11_distances

Machine learning making sense of data 2 2 p 2 2 r if

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ata 2 2 p 2 2 R= If the second condition is weakened to a non-strict 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 pseudo-metric. 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 rotation-invariant 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; order-p Minkowski S x = 1/4 and the circle x x = for (left) Lines connectingSpoints at the axis-parallel 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.

Ask a homework question - tutors are online