数据拟合中光滑参数的优化

doi:10.11896/j.issn.1002-137X.2015.09.043

摘要/Abstract

摘要： 数据的函数化是函数数据分析(Functional Data Analysis,FDA)的基础,也是区别于其它分析方法的关键步骤。数据拟合作为数据函数化的主要方法,通常可转化为损失函数和正则项的优化问题,其中的光滑参数就起着权衡损失和过拟合风险的作用。在光滑参数的选择方法中,广义交叉验证(Generalized Cross-Validation,GCV)是一种通用而且较好的参数选择方法,然而GCV是对离散值进行计算,欲得到较准确的光滑参数仍需做大量的计算。针对此问题,提出拟合优化和差分两种求解策略以提高最优光滑参数的求解效率,并在算法精度及效率方面进行了比较分析。在模拟数据和真实数据上的实验结果表明:两种策略与常用的网格法相比,求解效率有较大提高,且算法精度方面几乎相同,此外差分求解策略在精度方面略优于拟合优化求解策略,而拟合优化求解策略的效率更高。

关键词: 光滑参数,广义交叉验证,差分求解策略,拟合优化求解策略

Abstract: Data functionalizing is the basis of functional data analysis (FDA) and important step differed from other analysis methods.As the main approach of data functionalizing,data fitting usually can be converted into an optimization problem including loss function and the regularization term,and smoothing parameter plays a compromising role in weighing loss and the risk of over fitting.Generalized cross-validation (GCV) is a general and better parameter selection way,but massive calculation may be needed in order to get a more accurate smoothing parameter because GCV is calculated on discrete values.Aiming at this problem,the fitting optimization and the finite difference solution strategies were proposed to improve the solution efficiency of selection of the optimal smoothing parameter,and their precision and efficiency were compared and analyzed.The experiment results on simulated and real data sets demonstrate that the two proposed strategies are greatly improved in efficiency compared with the conventional grid method with almost the same precision.The finite difference solution strategy is better than the fitting optimization solution strategy in terms of algorithm precision,and the latter is more efficient.

Key words: Smoothing parameter,Generalized cross-validation,Finite difference solution strategy,Fitting optimization solution strategy

王丽,王文剑,姜高霞. 数据拟合中光滑参数的优化[J]. 计算机科学, 2015, 42(9): 226-229. https://doi.org/10.11896/j.issn.1002-137X.2015.09.043

WANG Li, WANG Wen-jian and JIANG Gao-xia. Optimization for Smoothing Parameter in Process of Data Fitting[J]. Computer Science, 2015, 42(9): 226-229. https://doi.org/10.11896/j.issn.1002-137X.2015.09.043

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