RoughSets (version 1.0-0)

D.local.discernibility.matrix.RST: The local strategy algorithm

Description

This is a function that implements the local strategy algorithm based on rough set theory proposed by (Jan G. Bazan et al, 2000), for discretization tasks.

Usage

D.local.discernibility.matrix.RST(decision.table, ...)

Arguments

decision.table

a "DecisionTable" class representing the decision table. See SF.asDecisionTable.

...

other parameters,

Value

• A class "Discretization" that contains the following components:
  • cut.values: a list representing cut values of each considered attributes.
  • type.method: a type of method which is used to define cut values.

    In this case, it is"local.strategy".

  • type.task: a type of task which is"discretization".
  • model: a type of model which is"RST".

Details

The local strategy is an algorithm which implements a decision tree to calculate the quality of a cut (i.e. number of objects discerned by cut). In other words, it finds the best cut by dividing the object set into two subsets of objects, then calculating and repeating the processes until some stopping condition holds. The quality is measured by the number of pairs of objects from X discerned by cut values. The following is the equation used to calculate the number of pairs of objects $W$. For any cut $(a, c) \in C_{A}$, and $X \subseteq U$:

$W^X(a,c) = l^X(a,c) \cdot r^X(a,c) - \displaystyle\sum\limits_{i=1}^r {l_{i}^X(a,c) \cdot r_{i}^X(a,c)}$

where $l^X$ and $r^X$ are the number of objects on either side of $(a,c)$ and $l_{i}^X$ and $r_{i}^X$ are numbers of objects form $X$ belonging to the $j^{th}$ decision class and being on the left-hand-side and right-hand-side of the cut $(a,c)$, respectively.

This function will detect and perform converting the continuous attributes into nominal ones according to states FALSE in parameter nominal.attributes. And, it should be noted that the output of this function is a class containing cut values. In order to generate new decision table, SF.applyDecTable is executed.

References

Jan G. Bazan, Hung Son Nguyen, Sinh Hoa Nguyen, Piotr Synak, and Jakub Wroblewski, "Rough Set Algorithms in Classification Problem", Chapter 2 In: L. Polkowski, S. Tsumoto and T.Y. Lin (eds.): Rough Set Methods and Applications Physica-Verlag, Heidelberg, New York, p. 49 - 88 ( 2000).

See Also

D.max.discernibility.matrix.RST, D.discretize.quantiles.RST,

D.discretize.equal.intervals.RST, and D.global.discernibility.heuristic.RST

Examples

#################################################################
## Example: Determine cut values and generate new decision table
#################################################################
dt.ex1 <- data.frame(c(1, 2, 3, 3, 4, 5, 6, 7, 7, 8), c(2,5, 7, 6, 6, 6, 1, 8, 1, 1),
                             c(3, 5, 1, 1, 3, 6, 8, 8, 1, 1), c(0, 1, 2, 1, 0, 1, 2, 2, 0, 0))
colnames(dt.ex1) <- c("a1", "a2", "a3", "d")
decision.table <- SF.asDecisionTable(dataset = dt.ex1, decision.attr = 4, indx.nominal = c(4))

cut.values <- D.local.discernibility.matrix.RST(decision.table)

## generate new decision table
new.decTable <- SF.applyDecTable(decision.table, cut.values)