Euclidean Distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, which can be proven by repeated application of the Pythagorean theorem. By using this formula as distance, Euclidean space becomes a metric space (even a Hilbert space). Older literature refers to this metric as Pythagorean metric. The technique has been rediscovered numerous times throughout history, as it is a logical extension of the pythagorean theorem.
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One can think of the independent variables (in a regression equation ) as defining a multidimensional space in which each observation can be plotted. The Euclidean distance is the geometric distance in that multidimensional space. It is computed as
distance(x,y)={ i (xi - yi)2}1/2
Note that Euclidean (and squared Euclidean) distances are computed from raw data, and not from standardized data. For more information on Euclidean distances and other distance measures, see Distance Measures in the Cluster Analysis chapter.

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