Xi {discretization}

Auxiliary function for performing the Extended Chi2 discretization algorithm

Description

This function is the \xi, required to perform the Extended Chi2 discretization algorithm.

Usage

Xi(data)

Arguments

data

data matrix

Details

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.

Value

Xi

numeric value, \xi

Author(s)

HyunJi Kim [e-mail]

References

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.

See Also

extendChi2