C.FRNN.O.FRST: The fuzzy-rough ownership nearest neighbor algorithm

Description

It is used to predict classes of new datasets/patterns based on the fuzzy-rough ownership nearest neighbor algorithm (FRNN.O) proposed by (Sarkar, 2007).

Usage

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

Value

A matrix of predicted classes of newdata.

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 strings/characters.

newdata

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

See SF.asDecisionTable.

control

a list of other parameters.

m: the weight of distance. The default value is 2.

Author

Lala Septem Riza

Details

This method improves fuzzy \(k\)-nearest neighbors (FNN) by introducing rough sets into it. To avoid determining \(k\) by trial and error procedure, this method uses all training data. Uncertainties in data are accommodated by introducing the rough ownership function. It is the following equation \(o_c\) of each class expressing a squared weighted distance between a test pattern and all training data \(d\) and constrained fuzzy membership \(\mu_{C_c}\).

\(o_c(y) = \frac{1}{|X|}\mu_{C_c}(x)\exp{(-d^{1/(q-1)})}\)

where \(d = \sum_{j=1}^{N}K_j(y_j-x_{ij})^2\)

The predicted value of \(y\) is obtained by selecting class \(c\) where \(o_c(y)\) is maximum.

References

M. Sarkar, "Fuzzy-Rough Nearest-Neighbor Algorithm in Classification" Fuzzy Sets and Systems, vol. 158, no. 19, p. 2123 - 2152 (2007).

Examples

Run this code

#############################################################
## 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]

## convert into the standard decision table
colnames(iris.training) <- c("Sepal.Length", "Sepal.Width", "Petal.Length", 
                             "Petal.Width", "Species")
decision.table <- SF.asDecisionTable(dataset = iris.training, decision.attr = 5, 
                                    indx.nominal = c(5))
tst.iris <- SF.asDecisionTable(dataset = iris.testing)

## in this case, we are using "gradual" for type of membership					   
control <- list(m = 2)

if (FALSE) res.test.FRNN.O <- C.FRNN.O.FRST(decision.table = decision.table, newdata = tst.iris, 
                                 control = control)

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