A nonlinear correlation measure with applications to gene expression data.

Area of Science:

• Biostatistics
• Bioinformatics
• Genomics

Background:

• Nonlinear correlations are prevalent in biomedical data, particularly in gene expression across time.
• Understanding these nonlinear relationships is crucial for biological discovery, such as in T helper (Th17) cell differentiation.

Purpose of the Study:

• To introduce Kernelized correlation (Kc), a new statistical procedure for measuring nonlinear correlations.
• To evaluate Kc's performance against established methods like Pearson's correlation and distance correlation.

Main Methods:

• Kc transforms data into a high-dimensional space using a kernel function.
• The transformed data is then analyzed using a classical correlation coefficient (e.g., Pearson's r).
• The algorithm and R code for Kc are provided.

Main Results:

• Kc, particularly with the RBF kernel (Kc-RBF), outperforms Pearson's r and distance correlation (dCor) in moderately noisy nonlinear data.
• Kc successfully identified nonlinear gene correlations in Th17 cell differentiation, surpassing dCor and DESeq.
• Kc demonstrated superior performance in estimating nonlinear correlations for gene pairs in yeast cell cycle regulation.

Conclusions:

• Kernelized correlation (Kc) is a simple yet effective method for quantifying pairwise nonlinear correlations.
• Kc offers advantages in detecting complex biological relationships, especially in gene expression data.
• The findings suggest Kc as a valuable tool for biomedical data analysis and discovery.