Distance Correlation

Distance correlation measures dependence between two variables or vectors from their pairwise distances, equalling zero only under independence, so it detects nonlinear and non-monotonic relationships.

거리상관은 두 변수(또는 벡터)의 쌍별 거리로 의존성을 재며 독립일 때만 0이 되므로 비선형·비단조 관계도 잡아냅니다.

My scatterplot looks U-shaped and Pearson r is near zero; is there still a relationship?

산점도가 U자 모양이고 피어슨 상관은 0에 가까운데, 그래도 관계가 있는 건가요?

Distance correlation compares double-centred pairwise distance matrices of the two variables and ranges from 0 to 1, with 0 implying independence when first moments are finite. A permutation test that reshuffles one variable gives a p value without distributional assumptions.

When to use Distance Correlation

• The relationship may be nonlinear or non-monotonic
• Testing independence between a variable and a set of variables
• Screening features for any kind of dependence

When to use something else

• The relationship is linear and an interpretable slope is needed, where Pearson correlation or regression is better
• Both variables are nominal categories, where Cramér's V or mutual information is more natural

Assumptions and requirements

• Independent observations
• Finite first moments
• Variables in a multivariate set are on comparable scales
• Samples above 2,000 rows are randomly subsampled for the distance matrices

What the analysis reports

• Distance correlation
• Squared distance covariance and n·dCov² statistic
• Permutation p value
• Pearson correlation for comparison
• Per-feature distance correlations

How to report it

The distance correlation between [X] and [Y] was dCor = [value] (N = [value]), permutation p = [value] ([value] permutations).

Related methods

• Pearson Correlation Analysis
• Spearman Rank Correlation
• Entropy and Mutual Information Analysis

Run Distance Correlation on Quorant