In this paper, a class of statistics named ART (the alternant recursivetopology statistics) is proposed to measure the properties of correlationbetween two variables. A wide range of bi-variable correlations both linear andnonlinear can be evaluated by ART efficiently and equitably even if nothing isknown about the specific types of those relationships. ART compensates thedisadvantages of Reshef's model in which no polynomial time precise algorithmexists and the "local random" phenomenon can not be identified. As a class ofnonparametric exploration statistics, ART is applied for analyzing a dataset of10 American classical indexes, as a result, lots of bi-variable correlationsare discovered.
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