Vol.28 No.8 郭辉等：基于最小二乘支持向量机对偶优化问题的核偏最小二乘 ·793。 kernel Hilbert pace.J Mach Learning Res.2001,2:97 [7]HAoskuldsson A.PIS regression methods.J Chemometrics. [6]RAannar B.Lindgren J.GeladiS.et al.A PLS kernel algo 1988.2:211 rithm for data sets with many variables and fewer objects. [8 Barker B E,Rayens I M.Partial least squares for discrimina Chemometrics Intell Lab Syst,1994.8:111 tion.J Chemometrics 2003.17:166 Kernel partial least squares based on least squares support vector machine pri- mal-dual optimization problem GUO Hui,LIU Heping,WANG Ling Irfomation Engineering School.University of Science and Technology Beijing.Beijng 100083.China ABSTRACT A kemel partial least squares(KPLS)method based on dual optimization was proposed, which was expressed by least squares support vector machine.The KPLS formulae in the fom of dual opti- mization were deduced,which had the style of least squares support vector machine.The optimization prob- lem was constructed in a prime space,the dual problem was solved in a eigenspace by the kemel skill and the solut ions were the same as nonlinear KPLS.The model was illustrated with some examples.The results show that the proposed method is effective and superior. KEY WORDS optimization problem;partial least squares (PLS);least squares support vector machines (LS-SVM);kernel partial least squares KPLS) Microstructure of flow pattern defects in boron-doped Czochralski-grown silicon LIU Caichi,HAO Qiuyan,ZHANG Jianfeng",TENG Xiooyun,Sun Shilong,Qigang Zhou2,WANGJing2,XIAO Qinghua? 1)Institute of Infomation Functional Material.Hebei University of Technology,Tianjin 300130 China 2)General Research Institute of Norferrous Metals.Beijing 100088.China ABSTRACT The morphology and microstructure of flow pattern defects(FPDs)in lightly boron-doped Czochralskigrown silicon(Cz Si)crystals were investigated using optical microscopy and atomic force mi- croscopy.The experimental results show ed that the morphology of FPDs was parabola-like with several steps.Single-type and dual-type voids were found on the tip of FPDs and two heaves exist on the left and right sides of the void.All the results have proved that FPDs were void-ty pe defects.These results are very useful to investigate FPDs in Cz Si w afers further and explain the annihilation of FPDs during high-tem- perature annealing. KEY WORDS flow pattern defects;grow n-in defects;atomic force microscopy:Czochralski-grown silicon 【摘自Rare Metals,2006,25(4):389kernel Hilbert space.J Mach Learning Res, 2001, 2:97 [ 6] R annar B, Lindgren J, Geladi S , et al.A PLS kernel algo￾rithm for dat a sets w ith many variables and f ew er objects. Chemometri cs Intell Lab Syst, 1994, 8:111 [ 7] H oskuldsson A.PLS regression methods.J Chemometri cs, 1988, 2:211 [ 8] Barker B E, Rayens I M .Partial least squares f or discrimina￾tion.J Chemometrics, 2003, 17:166 Kernel partial least squares based on least squares support vector machine pri￾mal-dual optimization problem GUO Hui, LIU Heping , WANG Ling Inf ormation Engineering School, Universit y of Science and Technology Beijing, Beijing 100083, China ABSTRACT A kernel partial least squares ( KPLS ) method based on dual optimization w as proposed, w hich w as expressed by least squaressupport vecto r machine .The KPLS formulae in the fo rm of dual opti￾mization were deduced, w hich had the style of least squares support vecto r machine.The optimization prob￾lem w as constructed in a prime space, the dual problem w as solved in a eigenspace by the kernel skill and the solutions w ere the same as nonlinear KPLS .The model wasillustrated with some examples .The results show that the proposed method is effective and superio r. KEY WORDS optimization problem ;partial least squares ( PLS) ;least squares support vector machines ( LS -SVM) ;kernel partial least squares ( KPLS) Microstructure of flow pattern defects in boron-doped Czochralski-g rown silicon LIU Caichi 1) , HAO Qiuyan 1) , ZHANG J ianfeng 1) , TENG X iaoyun 1) , S un Shilong 1) , Qigang Zhou 2) , WANG Jing 2) , X IAO Qinghua 2) 1) Institut e of Inf ormation Functional Materials, Hebei University of Technology, Tianjin 300130, China 2) General Research Institute of Non-f errous Met als, Beijing 100088, China ABSTRACT The morphology and microstructure of flow pattern defects ( FPDs) in lightly bo ron-doped Czochralski-g row n silicon ( Cz-Si) crystals were investigated using optical microscopy and atomic force mi￾croscopy .The experimental results show ed that the morphology of FPDs w as parabola-like with several steps .Single-ty pe and dual-type voids w ere found on the tip of FPDs and two heaves exist on the left and right sides of the void .All the results have proved that FPDs w ere void-ty pe defects.These results are very useful to investigate FPDs in Cz-Si w afers further and explain the annihilation of FPDs during high-tem￾perature annealing . KEY WORDS flow pattern defects ;g row n-in defects ;atomic force microscopy ;Czochralski-g row n silicon [ 摘自 Rare Metals, 2006, 25( 4) :389] Vol.28 No.8 郭辉等:基于最小二乘支持向量机对偶优化问题的核偏最小二乘 · 793 ·