New Similarity Correlation Functions for Sets and Binary Data Based on Jaccard Similarity Measure

Many similarity, distance, association, and correlation measures for binary data, 2x2 tables, and sets are used in ecology, biology, and social sciences in pattern recognition, machine learning, and data analysis. The Jaccard similarity measure is widely used in these tasks. We consider several extensions of this measure using the negation of binary data to avoid some of its limitations. We propose new association (correlation) measures based on the Jaccard similarity measure. These measures provide new methods for evaluating associations between sets, binary vectors, and dichotomous variables. The paper discusses possible applications of new measures in data analysis, pattern recognition, and machine learning.