Active Learning by Spherical Subdivision
Active Learning by Spherical Subdivision
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通过球形细分进行主动学习
DOI：
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发表时间：
2008
影响因子：
6
通讯作者：
K. Obermayer
中科院分区：
文献类型：
--
作者：
F. Henrich;K. Obermayer
我们介绍了一种计算上可行的、“建设性”的主动学习方法用于二分类。学习算法最初是为可分离分类问题，为具有恒定数据密度的超球面数据空间，以及为作为分类器的大球体而制定的。为了降低计算复杂度，将版本空间限制为球面简式，并通过细分最大长度的边来学习过程。我们证明了这个过程最优地减小了泛化误差的紧上界。然后将该方法推广到使用球体积作为数据空间的其他可分离分类问题，并由球体图诱导出等距。对于球体上的非恒定数据密度，提供了分类器之间不一致的概率（因此泛化误差）的上界。这项工作的重点在于为主动学习策略提供数学上精确的性能估计。
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.