流形学习中非线性维数约简方法概述-计算机应用研究.PDFVIP

第 24 卷第 11 期 计 算 机 应 用 研 究 Vol. 24 No. 11 2007 年 11 月 Application Research of Computers Nov. 2007 流形学习中非线性维数约简方法概述 黄启宏, 刘 钊 ( 电子科技大学 电子工程学院, 成都 610054) 摘 要: 较为详细地回顾了流形学习中非线性维数约简方法 , 分析了它们各自的优势和不足。与传统的线性维 数约简方法相比较, 可以发现非线性高维数据的本质维数, 有利于进行维数约简和数据分析。最后展望了流形 学习中非线性维数方法的未来研究方向, 期望进一步拓展流形学习的应用领域。 关键词: 维数约简; 流形学习; 多维尺度; 等距映射; 拉普拉斯特征映射; 局部线性嵌入; 局部切空间排列 中图分类号: TP391 文献标志码: A 文章编号: 1001- 3695( 2007) 11- 0019- 07 Overview of nonlinear dimensionality reduction methods in manifold learning HUANG Qi-hong, LIU Zhao ( School of Electronic Engineering, University of Electronic Science Technology of China, Chengdu 610054, China) Abstract: A detailed retrospection was made on nonlinear dimensionality reduction methods in manifold learning, whose ad- vantages and defects were pointed out respectively. Compared with traditional linear method, nonlinear dimensionality reduc- tion methods in manifold learning could discover the intrinsic dimensions of nonlinear high-dimensional data effectively, help researcher to reduce dimensionality and analyzer data better. Finally, the prospect of nonlinear dimensionality reduction me- thods in manifold learning was discussed, so as to extend the application area of manifold learning. Key words: dimensional reduction; manifold learning; multidimensional scaling( MDS) ; isomap; Laplacian eigenmap; locally linear embedding( LLE) ; local tangent space alignment( LTSA) 维数约简方法的基本原理是将样本从输入空间通过线性 对应的基于核的非线性维数约简方法, 如 KPCA[ 9] 、KICA[ 10] 、 或非线性映射到一个低维空间, 从而获得一个关于原数据集紧 KFDA[ 11]