A Comparison of Multi-way Similarity Coefficients for Binary Sequences

The paper compares three formulations of n-way (for groups of size n ≥ 2) similarity coefficients for binary sequences. Properties that the similarity coefficients may have in general, not just for specific data, are discussed, and it is investigated how the different n-way formulations are related. Using the n-way Bennani-Heiser coefficients, the similarity between m sequences (2 ≤ m ≤ n) is always equal to or greater than the similarity between the m sequences and n – m other sequences. n-Way coefficients based on 2-way information lack several of the properties that the Bennani-Heiser coefficients possess. For example, with the former coefficients it is possible to have zero similarity between two objects, but positive similarity between the two objects and a third object.