Metrics in Symbolic Data Analysis

On the order equivalence relation of binary association measures

“…Sokal-Sneath (Hubalek, 1982) SS3 (Gower and Legendre, 1986) S θ a+d a+d+θ (b+c) , θ > 0 S -Nieddu (Nieddu and Rizzi, 2007) SNR a+αd a+βd+γ (b+c) : (Cheetham and Hazel, 1969) K1 (Duarte et al, 1999) And (Tversky, 1977) ST (Gower and Legendre, 1986) T θ a a+θ (b+c) , θ > 0 T Φ(1, 0, −1) Nieddu (Nieddu and Rizzi, 2007) SNR a+αd a+βd+γ (b+c) : (Cheetham and Hazel, 1969) Y Q ad−bc ad+bc Q -Yulle's ω (Hubalek, 1982) Y ω…”

“…The proposed generalized Φ coefficient is conceptually different from generalizations proposed by Tversky (1977), Gower and Legendre (1986) or Nieddu and Rizzi (2007). They focused on generalizing the definition based on a, b, c and d elementary object counts.…”

“…Having different sources of origin and interpretation, they often share some common properties. Association measures have been frequently reviewed and analyzed (Cheetham and Hazel, 1969;Wolda, 1981;Batagelj and Bren, 1995;Clarke et al, 2006;Nieddu and Rizzi, 2007). Despite over a century of research, new association coefficients constantly appear (e.g., Washtell and Markert, 2009;Consonni and Todeschini, 2012).…”

“…Binary association measures are in a large majority defined using four basic values (e.g., Batagelj and Bren, 1995;Nieddu and Rizzi, 2007;Choi et al, 2010). These values represent the frequency of measured objects.…”

“…Following earlier works, the authors identify three groups (named S, T and Q) of coefficients sharing equal rankings. A comprehensive overview and a further generalization of association measures are given by Nieddu and Rizzi (2007). Coefficients S θ and T θ are special cases of their S NR coefficient: Rifqi et al (2008) presented an interesting discussion on relations between 10 coefficients and formed three groups.…”