This package contains all the components necessary for performing an identity correlation analysis. The identity correlation value (Icorr) is a scale-invariant measure of the total deviation from the identity line, with a slope of 1 and an origin intercept of 0 (Y = 1X+0). This is a special case of Pearson correlation, which instead quantifies any linear relationship.
The identity correlation value is derived from a linear transformation of the dissimilarity metric D (icorr = 1-2D). D is the average squared perpendicular distance of all data point pairs (x_i, y_i) to the identity line, which is normalized to the summed variance of X and Y. In the end, the Icorr value ranges between 1 (coherence), 0 (dis-coherence), and -1 (anti-coherence). Depending on the specific 2D configuration OMEGA, one can calculate a p-value for the null hypothesis icorr=0.
A detailed description of this approach can be found in the supplementary notes of Bayer et al. 2025, where it is used to measure kinase-substrate relationships in the experimental perturbation potency dimensions of kinase inhibitors. If you use identity correlation analysis in your work, please cite us.
We have registered this package on pypi. To install, it simply do:
$ pip install icorrimport icorr
# some toy data x and y
x = np.random.normal(loc=0, scale=2, size=30)
y = np.random.normal(loc=0, scale=2, size=30)
icv = icorr.identity_correlation(x, y)
omega = icorr.omega(x,y)
# Calculate p values either by numerical (slow) or beta (fast) approximation
p_value = pvalues_numerical_approximation(icv, omega)
p_value = pvalues_beta_approximation(icv, omega)
# Plot the x and y data in a coherence map
icorr.coherence_map(x, y)
# For FDR correction (Benjamini-Hochberg) of many p-values
p_values_adjusted = icorr.fdr_correction(p_values)
# sample and plot a random (H0) icorr distribution given a omega configuration.
random_icvs = icorr.random_sample(omega=(30,5,5,10))
plt.hist(random_icvs, bins=np.linspace(-1, 1, 101))