Coefficient of determination in nonlinear signal processing
Coefficient of determination in nonlinear signal processing
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DOI：
10.1016/s0165-1684(00)00079-7
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发表时间：
2000-10-01
影响因子：
4.4
通讯作者：
Chen, YD
中科院分区：
文献类型：
--
作者：
Dougherty, ER;Kim, S;Chen, YD
对于最优滤波器的统计设计，采用大量观测随机变量在概率上是有利的；然而，估计误差随着变量数量的增加而增加，因此对目标变量的确定没有贡献的变量可能会产生不利影响。在线性过滤中，确定涉及输入变量和目标变量之间的相关系数。本文讨论了非线性滤波中更通用的确定系数的使用。根据滤波器估计目标变量的程度超出通过目标变量的均值估计的程度来定义确定系数。滤波器约束降低了系数，但也降低了滤波器设计中的估计误差。因为与观察变量的数量相比样本相对较小的情况是人们最感兴趣的，所以要详细考虑确定系数的估计。人们可能无法获得最佳滤波器的良好估计，但仍然可以使用系数的粗略估计来找到有用的观察变量集。由于最小误差估计是确定的基础，因此该材料处于信号处理、计算学习和模式识别的界面。几个信号处理因素影响应用：信号模型、形态算子表示和所需的算子属性。特别是，本文根据形态核/基表示来讨论增算算子的 VC 维。考虑两个应用：用于恢复退化的二值图像的窗口大小；寻找相对于基因组调控中的目标基因具有显着预测能力的基因组。 (C) 2000 Elsevier Science B.V. 保留所有权利。
For statistical design of an optimal filter, it is probabilistically advantageous to employ a large number of observation random variables; however, estimation error increases with the number of variables, so that variables not contributing to the determination of the target variable can have a detrimental effect. In linear filtering, determination involves the correlation coefficients among the input and target variables. This paper discusses use of the more general coefficient of determination in nonlinear filtering. The determination coefficient is defined in accordance with the degree to which a filter estimates a target variable beyond the degree to which the target variable is estimated by its mean. Filter constraint decreases the coefficient, but it also decreases estimation error in filter design. Because situations in which the sample is relatively small in comparison with the number of observation variables are of salient interest, estimation of the determination coefficient is considered in detail. One may be unable to obtain a good estimate of an optimal filter, but can nonetheless use rough estimates of the coefficient to find useful sets of observation variables. Since minimal-error estimation underlies determination, this material is at the interface of signal processing, computational learning, and pattern recognition. Several signal-processing factors impact application: the signal model, morphological operator representation, and desirable operator properties. In particular, the paper addresses the VC dimension of increasing operators in terms of their morphological kernel/basis representations. Two applications are considered: window size for restoring degraded binary images; finding sets of genes that have significant predictive capability relative to target genes in genomic regulation. (C) 2000 Elsevier Science B.V. All rights reserved.