电子学报Issue(3)：547-555,9.DOI:10.3969/j.issn.0372-2112.2014.03.019
主元分析中的平滑性
Smoothness in Principal Component Analysis:A Survey
摘要
Abstract
Some of the sample observations ,which seem like time series or discrete signals ,are in fact smooth curves (func-tional 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 con-tinuous 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 them-selves .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 .关键词
主元分析/平滑/函数型数据/相位变异Key words
principal component analysis/smooth/functional data/phase variation分类
信息技术与安全科学引用本文复制引用
向馗,周申培,李炳南..主元分析中的平滑性[J].电子学报,2014,(3):547-555,9.基金项目
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 （）
