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流形学习中基于局部线性结构的自适应邻域选择
  • 摘要

    近年来,流形学习成为包括机器学习、模式识别和计算机视觉等相关领域的研究热点.流形学习算法中,邻域选择直接关系到算法的性能,而传统的邻域选择算法如k近邻和ε邻域算法存在参数难以确定,所构建邻域不能反映流形学习算法对邻域要求等缺点.提出了一种基于流形局部线性结构的自适应邻域选择算法(ANSLL).首先通过分析现有流形学习算法,总结出构建邻域的两个基本原则:1)同一邻域的所有点都近似地位于某一d维线性子空间内(d为流形维数);2)每个邻域包含尽可能多的点.基于这两个基本原则,ANSLL 算法采用主成分分析技术(PCA)度量有限点集的线性程度,通过邻域压缩或扩张方式自适应地构建邻域.针对邻域线性结构的特点,还提出了一种改进的邻域图构建方法,以提高等度映射(Isomap)算法中测地线距离估计的准确性.最后大量系统的实验表明,ANSLL算法能够依据流形的局部曲率自适应地构建邻域,从而提高大多数流形学习算法(如Isomap和LLE)的性能.

  • 作者

    詹宇斌  殷建平  刘新旺  张国敏  Zhan Yubin  Yin Jianping  Liu Xinwang  Zhang Guomin 

  • 作者单位

    国防科学技术大学计算机学院,长沙,410073/国防科学技术大学计算机学院,长沙,410073;海军工程大学装备经济管理系,武汉,430033

  • 刊期

    2011年4期 ISTIC EI PKU

  • 关键词

    邻域选择  流形学习  局部线性结构  测地线距离  局部线性嵌入 

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