电子学报 ›› 2014, Vol. 42 ›› Issue (3): 547-555.DOI: 10.3969/j.iss.0372-2012-2014.03.019

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主元分析中的平滑性

向馗1, 周申培1, 李炳南2   

  1. 1. 武汉理工大学自动化学院, 湖北武汉 430070;
    2. 合肥工业大学医学工程学院, 安徽合肥 230009
  • 收稿日期:2013-05-23 修回日期:2013-09-28 出版日期:2014-03-25
    • 通讯作者:
    • 李炳南
    • 作者简介:
    • 向馗 男,1976年10月出生于湖北省秭归县.现为武汉理工大学自动化学院副教授,从事生理信号处理和人机协作方面的研究工作.E-mail:xkarcher@126.com
    • 基金资助:
    • 国家自然科学基金 (No.61101022); 湖北省自然科学基金 (No.2012FFB05004); 武汉理工大学自主创新研究基金 (No.2012-Ⅱ-017,No.2013-IV-063)

Smoothness in Principal Component Analysis:A Survey

XIANG Kui1, ZHOU Shen-pei1, LI Bing-nan2   

  1. 1. School of Automation, Wuhan University of Technology, Wuhan, Hubei 430070, China;
    2. School of Medical Engineering, Hefei University of Technology, Hefei, Anhui 230009, China
  • Received:2013-05-23 Revised:2013-09-28 Online:2014-03-25 Published:2014-03-25
    • Supported by:
    • National Natural Science Foundation of China (No.61101022); Natural Science Foundation of Hubei Province,  China (No.2012FFB05004); Independent Innovation Research Fund of Wuhan University of Technology (No.2012-Ⅱ-017, No.2013-IV-063)

摘要: 某些样本观测形如时间序列或离散信号,其本质为平滑曲线(即函数型数据),代表一个潜在的连续过程.在主元分析中引入平滑性,可更加全面地刻画样本观测中包含的连续动态特性.本文介绍了从离散样本过渡到连续曲线的平滑处理方法,陈述了线性平滑主元的基本框架——基函数空间下的多元统计.平滑曲线兼具幅度变异和相位变异,可通过配准分离两种变异.据此重点讨论了非线性平滑主元分析:既可采用混合数据形式,一并考察两种变异性;也可借助微分流形,在非欧氏空间描述相位变异.基于开源的步态数据集,给出了3组分析结果:未经配准的平滑主元分析;配准后的幅度变异分析和相位变异分析.最后,综述了平滑主元在生物信号处理中的典型应用.

关键词: 主元分析, 平滑, 函数型数据, 相位变异

Abstract: Some of the sample observations,which seem like time series or discrete signals,are in fact smooth curves (functional data) corresponding to a latent continuous process.The smooth principal component analysis (PCA) focusing on functional data variation can fully characterize the dynamic features hidden in observations.The approaches smoothing discrete samples to continuous curves were introduced.The linear framework of smooth PCA was described as multivariate statistics in basis function spaces.The amplitude variation and phase variation embedded in smooth curves needed registration operations to separate themselves.The nonlinear framework of smooth PCA was discussed in two aspects:depicting two types of variation together with mixed data;depicting phase variation separately with differential manifolds in non-Euclidean space.Three groups of smooth PCA results were presented,which are raw gait data without registration,gait amplitude variation with registration and phase variation.Finally,the applications of smooth PCA in bio-signal processing were reviewed.

Key words: principal component analysis, smooth, functional data, phase variation

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