This function is the \(\xi\), required to perform the Extended Chi2 discretization algorithm.
Xi(data)data matrix
numeric value, \(\xi\)
The following equality is used for calculating the least upper bound(\(\xi\)) of the data set(Chao and Jyh-Hwa (2005)). $$\xi(C,D) = max(m_1, m_2)$$ where \(C\) is the equivalence relation set, \(D\) is the decision set, and \(C^{*}=\{E_1, E_2, \ldots, E_n \}\) is the equivalence classes. \(m_1 = 1- min\{c(E, D) | E \in C^*\) and \( 0.5 < c(E,D) \} \), \(m_2 = 1- max\{c(E, D) | E \in C^*\) and \(c(E,D) < 0.5\} \). $$c(E, D) = 1- \frac{card(E \cap D)}{card(E)}$$ \(card\) denotes set cardinality.
Chao-Ton, S. and Jyh-Hwa, H. (2005). An Extended Chi2 Algorithm for Discretization of Real Value Attributes, IEEE transactions on knowledge and data engineering, Vol. 17, No. 3, 437--441.
Ziarko, W. (1993). Variable Precision Rough Set Model, Journal of computer and system sciences, Vol. 46, No. 1, 39--59.