Fast and accurate kernel density approximation using a divide-and-conquer approach  

作　　者：Yan-xia JIN Kai ZHANG James T. KWOK Han-chang ZHOU 

机构地区：[1]School of Electronics and Computer Science and Technology, North University of China, Taiyuan 030051, China [2]Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong, China [3]Key Laboratory of Instrumentation Science and Dynamic Measurement, North University of China, Taiyuan 030051, China

出　　处：《Journal of Zhejiang University-Science C(Computers and Electronics)》2010年第9期677-689,共13页浙江大学学报C辑（计算机与电子（英文版）

基　　金：Project (No. 9140C1204060809) supported by the National Key Laboratory Foundation of China

摘　　要：Density-based nonparametric clustering techniques,such as the mean shift algorithm,are well known for their flexibility and effectiveness in real-world vision-based problems.The underlying kernel density estimation process can be very expensive on large datasets.In this paper,the divide-and-conquer method is proposed to reduce these computational requirements.The dataset is first partitioned into a number of small,compact clusters.Components of the kernel estimator in each local cluster are then fit to a single,representative density function.The key novelty presented here is the efficient derivation of the representative density function using concepts from function approximation,such that the expensive kernel density estimator can be easily summarized by a highly compact model with very few basis functions.The proposed method has a time complexity that is only linear in the sample size and data dimensionality.Moreover,the bandwidth of the resultant density model is adaptive to local data distribution.Experiments on color image filtering/segmentation show that,the proposed method is dramatically faster than both the standard mean shift and fast mean shift implementations based on kd-trees whileDensity-based nonparametric clustering techniques, such as the mean shift algorithm, are well known for their flexibility and effectiveness in real-world vision-based problems. The underlying kernel density estimation process can be very expensive on large datasets. In this paper, the divide-and-conquer method is proposed to reduce these computational requirements. The dataset is first partitioned into a number of small, compact clusters. Components of the kernel estimator in each local cluster are then fit to a single, representative density function. The key novelty presented here is the efficient derivation of the representative density function using concepts from function approximation, such that the expensive kernel density estimator can be easily summarized by a highly compact model with very few basis functions. The proposed method has a time complexity that is only linear in the sample size and data dimensionality. Moreover, the bandwidth of the resultant density model is adaptive to local data distribution. Experiments on color image filtering/segmentation show that, the proposed method is dramatically faster than both the standard mean shift and fast mean shift implementations based on kd-trees while producing competitive image segmentation results.

关 键 词：Nonparametric clustering Kernel density estimation Mean shift Image filtering 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]