Two-Group k-Adic Similarity Coefficients for Binary Classifiers

When using two different sets of binary classification rules on the same items, we obtain two sets of binary vectors. We can, for example, consider the case of two groups of doctors with different experiences classifying patients as diseased or disease-free or two sets of different algorithms classifying consumers as churners or non-churners. In this paper, we propose to extend the well-known Jaccard coefficient and simple matching coefficient to quantify the similarity between two sets of binary vectors. The generalization will be based on the k-adic definition of similarity within sets. We derive the large sample variances of the new coefficients, investigate desirable properties of the established similarity coefficients, and present the applications to real-world datasets.