y) {
return Math.sqrt( Math.pow(x-y,2) );
}
public static double distance(double x[], double y[]) {
double ds=0.0;
for(int n=0;n<x.length;n++)
ds += Math.pow(x[n]-y[n],2.0);
ds=Math.sqrt(ds);
return ds;
}
public static double distance(int x[], int y[]) {
double ds=0.0;
for(int n=0;n<x.length;n++)
ds += Math.pow(x[n]-y[n],2.0);
ds=Math.sqrt(ds);
return ds;
}
public static double[] distance(int x[][], int y[]) {
double ds[]=new double[x.length];
for(int n=0;n<x.length;n++)
ds[n]= distance(x[n],y);
return ds;
}
public static double[] distance(double x[][], double y[]) {
double ds[]=new double[x.length];
for(int n=0;n<x.length;n++)
ds[n] = distance(x[n],y);
return ds;
}
}
Euclidean Distance - Main Java program
import java.util.Arrays;
public class EuclideanMain {
public static void main(String[] args)
{
System.out.println("\nEuclidean Distance between
scalar integer x and y " );
int ix=20;
int iy=30;
double dist=Euclidean.distance(ix, iy);
System.out.println("x="+ix +",y="+iy);
System.out.println("Distance :" + dist);
System.out.println("\nEuclidean Distance between
scalar double x and y " );
double dx=2.6;
double dy=3.2;
double ds2=Euclidean.distance(dx, dy);
System.out.println("x="+dx +",y="+dy);
System.out.println("Distance :" + ds2);
System.out.println("\n Euclidean Distance between two vectors x and y " );
int aix[]={2,3,5};
int aiy[]={3,5,7};
double ds3=Euclidean.distance(ix, iy);
System.out.println("x="+Arrays.toString(aix) +",y="
+Arrays.toString(aiy));
System.out.println("Distance :" + ds3);
System.out.println("\n Euclidean Distance between two 2D-vectors x and y " );
double adx[]={2.4,3.1,5.2};
double ady[]={3.1,5.6,7.8};
System.out.println("x="+Arrays.toString(adx) +",
y="+Arrays.toString(ady));
double ds4=Euclidean.distance(adx, ady);
System.out.println("Distance :" + ds4);
System.out.println("\n Euclidean Distance between two vectors x and y having N-dimensional element " );
int aix2[][]={ {2,3,5} ,{1,7,4}};
int aiy2[]={3,5,7};
double ds5[]=Euclidean.distance(aix2, aiy2);
System.out.println("x="+Arrays.toString(aix2[0]) + ","
+ Arrays.toString(aix2[1]) +",y="+Arrays.toString(aiy2));
System.out.println( "Distance :" + Arrays.toString(ds5));
System.out.println("\n Euclidean Distance between two vectors x and y having N-dimensional element " );
double adx2[][]={ {2.4,3.1,5.2},{1.2,7.2,4.5}};
double ady2[]={3.1,5.6,7.8};
double ds6[]=Euclidean.distance(adx2, ady2);
System.out.println("x="+ Arrays.toString(adx2[0])+","
+Arrays.toString(adx2[1]) +",y="+Arrays.toString(ady2));
System.out.println( "Distance :" + Arrays.toString(ds6));
}
}
Euclidean Distance - Java program output
1D distance Euclidean Distance between scalar x and y x=20,y=30 Distance :10.0 Euclidean Distance between scalar x and y in datatype double x=2.6,y=3.2 Distance :0.6000 2D distance Euclidean Distance between two vectors x and y in integer datatype x=[2, 3],y=[3, 5] Distance :2.2361 Euclidean Distance between two 2D vectors x and y in double datatype x=[2.4, 3.1],y=[3.1, 5.6] Distance :2.5962 N-D distance Euclidean Distance between two vectors x and y having N-dimensional element in integer datatype x=[2, 3, 5],[1, 7, 4],y=[3, 5, 7] Distance :[3.0, 4.1231] Euclidean Distance between two vectors x and y having N-dimensional element in double datatype x=[2.4, 3.1, 5.2],[1.2, 7.2, 4.5],y=[3.1, 5.6, 7.8] Distance :[3.6742, 4.1304]
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