Affiliations: [a] State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China | [b] College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
Correspondence:
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Corresponding author: Keping Li, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China. E-mail:kpli@bjtu.edu.cn
Abstract: Since the maximal information coefficient (MIC) was proposed by Reshef et al. [20], it has been successfully applied into many fields to discover hidden but valuable two-variable relationships. But the algorithm proposed by Reshef et al. [20] can only calculate the MIC of two-variable relationships. In this paper, to the best of our knowledge, the definition of MIC of multi-variable relationships is proposed for the first time, and afterward, an adaptive algorithm, named Adaptive-MIC, is presented which can deal with not only relationships of pairs of variables, but also multi-variable relationships. Compared to the algorithm of Reshef et al. [20], the proposed Adaptive-MIC algorithm is much faster when dealing with two-variable relationships. Furthermore, with the increasing of the size of data sets and the dimensions of relationships, the computing time of the proposed Adaptive-MIC algorithm increases slowly. The fast Adaptive-MIC algorithm is scalable for high-dimensional relationships, and therefore, it is suitable for big data.
Keywords: The maximal information coefficient (MIC), mutual information, the bisecting k-means clustering algorithm, big data
