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Conversion from a Distance Metric
The Minkowski distances
are the standard metrics for geometrical problems. For we obtain
the Euclidean distance. There are several possibilities for converting
such a distance metric (in , with 0 closest) into a
similarity measure (in , with 1 closest) by a monotonic
decreasing function. For Euclidean space, we chose to relate
distances and similarities using
. Consequently,
we define Euclidean [0,1]normalized similarity as

(4.1) 
which has important desirable properties (as we will see in the
discussion) that the more commonly adopted
lacks.
Other distance functions can be used as well. The Mahalanobis distance
normalizes the features using the covariance matrix. Due to the
highdimensional nature of text data, covariance estimation is
inaccurate and often computationally intractable, and normalization is
done if need to be, at the document representation stage itself,
typically by applying TFIDF.
Next: Cosine Measure
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Alexander Strehl
20020503