This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ata 2
2
p
2
2 R= If the second condition is weakened to a nonstrict inequality – i.e., Dis(x , y ) may
be zero even ifcondition is called the triangle inequality
The last x 6= y – the function Dis is called a pseudometric. Peter Flach (University of Bristol) that are a fixed distance away.
Figure 8.3: Circles and ellipses blue rectangle). Notice that for points on the coordinate axes all distances agree. For the
other points, our reach increases with p ; however, if we require a rotationinvariant
distance metric then Euclidean distance is our only choice. (right)Figure 8.3 ellipse
The rotated
227 / 349
9 TT2 T2 T x R Rx = 1/4; orderp Minkowski S x = 1/4 and the circle x x = for
(left) Lines connectingSpoints at the axisparallel ellipse xdistance ;1 from the origin 1/4. (from
10 inside) p = 0.8; p = 1 (Manhattan distance, the rotated square in red); p =August 25, p = 2 / 349
1.5; 2012 226
Peter Flach (University of Bristol) Machine Learning: Making Sense of Data (Euclidean distance, the violet circle); p = 4; p = 8; and p = 1 (Chebyshev distance, the
blue rectangle). Notice that for points on the coordinate a...
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.
 Fall '08
 Anderson,C
 Machine Learning

Click to edit the document details