11_distances

We will often refer to disp simply as the p norm

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 02/10/2014 for the course CS 545 taught by Professor Anderson,c during the Fall '08 term at Colorado State.

Ask a homework question - tutors are online