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| 1 | The new interpretation of support vector machines on statistical learning theory显示文摘This paper is concerned with the theoretical foundation of support vector machines (SVMs). The purpose is to develop further an exact relationship between SVMs and the statistical learning theory (SLT). As a representative, the standard C-support vector classification (C-SVC) is considered here. More precisely, we show that the decision function obtained by C-SVC is just one of the decision functions obtained by solving the optimization problem derived directly from the structural risk minimization principle. In addition, an interesting meaning of the parameter C in C-SVC is given by showing that C corresponds to the size of the decision function candidate set in the structural risk minimization principle. | ZHANG ChunHua 1 , TIAN YingJie 2 & DENG NaiYang 3,1 School of Information, Renmin University of China, Beijing 100872, China 2 Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing 100080, China 3 College of Science, China Agricultural University, Beijing 100083, China | 2010 | Science China Mathematics2010，53，1： | 12 |
| 2 | A theoretical analysis on efficiency of some Newton-PCG methods显示文摘In this paper, we study the efficiency issue of inexact Newton-type methods for smooth unconstrained optimization problems under standard assumptions from theoretical point of view by discussing a concrete Newton-PCG algorithm. In order to compare the algorithm with Newton's method, a ratio between the measures of their approximate efficiencies is investigated. Under mild conditions, it is shown that first, this ratio is larger than 1, which implies that the Newton-PCG algorithm is more efficient than Newton's method,and second, this ratio increases when the dimension n of the problem increases and tends to infinity at least at a rate ln n/ln 2 when n →∞, which implies that in theory the NewtonPCG algorithm is much more efficient for middle- and large-scale problems. These theoretical results are also supported by our preliminary numerical experiments. | DENG Naiyang, ZHANG Jianzhong & ZHONG Ping China Agricultural University, Beijing 100083, China City University of Hong Kong, Hong Kong, China | 2005 | Science China Mathematics2005，48，8： | 4 |
| 3 | A NEW CONJUGATE GRADIENT METHOD AND ITS GLOBAL CONVERGENCE PROPERTIES显示文摘This paper presents a new conjugate gradient method for unconstrained opti-mization. This method reduces to the Polak-Ribiere-Polyak method when line searches areexact. But their performances are differellt in the case of inexact line search. By a simpleexample, we show that the Wolf e conditions do not ensure that the present method and thePolak- Ribiere- Polyak method will pro duce descent direct i0ns even u nder t h e ass umpt ionthat the objective function is Strictly convex. This result contradicts the F0lk axiom thatthe Polak-Ribiere-Polyak with the Wolf e line search should find the minimizer of a strictlyconvex objective function. Finally, we show that there are two ways to improve the newmethod such that it is globally convergent. | LI Zhengfeng CHEN Jing DENG Naiyang(Division of Basic Sciences, China Agricultural University East Campus, Beijing 100083, China) | 1998 | Systems Science and Mathematical Sciences1998，11，1： | 2 |
| 4 | Im- proved generalized eigenvalue proximal support vector Machine 显示文摘 | SHAO Yanhai DENG Naiyang CHEN Weijie | 2013 | IEEE signal processing letters2013，20，3： | 1 |
| 5 | A new Quasi-Newton equation and related methods for unconstrained optlmization显示文摘 | Zhang JianZhon Deng Naiyang Chen Lihua | 1999 | JOTA1999，102，1： | 1 |
| 6 | A new quasi-Newton equation and related methods for unconstrained optimization显示文摘 | ZHANG Jianzhong DENG Naiyang CHEN Lihua | 1999 | JOTA1999，102，3： | 1 |
| 7 | Improvements on twin support vector machine显示文摘 | SHAO Yuanhai ZHANG Chunhua DENG Naiyang | 2011 | IEEE Transaction on Neural Networks2011，22，6： | 1 |
| 8 | Probabilistic outputs for twin support vector machines显示文摘 | Shao Yuanhai Deng Naiyang Yang Zhimin Chen Weijie Wang Zhen | 2012 | Knowledge-Based Systems2012，33，9： | 1 |
| 9 | A proximal classifier with consistency 显示文摘 | Shao Yuanhai Deng Naiyang Chen Weijie | 2013 | Knowledge-Based Systems2013，49，1： | 1 |
| 10 | New method for data dig-SVM显示文摘 | Deng Naiyang Tian Yingjie | 2004 | Beijing:Science Publishing House2004，28，10： | 1 |
| 11 | Probabilistic outputs for twin support vector machines显示文摘 | SHAO Yuanhai DENG Naiyang YANG Zhimin | 2012 | Knowledge-Based Systems2012，33，9： | 1 |
| 12 | SEQUENCE-BASED PROTEIN-PROTEIN INTERACTION PREDICTION VIA SUPPORT VECTOR MACHINE显示文摘 | Yongcui WANG Jiguang WANG Zhixia YANG Naiyang DENG | 2010 | Journal of Systems Science & Complexity2010，23，5： | 1 |
| 13 | A new QuasiNewton equation and related methods for unconstrained optimization显示文摘 | Deng Naiyang Chen Lihua | 1999 | JOTA1999，102，3： | 1 |
| 14 | Nonmonotonic trust region algorithm显示文摘 | Deng Naiyang Xiao Y Zhou F J | 1993 | Journal of Optimization Theory and Applications1993，76，2： | 1 |
| 15 | ON THE CONVERGENCE OF CONJUGATE GRADIENT METHODS INVARIANT TO NONLINEAR SCALING显示文摘ONTHECONVERGENCEOFCONJUGATEGRADIENTMETHODSINVARIANTTONONLINEARSCALINGDENGNaiyang;LIZhengfeng(DivisionofBasicScience,BeijingAg... | DENG Naiyang LI Zhengfeng (Division of Basic Science, Beijing Agricultural Engineering University, Beijing 100083, China) | 1996 | Systems Science and Mathematical Sciences1996，9，2： | 0 |
| 16 | Can Newton method be surpassed显示文摘A local algorithm is proposed for unconstrained optimization problem. Compared with the traditional Newton method with Choleski factorization, this algorithm has the same quadratic convergence. But its computation cost per iteration in average is less when the dimension n≥55. The saving is estimated in the theoretical framework. | Naiyang Deng Zhaozhi Wang | 1999 | Chinese Science Bulletin1999，44，2： | 0 |
| 17 | NEW ROBUST UNSUPERVISED SUPPORT VECTOR MACHINES显示文摘这篇论文基于标准 SVM 的最初的问题的修改柔韧的版本建议柔韧的版本到无指导的分类算法,它直接与标签变量放松它到半明确的编程。数字结果证实建议方法的坚韧性。 | Kun ZHAO Mingyu ZHANG ~ Naiyang DENG | 2011 | Journal of Systems Science & Complexity2011，24，3： | 0 |
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