Diff for "FAQ/euclid" - CBU statistics Wiki
location: Diff for "FAQ/euclid"
Differences between revisions 1 and 3 (spanning 2 versions)
Revision 1 as of 2010-07-01 14:58:49
Size: 1026
Editor: PeterWatson
Comment:
Revision 3 as of 2010-07-01 15:05:10
Size: 1024
Editor: PeterWatson
Comment:
Deletions are marked like this. Additions are marked like this.
Line 1: Line 1:
Line 6: Line 5:
ED = for vectors, observations with vectors $$x_text{i} = (x_text{1i}, ..., x_text_{pi})^text{T}$$ and $$x_text{j} = (x_text{1j}, ..., x_text_{pj})^text{T}$$ equals $$ \sqrt{x_text{i} - x_text{j})^text{T)(x_text{i} - x_text{j})}$$ ED = for vectors, observations with vectors $$x_text{i} = (x_text{1i}, ..., x_text_{pi})^text{T}$$ and $$x_text{j} = (x_text{1j}, ..., x_text_{pj})^text{T}$$ equals $$ \sqrt{(x_text{i} - x_text{j})^text{T}(x_text{i} - x_text{j})}$$
Line 11: Line 10:
The Euclidean distance is the distance on a graph between two points. This is easily seen in two dimensions since by Pythagoras's theorem the distance (hypoteneuse) between two points (x11, x21) and (x12, x22) equals the square root of the squared difference in x and y co-ordinates = The Euclidean distance is the distance on a graph between two points. This is easily seen in two dimensions since by Pythagoras's theorem the distance (hypotenuse) between two points (x11, x21) and (x12, x22) equals the square root of the squared difference in x and y co-ordinates =

What is the formula for Euclidean distance ?

Euclidean distance measures the distance between two vectors of length p denoting p traits of various observations and is a specific example of Mahalanobis distance with an identity covariance matrix (ie uncorrelated traits).

ED = for vectors, observations with vectors $$x_text{i} = (x_text{1i}, ..., x_text_{pi})text{T}$$ and $$x_text{j} = (x_text{1j}, ..., x_text_{pj})text{T}$$ equals $$ \sqrt{(x_text{i} - x_text{j})^text{T}(x_text{i} - x_text{j})}$$

This can be written in long hand as $$ \sqrt{(x_text{1i}-x_text{1j})text{2} + .. + (x_text{pi}-x_text{pj})text{2}}$$

The Euclidean distance is the distance on a graph between two points. This is easily seen in two dimensions since by Pythagoras's theorem the distance (hypotenuse) between two points (x11, x21) and (x12, x22) equals the square root of the squared difference in x and y co-ordinates = square root of (x11-x12)(x11-x12) + (x21-x22)(x22-x21). See [attachment:euclide.bmp here.]

None: FAQ/euclid (last edited 2013-03-08 10:17:55 by localhost)