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- F.-F. Henrich and
K. Obermayer. Learning by Spherical Subdivision.
.
Journal of Machine Learning Research, 9:105-130, 2008.
(PDF)
We introduce a computationally feasible, ''constructive`` active
learning method for binary classification. The learning algorithm is
initially formulated for separable classification problems, for a
hyperspherical data space with constant data density, and for great spheres
as classifiers. In order to reduce computational complexity the version space
is restricted to spherical simplices and learning procedes by subdividing the
edges of maximal length. We show that this procedure optimally reduces a
tight upper bound on the generalization error. The method is then extended to
other separable classification problems using products of spheres as data
spaces and isometries induced by charts of the sphere. An upper bound is
provided for the probability of disagreement between classifiers (hence the
generalization error) for non-constant data densities on the sphere. The
emphasis of this work lies on providing mathematically exact performance
estimates for active learning strategies.
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