An Information-Theoretic Definition of Similarity
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Given a set of people and a set of events attended by them, we address the problem of measuring connectedness or tie strength between each pair of persons. The underlying assumption is that attendance at mutual events gives an implicit social network between people. We take an axiomatic approach to this problem. Starting from a list of axioms, which a measure of tie strength must satisfy, we characterize functions that satisfy all the axioms. We then show that there is a range of tie-strength measures that satisfy this characterization. A measure of tie strength induces a ranking on the edges of the social network (and on the set of neighbors for every person). We show that for applications where the ranking, and not the absolute value of the tie strength, is the important thing about the measure, the axioms are equivalent to a natural partial order. To settle on a particular measure, we must make a non-obvious decision about extending this partial order to a total order. This decision is best left to particular applications. We also classify existing tie-strength measures according to the axioms that they satisfy; and observe that none of the "self-referential" tie-strength measures satisfy the axioms. In our experiments, we demonstrate the efficacy of our approach; show the completeness and soundness of our axioms, and present Kendall Tau Rank Correlation between various tie-strength measures.