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 multiclass 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. Distancebased models 14 Voronoi diagrams 8.1 Neighbours and exemplars Decision boundary: of the closest centroid algorithm when using
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Figure 8.6 Twoexemplar decision boundaries
L2 and L1 norms: The Voronoi diagram depends on the distance measure that is
used: (left) For two exemplars the nearestexemplar 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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 Fall '08
 Anderson,C
 Machine Learning, Distance, Nearest neighbor search, University of Bristol, nearest neighbor, Peter Flach

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