Detecting Trivariate Associations in High-Dimensional Datasets

Abstract

Detecting correlations in high-dimensional datasets plays an important role in data mining and knowledge discovery. While recent works achieve promising results, detecting multivariable correlations especially trivariate associations still remains a challenge. For example, maximal information coefficient (MIC) introduces generality and equitability to detect bivariate correlations but fails to detect multivariable correlation. To solve the problem mentioned above, we proposed quadratic optimized trivariate information coefficient (QOTIC). Specifically, QOTIC equitably measures dependence among three variables. Our contributions are three-fold: (1) we present a novel quadratic optimization procedure to approach the correlation with high accuracy; (2) QOTIC exceeds existing methods in generality and equitability as QOTIC has general test functions and is applicable in detecting multivariable correlation in datasets of various sample sizes and noise levels; (3) QOTIC achieved both higher accuracy and higher time-efficiency than previous methods. Extensive experiments demonstrate the excellent performance of QOTIC.