Journal of Frontiers of Computer Science and Technology ›› 2016, Vol. 10 ›› Issue (4): 589-599.DOI: 10.3778/j.issn.1673-9418.1505046

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Probability Density Estimation for Non-flat Functions

WANG Hongqiao1+, CAI Yanning2, FU Guangyuan1, WANG Shicheng3   

  1. 1. Department of Information Engineering, the Second Artillery Engineering University, Xi’an 710025, China
    2. College of Science, the Second Artillery Engineering University, Xi’an 710025, China
    3. Department of Control Engineering, the Second Artillery Engineering University, Xi’an 710025, China
  • Online:2016-04-01 Published:2016-04-01



  1. 1. 第二炮兵工程大学 信息工程系,西安 710025
    2. 第二炮兵工程大学 理学院,西安 710025
    3. 第二炮兵工程大学 控制工程系,西安 710025

Abstract: Aiming at the probability density estimation problem for non-flat functions, this paper constructs a single slack factor multi-scale kernel support vector machine (SVM) probability density estimation model, by improving the form of constraint condition of the traditional SVM model and introducing the multi-scale kernel method. In the model, a single slack factor instead of two types of slack factors is used to control the learning error of SVM, which reduces the computational complexity of model. At the same time, by introducing the multi-scale kernel method, the model can well fit the functions with both the fiercely changed region and the flatly changed region. Through several probability density estimation experiments with typical non-flat functions, the results show that the single slack probability density estimation model has faster learning speed than the common SVM model. And compared with the single kernel method, the multi-scale kernel SVM probability density estimation model has better estimation precision.

Key words: probability density estimation, support vector machine (SVM), multiple kernel learning, non-flat function

摘要: 针对非平坦函数的概率密度估计问题,通过改进支持向量机(support vector machine,SVM)概率密度估计模型约束条件的形式,并引入多尺度核方法,构建了一种单松弛因子多尺度核支持向量机概率密度估计模型。该模型采用合并的单个松弛因子来控制支持向量机的学习误差,减小了模型的计算复杂度;同时引入了多尺度核方法,使得模型既能适应函数剧烈变化的区域,也能适应平缓变化的区域。基于几种典型非平坦函数进行概率密度估计实验,结果证明,单松弛因子概率密度估计模型比常规支持向量机概率密度估计模型具有更快的学习速度;且相比于单核方法,多尺度核支持向量机概率密度估计模型具有更优的估计精度。

关键词: 概率密度估计, 支持向量机(SVM), 多核学习, 非平坦函数