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快速核密度估计定理和大规模图论松弛聚类方法

DOI: 10.3724/SP.J.1004.2011.01422, PP. 1422-1434

Keywords: 核密度估计,大规模数据集,聚类,抽样子集

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Abstract:

?首先证明了快速核密度估计(Fastkerneldensityestimate,FKDE)定理:基于抽样子集的高斯核密度估计(KDE)与原数据集的KDE间的误差与抽样容量和核参数相关,而与总样本容量无关.接着本文揭示了基于高斯核形式的图论松弛聚类(Graph-basedrelaxedclustering,GRC)算法的目标表达式可分解成“Parzen窗加权和+平方熵”的形式,即此时GRC可视作一个核密度估计问题,这样基于KDE近似策略,本文提出了大规模图论松弛聚类方法(ScalingupGRCbyKDEapproximation,SUGRC-KDEA).较之先前的工作,这一方法的优势在于为GRC作用于大规模数据集提供了更简单和易于实现的方案.

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