Application of the Gini Correlation Coefficient to Infer Regulatory Relationships in Transcriptome Analysis

The GCC can detect the regulatory relationships missed by the PCC, SCC, and BiWt methods. A, The GCC can detect a linear relationship with similar correlation values to the PCC and SCC correlations. B, The PCC failed to infer the relationship in the samples containing outliers, which was detected by the GCC, SCC, and BiWt. The five outlier samples are represented by the red circles in the gray region in seed. C, The GCC was able to identify transient interactions that were overlooked by the PCC, SCC, and BiWt. The expression values of TF and target are only correlated in nine samples in apex out of the 79 samples (red circles in the gray region). Two correlations, GCC1 and GCC2, are produced by the GCC reciprocally using rank and value information of the two genes’ expression data. In the last two columns, the expression data of genes sorted with their own rank information are displayed as black dashed curves, while the expression data of genes sorted with the other gene’s rank information are shown as blue and red solid curves. The Gini correlation can be explained as the difference between the solid and dashed curves weighted by the rank information. “Value” and “Rank” denote the value and the rank information of the gene expression data, respectively.

Assessment of the influences from the outlier data points on the five methods. The performances of the correlation methods were evaluated on the pairs TF-target, TF-cofactor, and cofactor-target gene sets, with influences of zero, one to five, six to 10, and more than 10 outliers by ROC analyses.

Assessment of the influences from sample size on the five methods. A and B, A significant linear relationship exists between the gene expression profiles of the TF-target (AGL-Hsp40) gene pair. C, The average correlation of the different correlation methods for 1,000 gene pairs with five to 75 samples randomly selected from the gene expression profiles of the AGL-Hsp40 gene pair. D, The differences between the correlations computed on simulated gene pairs (sCor) and the Pearson correlations on the real gene pairs (rCor), computed with the formula (sCor − rCor)/rCor. “Log2 value” denotes the log2-transformed value of the gene expression data.

The compatibility of the five correlation methods on RNA-Seq data. A, The kernel density estimation of the read counts and the RPKM values were generated from the Arabidopsis RNA-Seq data (Gene Expression Omnibus accession nos. GSM838184 and GSM764078). By using the RNA-Seq data without (B) and with (C) log transformation, the average correlation coefficients of each method were calculated from 2,000 random gene pairs with an expected correlation coefficient of 0.70 across the five to 100 simulated samples. “Ave correlation” represents the average correlation coefficients.