| Levenberg-Marquardt算法的一种新解释 |
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| 引用本文： | 张鸿燕,耿征. Levenberg-Marquardt算法的一种新解释[J]. 计算机工程与应用, 2009, 45(19): 5-8. DOI: 10.3778/j.issn.1002-8331.2009.19.002 |
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| 作者姓名： | 张鸿燕 耿征 |
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| 作者单位： | 中国科学院,自动化研究所,复杂系统与智能科学重点实验室,北京,100190;中国科学院,自动化研究所,复杂系统与智能科学重点实验室,北京,100190 |
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| 基金项目： | 国家高技术研究发展计划(863) |
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| 摘 要： | Levenberg-Marquard(tLM)算法与最小二乘(Least Square,LS)方法关系密切,标度总体最小二乘(Scaled Total Least Square,STLS)是最小二乘,数据最小二乘(Data Least Square,DLS)与总体最小二乘(Total Least Square,TLS)的统一与推广,但是它与LM算法的关系尚不清楚。给出了一种求STLS解的算法及其子空间解释与拓扑解释,利用矩阵分解揭示了LM算法与STLS的密切关系,结果表明:阻尼因子使得LS解转变为STLS解;噪声子空间的剔除与系数矩阵条件数的控制保证了LM算法的稳健性与收敛速度;STLS的鲁棒性保障了LM算法处理过参数化问题的能力。
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| 关 键 词： | 标度总体最小二乘 Levenberg-Marquardt(LM)算法 计算机视觉 |
| 收稿时间： | 2008-12-26 |
| 修稿时间： | 2009-2-11 |
Novel interpretation for Levenberg-Marquardt algorithm |
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| ZHANG Hon-yan,GENG Zheng. Novel interpretation for Levenberg-Marquardt algorithm[J]. Computer Engineering and Applications, 2009, 45(19): 5-8. DOI: 10.3778/j.issn.1002-8331.2009.19.002 |
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| Authors: | ZHANG Hon-yan GENG Zheng |
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| Affiliation: | ZHANG Hong -yan,GENG Zheng.Key Laboratory of Complex Systems , Intelligence Science,Institute of Automation,CAS,Beijing 100190,China |
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| Abstract: | The Levenberg-Marquard(tLM) algorithm is closely related with the Least Squares(LS) approach.The Scaled Total Least Squares(STLS) approach is a unification and generalization of the LS,Data Least Squares(DLS) and Total Least Squares (TLS) approaches,but its relation with the LM algorithm is not clear.In this paper,a STLS algorithm and its interpretations via subspace and topology are proposed.The relation of the STLS approach and the LM algorithm are explored by matrix decomposition and the results show tha... |
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| Keywords: | Scaled Total Least Squares（STLS） Levenberg-Marquardt（LM） algorithm computer vision |
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