CAJ | 학술논문

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。
모사양본관측형여시간서렬혹리산신호，기본질위평활곡선（즉함수형수거），대표일개잠재적련속과정。재주원분석중인입평활성，가경가전면지각화양본관측중포함적련속동태특성。본문개소료종리산양본과도도련속곡선적평활처리방법，진술료선성평활주원적기본광가---기함수공간하적다원통계。평활곡선겸구폭도변이화상위변이，가통과배준분리량충변이。거차중점토론료비선성평활주원분석：기가채용혼합수거형식，일병고찰량충변이성；야가차조미분류형，재비구씨공간묘술상위변이。기우개원적보태수거집，급출료3조분석결과：미경배준적평활주원분석；배준후적폭도변이분석화상위변이분석。최후，종술료평활주원재생물신호처리중적전형응용。
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 .