RoughSets (version 1.3-8)

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

Description

It is used to predict new datasets/patterns based on the fuzzy-rough nearest neighbor algorithm (FRNN) proposed by (Jensen and Cornelis, 2011).

Usage

C.FRNN.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 string/char.

newdata

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

See SF.asDecisionTable.

control

a list of other parameters as follows.

• type.LU: a type of lower and upper approximations. See Section Details. The default value is type.LU = "implicator.tnorm".

• k: the number of neighbors. It should be taken into account that this value could affect the accuracy. The default value is 5.

• type.aggregation: the type of the aggregation operator. See BC.IND.relation.FRST. The default value is type.aggregation = c("t.tnorm", "lukasiewicz").

• type.relation: the type of relation. See BC.LU.approximation.FRST.

  The default value is c("tolerance", "eq.1").

• type.implicator: the type of implicator operator.

  See BC.LU.approximation.FRST. The default value is "lukasiewicz".

• q.some: a vector of values of alpha and beta parameters of VQRS.

  See BC.LU.approximation.FRST. The default value is c(0.1, 0.6).

• q.most: a vector of values of alpha and beta parameter of VQRS.

  See BC.LU.approximation.FRST. The default value is c(0.2, 1).

Author

Lala Septem Riza

Details

This method uses the fuzzy lower and upper approximations to improve the fuzzy nearest neighbor (FNN) algorithm. This algorithm assigns a class to a target instance \(t\) as follows.

• Determine \(k\) nearest neighbors considering their similarity to new patterns.

• Assign new patterns to the class based on maximal value of fuzzy lower and upper approximations. If a value of fuzzy lower approximation is high, it shows that neighbors of newdata belong to a particular class, e.g. C. On the other hand, a high value of fuzzy upper approximation means that at least one neighbor belongs to that class.

In this function, we provide two approaches based on types of fuzzy lower and upper approximations. The following is a list of the considered approximations:

• "implicator.tnorm": It refers to lower and upper approximations based on implicator/t-norm approach. For more detail, it can be seen in BC.LU.approximation.FRST. When using this approach, we need to assign the control parameter as follows:

  control <- list(type.LU = "implicator.tnorm", k,

  type.aggregation, type.relation, t.implicator)

  The detailed description of the components in the control parameter can be seen in

  BC.LU.approximation.FRST.

• "vqrs": It refers to lower and upper approximations based on vaguely quantified rough sets. For more detail, it can be seen in BC.LU.approximation.FRST. When using this approach, we need to assign the control parameter as follows:

  control <- list(type.LU = "vqrs", k, q.some, q.most,

  type.relation, type.aggregation)

  The detailed description of the components in the control parameter can be seen in

  BC.LU.approximation.FRST.

References

R. Jensen and C. Cornelis, "Fuzzy-rough Nearest Neighbour Classification and Prediction", Theoretical Computer Science, vol. 412, p. 5871 - 5884 (2011).

See Also

C.FRNN.O.FRST, C.POSNN.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 a 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, 
                type.aggregation = c("t.tnorm", "lukasiewicz"), 
                type.relation = c("tolerance", "eq.1"), t.implicator = "lukasiewicz") 									   
if (FALSE) res.1 <- C.FRNN.FRST(decision.table = decision.table, newdata = tst.iris,
                             control = control)

###### FRNN algorithm using VQRS
control <- list(type.LU = "vqrs", k = 20, q.some = c(0.1, 0.6), q.most = c(0.2, 1), 
                 type.relation = c("tolerance", "eq.1"), 
                 type.aggregation = c("t.tnorm","lukasiewicz"))
if (FALSE) res.2 <- C.FRNN.FRST(decision.table = decision.table, newdata = tst.iris,
                             control = control)