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11_distances

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

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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...
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