χ2 similarity, metric, and distance
Symmetric uncertainty coefficient
The χ2 similarity, metric, and distance measures are based on contingency tables and can thus handle non-monotonic and qualitative variables (see this endpoint for details).
This coefficient is based in the logic of information theory. It expresses the amount of information shared between two variables using contingency tables and Shannon's information formula. Resorting to contingency tables is useful when dealing with qualitative variables with no monotonic relationships. Probabilities of association can be calculated and then translated into measures of dependence. Legendre and Legendre (1998) offer a developed discussion on information theory in numerical ecology.
Legendre P, Legendre L. Numerical Ecology. 2nd ed. Amsterdam: Elsevier, 1998. ISBN 978-0444892508.