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Unformatted text preview: ill often refer to Disp simply as the p norm. Machine Learning: Making Sense of Data August 25, 2012 d
X j =1 x j ° y j  p !1/p = x ° yp d
p
where zp =
is the p norm (sometimes denoted L p norm) of
j =1 z j 
the vector z. We will often refer to Disp simply as the p norm. The Euclidean and Manhattan distances are special cases Peter Flach (University of Bristol) ¥1/p √ What happens when p goes to infinity? 225 / 349 Peter Flach (University of Bristol) Machine Learning: Making Sense of Data August 25, 2012 5 225 / 349 6 8. Distancebased models p.234 Deﬁnition 8.1: Minkowski distance The Minkowski distance The Minkowski distance T Rd , the Minkowski distance of order
If X =he Minkowki distance of order p: p > 0 is deﬁned as Disp (x, y) =
≥P √ ¥1/p d
X j =1 x j ° y j  p !1/p . Distancebased models
The unit sphere for various values8of p p.235 = x ° yp Figure 8.3: Circles and ellipses d
p
where zp =
is the p norm (sometimes denoted L p norm) of
j =1 z j 
the vector z. We will often...
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 Fall '08
 Anderson,C
 Machine Learning

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