Chen Y Ann, Almeida Jonas S, Richards Adam J, Müller Peter, Carroll Raymond J, Rohrer Baerbel
Department of Biostatistics, Moffitt Cancer Center, Tampa, FL, USA,
J Comput Graph Stat. 2010 Sep 1;19(3):552-568. doi: 10.1198/jcgs.2010.08160.
We propose a distribution-free approach to detect nonlinear relationships by reporting local correlation. The effect of our proposed method is analogous to piece-wise linear approximation although the method does not utilize any linear dependency. The proposed metric, maximum local correlation, was applied to both simulated cases and expression microarray data comparing the rd mouse with age-matched control animals. The rd mouse is an animal model (with a mutation for the gene Pde6b) for photoreceptor degeneration. Using simulated data, we show that maximum local correlation detects nonlinear association, which could not be detected using other correlation measures. In the microarray study, our proposed method detects nonlinear association between the expression levels of different genes, which could not be detected using the conventional linear methods. The simulation dataset, microarray expression data, and the Nonparametric Nonlinear Correlation (NNC) software library, implemented in Matlab, are included as part of the online supplemental materials.
我们提出一种无分布方法，通过报告局部相关性来检测非线性关系。尽管该方法未利用任何线性相关性，但其效果类似于分段线性近似。所提出的度量标准——最大局部相关性，被应用于模拟案例和表达微阵列数据，将rd小鼠与年龄匹配的对照动物进行比较。rd小鼠是一种用于光感受器退化的动物模型（具有Pde6b基因突变）。使用模拟数据，我们表明最大局部相关性能够检测到非线性关联，而其他相关性度量方法则无法检测到。在微阵列研究中，我们提出的方法能够检测到不同基因表达水平之间的非线性关联，这是传统线性方法无法检测到的。作为在线补充材料的一部分，包含了模拟数据集、微阵列表达数据以及用Matlab实现的非参数非线性相关性（NNC）软件库。
