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11_distances

# Page 238 in the book 11 12 3 102113 the closest

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Unformatted text preview: roid classifier revisited Voronoi diagrams The arithmetic mean is a representative example (exemplar) that is used to represent each class. Voronoi diagram with respect to a collection of points m1,…,mk: The closest centroid classifier works for multi-class data – classify a point according to which mean is closest in Euclidean distance. How does the decision boundary look like? The Voronoi cell associated with point mi is the set of points that are closer to mi than every other point in the collection Image from http://en.wikipedia.org/wiki/Voronoi_diagram 13 Voronoi diagrams 8. Distance-based models 14 Voronoi diagrams 8.1 Neighbours and exemplars Decision boundary: of the closest centroid algorithm when using p.240 Figure 8.6 Two-exemplar decision boundaries L2 and L1 norms: The Voronoi diagram depends on the distance measure that is used: (left) For two exemplars the nearest-exemplar decision rule with Euclidean distance Voronoi diagram computed from Euclidean distance (L2 norm) results in a linear decision boundary coinciding with the perpendicular bisector of the line Voronoi diagram computed from Manhattan distance (L1 norm) connecting the two exemplars. (right) Using Manhattan distance the circles are replaced by diamonds....
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