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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
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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...
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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
- Machine Learning