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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
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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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