最小密度超平面
Minimum Density Hyperplanes
摘要：
将不同的对象组（聚类）与高概率密度的连续区域（高密度聚类）相关联是许多统计和机器学习方法对未标记数据进行分类的核心。我们提出了一种新的超平面分类器的聚类和半监督分类，这是出于这一目标。建议的最小密度超平面最小化沿它的经验概率密度函数的积分，从而避免与高密度集群的交叉。我们证明了最小密度和最大间隔超平面是渐近等价的，从而将这种方法与最大间隔聚类和半监督支持向量分类器联系起来。我们提出了一个投影寻踪制定相关的优化问题，使我们能够有效地找到最小密度超平面在实践中，并评估其性能的基准数据集的范围。所提出的方法被发现是非常有竞争力的最先进的聚类和半监督分类的方法。
英文摘要：
Associating distinct groups of objects (clusters) with contiguous regions of high probability density (high-density clusters), is central to many statistical and machine learning approaches to the classification of unlabelled data. We propose a novel hyperplane classifier for clustering and semi-supervised classification which is motivated by this objective. The proposed minimum density hyperplane minimises the integral of the empirical probability density function along it, thereby avoiding intersection with high density clusters. We show that the minimum density and the maximum margin hyperplanes are asymptotically equivalent, thus linking this approach to maximum margin clustering and semi-supervised support vector classifiers. We propose a projection pursuit formulation of the associated optimisation problem which allows us to find minimum density hyperplanes efficiently in practice, and evaluate its performance on a range of benchmark datasets. The proposed approach is found to be very competitive with state of the art methods for clustering and semi-supervised classification.
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