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无界抽样情形下不定核的系数正则化回归
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作者 蔡佳 王承 《中国科学:数学》 CSCD 北大核心 2013年第6期613-624,共12页
本文讨论样本依赖空间中无界抽样情形下最小二乘损失函数的系数正则化问题.这里的学习准则与之前再生核Hilbert空间的准则有着本质差异:核除了满足连续性和有界性之外,不需要再满足对称性和正定性;正则化子是函数关于样本展开系数的l2-... 本文讨论样本依赖空间中无界抽样情形下最小二乘损失函数的系数正则化问题.这里的学习准则与之前再生核Hilbert空间的准则有着本质差异:核除了满足连续性和有界性之外,不需要再满足对称性和正定性;正则化子是函数关于样本展开系数的l2-范数;样本输出是无界的.上述差异给误差分析增加了额外难度.本文的目的是在样本输出不满足一致有界的情形下,通过l2-经验覆盖数给出误差的集中估计(concentration estimates).通过引入一个恰当的Hilbert空间以及l2-经验覆盖数的技巧,得到了与假设空间的容量以及与回归函数的正则性有关的较满意的学习速率. 展开更多
关键词 学习理论 最小二乘回归 再生核Hilbet空间 l2-经验覆盖数
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基于投影算子的正则化最小二乘回归 被引量:2
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作者 杨运中 冯云龙 《武汉大学学报(理学版)》 CAS CSCD 北大核心 2012年第2期100-104,共5页
通过引入经验覆盖数(empirical covering number)和投影算子(projection-operator),从理论上研究正则化最小二乘回归学习算法.与已有的方法相比,一方面简化了回归分析的过程;另一方面,提高了最小二则回归学习算法的误差收敛阶.即,通过... 通过引入经验覆盖数(empirical covering number)和投影算子(projection-operator),从理论上研究正则化最小二乘回归学习算法.与已有的方法相比,一方面简化了回归分析的过程;另一方面,提高了最小二则回归学习算法的误差收敛阶.即,通过引入投影算子,得到了O(m-1)型的收敛阶,这是统计学习理论中关于泛化误差的最佳逼近阶. 展开更多
关键词 学习理论 正则化最小二乘回归 投影算子 经验覆盖数
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A new semi-empirical model for soil moisture content retrieval by ASAR and TM data in vegetation-covered areas 被引量:8
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作者 YU Fan ZHAO YingShi 《Science China Earth Sciences》 SCIE EI CAS 2011年第12期1955-1964,共10页
Active microwave and passive optical remote sensing data have demonstrated their respective advantages in inversion of surface soil moisture content. A new semi-empirical model is presented for soil moisture content r... Active microwave and passive optical remote sensing data have demonstrated their respective advantages in inversion of surface soil moisture content. A new semi-empirical model is presented for soil moisture content retrieval in vegetation-covered areas, using ENVISAT-ASAR and LANDSAT-TM data collaboratively. Derivation of the algorithm is based on simplification of the Michigan Microwave Canopy Scattering Model (MIMICS). In the model, the ground surface is divided into a canopy layer and a soil layer, and empirical relationships simulated among vegetation water mass We, the backscatter coefficient σpq1, the bidirectional scattering coefficient σpq2 and the extinction coefficient τp. The key input parameters of the semi-empirical model are reduced to only the leaf area index (LAI), which can be easily inverted by the optical model PROSAIL, allowing coupling of the microwave and optical models to be achieved. Also, vegetation RMS height (Svcg) is introduced to correct for the radar-shadow effect caused by over-laying vegetation. Analysis of the parameter sensitivity of the semi-empirical model showed that when the regional Leaf Area Index is small (LAI≤3), the model is more applicable. Soil moisture distribution in the study area was mapped using the semi-empirical model and field ground measurements used for model validation. This showed that, after correction of the radar-shadow effect, the average relative error (Er) between ground-measured and semi-empirical model-derived estimates of soil moisture decreased from 17.6% to 10.4%, while the RMS reduced from 0.055 to 0.031 g cm^-3. The accuracy of soil moisture estimates from the semi-empirical model is much better than for the MIMICS model (Er = 22.7%, RMS = 0.068 g cm^-3), showing that the semi-empirical model is efficient at obtaining regional surface soil moisture contents when LAI is small. 展开更多
关键词 microwave and optic remote sensing MIMICS PROSAIL soil moisture
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