For binary vectors, this similarity counts agreements on both presences and absences. Its complement is the normalized Hamming distance. Whether joint absences should count as similarity depends on the application; rare-presence data may call for a different coefficient.
The displayed distance is the normalized Hamming distance. Each coordinate mismatch between implies a mismatch between or , so summing the indicator inequalities proves the triangle inequality. Nonnegativity, symmetry and separation follow immediately. It is a metric on profiles; on separately labelled individuals with identical profiles it is a pseudometric.
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The Simple Matching Coefficient (SMC) is a statistic used to measure the similarity between two sets or binary vectors. It provides a way to quantify the degree of similarity based on the presence or absence of certain characteristics. For binary vectors \( A \) and \( B \), each of length \( n \): - \( a \) is the number of features that are present in both \( A \) and \( B \) (i.e., both vectors have a value of 1).