11_distances

We will often refer to disp simply as the p norm

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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 ° y||p d p where ||z||p = 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. Distance-based 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 . Distance-based models The unit sphere for various values8of p p.235 = ||x ° y||p Figure 8.3: Circles and ellipses d p where ||z||p = is the p -norm (sometimes denoted L p norm) of j =1 |z j | the vector z. We will often...
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