Diff for "FAQ/euclid" - CBU statistics Wiki
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Differences between revisions 6 and 8 (spanning 2 versions)
 ⇤ ← Revision 6 as of 2010-07-01 15:07:42 → Size: 1022 Editor: PeterWatson Comment: ← Revision 8 as of 2010-07-01 15:10:05 → ⇥ Size: 1036 Editor: PeterWatson Comment: Deletions are marked like this. Additions are marked like this. Line 1: Line 1: = What is the formula for Euclidean distance ? = = What is Euclidean distance and how do I compute it ? = Line 10: 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 (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.] 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 linear 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.]

What is Euclidean distance and how do I compute it ?

Euclidean distance measures the distance between two vectors of length t denoting t 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 $$x_text{i} = (x_text{1i}, ..., x_text{ti})text{T}$$ and $$x_text{j} = (x_text{1j}, ..., x_text{tj})text{T}$$ equals $$\sqrt{(x_text{i} - x_text{j})^text{T}(x_text{i} - x_text{j})}$$

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

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 linear 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)