快速核密度估计定理和大规模图论松弛聚类方法

钱鹏江; 王士同; 邓赵红

doi:10.3724/SP.J.1004.2011.01422

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

1.
江南大学数字媒体学院无锡 214122

详细信息

通讯作者:
钱鹏江江南大学数字媒体学院副教授, 博士. 主要研究方向为模式识别, 智能计算及应用. E-mail: qianpjiang@126.com

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出版历程
- 收稿日期: 2010-12-30
- 修回日期: 2011-07-01
- 刊出日期: 2011-12-20

Fast Kernel Density Estimate Theorem and Scaling up Graph-based Relaxed Clustering Method

1.
School of Digital Media, Jiangnan University, Wuxi 214122

摘要

摘要: 首先证明了快速核密度估计 (Fast kernel density estimate, 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-based relaxed clustering, 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(Scaling up GRC by KDE approximation, 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.
- 核密度估计 /
- 大规模数据集 /
- 聚类 /
- 抽样子集
Abstract: In this paper, the fast kernel density estimate (FKDE) theorem is presented firstly, which points out that the integrated squared error between the Gaussian kernel based KDE of the whole dataset and the one of a sampled subset is related to the sample size and the kernel width, but not to the size of the whole dataset. Next, it is deduced that the objective function of graph-based relaxed clustering (GRC) algorithm based on Gaussian kernel can be represented as two parts: weight sum of Parzen window (PW) and “quadratic entropy”, that is, GRC can also be viewed as a KDE problem. So the scaling up GRC by KDE approximation (SUGRC-KDEA) method is proposed according to the FKDE theorem. Compared with the previous work, the advantage of this method lies in that it provides an easier and more straightforward implementation for GRC on large datasets.
- Kernel density estimate (KDE) /
- large data set /
- clustering /
- sampled subset

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参考文献(1)

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