RoughSets (version 1.0-0)

C.POSNN.FRST: The positive region based fuzzy-rough nearest neighbour algorithm

Description

It is a function used to implement the positive region based fuzzy-rough nearest neighbour algorithm (POSNN) which was proposed by (N. Verbiest et al, 2012) for predicting classes of new data.

Usage

C.POSNN.FRST(decision.table, newdata, control = list())

Arguments

decision.table

a "DecisionTable" class representing the decision table. See SF.asDecisionTable. It should be noted that the data must be numeric values instead of string/char.

newdata

a "DecisionTable" class representing data for the test process.

See SF.asDecisionTable.

control

a list of other parameters which is the same as C.FRNN.FRST.

Value

• A matrix of predicted classes of newdata.

Details

This method is aimed to improve the fuzzy-rough nearest neighbour algorithm (C.FRNN.FRST) algorithm by considering the fuzzy positive region. Basically the following steps are used to classify an instance $t$:

• determine the set of k-nearest neighbour of$t$,$NN$.
• assign$t$to the class$C$for which$\frac{\displaystyle\sum\limits_{x \in NN} R(x,t)C(x)POS(x)}{\displaystyle\sum\limits_{x \in NN} R(x,t)}$is maximal.

References

N. Verbiest, C. Cornelis and R. Jensen, "Fuzzy-rough Positive Region Based Nearest Neighbour Classification", In Proceedings of the 20th International Conference on Fuzzy Systems (FUZZ-IEEE 2012), p. 1961 - 1967 (2012).

See Also

C.FRNN.FRST, C.FRNN.O.FRST

Examples

#############################################################
## In this example, we are using Iris dataset.
## It should be noted that since the values of the decision attribute are strings,
## they should be transformed into numeric values using unclass()
#############################################################
data(iris)
## shuffle the data
set.seed(2)
irisShuffled <- iris[sample(nrow(iris)),]

## transform values of the decision attribute into numerics
irisShuffled[,5] <- unclass(irisShuffled[,5])

## split the data into training and testing data
iris.training <- irisShuffled[1:105,]
iris.testing <- irisShuffled[106:nrow(irisShuffled),1:4]

colnames(iris.training) <- c("Sepal.Length", "Sepal.Width", "Petal.Length",
                       "Petal.Width", "Species")

## convert into the standard decision table
decision.table <- SF.asDecisionTable(dataset = iris.training, decision.attr = 5,
                                     indx.nominal = c(5))
tst.iris <- SF.asDecisionTable(dataset = iris.testing)

## FRNN algorithm using lower/upper approximation: Implicator/tnorm based approach
control <- list(type.LU = "implicator.tnorm", k = 20, t.tnorm = "lukasiewicz",
                type.relation = c("tolerance", "eq.1"), t.implicator = "lukasiewicz")

res.test.POSNN <- C.POSNN.FRST(decision.table = decision.table,
                              newdata = tst.iris, control = control)