A general index for linear and nonlinear correlations for high dimensional genomic data
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METHODOLOGY ARTICLE
Open Access
A general index for linear and nonlinear correlations for high dimensional genomic data Zhihao Yao1,2 , Jing Zhang1,2 and Xiufen Zou1,2*
Abstract Background: With the advance of high throughput sequencing, high-dimensional data are generated. Detecting dependence/correlation between these datasets is becoming one of most important issues in multi-dimensional data integration and co-expression network construction. RNA-sequencing data is widely used to construct gene regulatory networks. Such networks could be more accurate when methylation data, copy number aberration data and other types of data are introduced. Consequently, a general index for detecting relationships between high-dimensional data is indispensable. Results: We proposed a Kernel-Based RV-coefficient, named KBRV, for testing both linear and nonlinear correlation between two matrices by introducing kernel functions into RV2 (the modified RV-coefficient). Permutation test and other validation methods were used on simulated data to test the significance and rationality of KBRV. In order to demonstrate the advantages of KBRV in constructing gene regulatory networks, we applied this index on real datasets (ovarian cancer datasets and exon-level RNA-Seq data in human myeloid differentiation) to illustrate its superiority over vector correlation. Conclusions: We concluded that KBRV is an efficient index for detecting both linear and nonlinear relationships in high dimensional data. The correlation method for high dimensional data has possible applications in the construction of gene regulatory network. Keywords: High-dimensional data, Nonlinear correlation, RV-coefficient
Background With the rapid advance in high throughput sequencing technologies, multiple, high-dimensional data types are widely available. In recent years, the advance in nextgeneration sequencing and single-cell sequencing offers a significantly increased level of biological details than just total gene expressions [1–5]. Moreover, research based on exon-level expression data, multiomics data and other high-dimensional biological data has led to a deeper understanding of biology [6–8]. Figuratively speaking, the *Correspondence: [email protected] School of Mathematics and Statistics, Wuhan University, 430072 Wuhan, China 2 Hubei Key Laboratory of Computational Science, Wuhan University, 430072 Wuhan, China 1
traditional genome data have been extended to transcriptome, DNA methylome data, etc., which reveal overall pictures of cells (Fig. 1). A useful practice in high-dimensional data integration is to measure and rank the dependence between pairs of datasets in a simple and comprehensive way and these datasets are usually represented as matrices or even tensors. Therefore, one of the challenging tasks is how to define a reasonable correlation coefficient between pairs of high-dimensional data sets in matrix form. Although a great number of tests and measures are available for identifying linear and nonlinear correlations between two variables, such as P
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