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首頁(yè)> 中文期刊> 《中國(guó)科學(xué)技術(shù)大學(xué)學(xué)報(bào)》 >一種基于RKHS及半?yún)?shù)理論的非線性充分降維方法

一種基于RKHS及半?yún)?shù)理論的非線性充分降維方法

     
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提出了一種基于再生核Hilbert空間(reproducing kernel Hilbert space,RKHS)及半?yún)?shù)理論的非線性充分降維新方法——廣義半?yún)?shù)核切片逆回歸(generalized semiparametric kernel sliced inverse regression,generalized semi-KSIR或GSKSIR).該方法將經(jīng)典的半?yún)?shù)方法拓展至感興趣參數(shù)為無窮維的廣義半?yún)?shù)方法,將半?yún)?shù)模型推廣到不僅冗余參數(shù)為無窮維而且感興趣參數(shù)也可為無窮維的廣義半?yún)?shù)模型情形,推導(dǎo)出相應(yīng)的廣義冗余切平面之正交補(bǔ)空間,進(jìn)而構(gòu)造了降維方向的估計(jì)方程,并由RKHS理論及正則化方法完成相應(yīng)目標(biāo)函數(shù)的求解,求得具有優(yōu)良性質(zhì)的非線性充分降維子空間的估計(jì),并且新方法不需要切片逆回歸(SIR)與核切片逆回歸(KSIR)等方法所要求的基本的線性設(shè)計(jì)條件(linear design condition,LDC),適用性較廣.最后進(jìn)行了統(tǒng)計(jì)模擬研究,顯示了新方法在有限樣本下具有良好表現(xiàn).%A nonlinear dimension reduction method,the generalized semiparametric kernel sliced inverse regression (GSKSIR for short),was proposed,developed based on the theory of reproducing kernel Hilbert Space (RKHS) and the semiparametric method.The method extends the classical semiparametric method into a more generalized semiparametric domain,and is capable of handling infinite dimensional interested a parameter spaces.With this method,both spaces of nuisance parameters and parameters of interests can be infinitely dimensional,the corresponding generalized nuisance tangent space orthogonal complement was derived,estimation equation for the purpose of dimension reduction was constructed,and optimization of the target function could be achieved based on RKHS theory and regularization method,which leads to a nonlinear estimated sufficient reduced dimension subspace with efficient properties.Furthermore,this new method does not impose the linearity design conditions (LDC) required by methods such as the sliced inverse regression (SIR) and the kernel SIR,and so on,and thus,is more general and can be more widely applied.Finally,a Monte Carlo simulation was conducted,and the results demonstrate the excellent finite sample properties of this new method.

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