evclass (version 2.0.2)

decision: Decision rules for evidential classifiers

Description

decision returns decisions from a loss matrix and mass functions computed by an evidential classifier.

Usage

decision(
  m,
  L = 1 - diag(ncol(m) - 1),
  rule = c("upper", "lower", "pignistic", "hurwicz"),
  rho = 0.5
)

Value

A n-vector with the decisions (integers between 1 and na).

Arguments

m

Matrix of masses for n test cases. Each row is a mass function. The first M columns correspond to the mass assigned to each of the M classes. The last column corresponds to the mass assigned to the whole set of classes.

L

The loss matrix of dimension (M,na) or (M+1,na), where na is the number of actions. L[k,j] is the loss incurred if action j is chosen and the true class is \(\omega_k\). If L has M+1 rows, the last row corresponds to the unknown class.

rule

Decision rule to be used. Must be one of these: 'upper' (upper expectation), 'lower' (lower expectations), 'pignistic' (pignistic expectation), 'hurwicz' (weighted sum of the lower and upper expectations).

rho

Parameter between 0 and 1. Used only is rule='hurwicz'.

Author

Thierry Denoeux.

Details

This function implements the decision rules described in Denoeux (1997), with an arbitrary loss function. The decision rules are the minimization of the lower, upper or pignistic expectation, and Jaffray's decision rule based on minimizing a convex combination of the lower and upper expectations. The function also handles the case where there is an "unknown" class, in addition to the classes represented in the training set.

References

T. Denoeux. Analysis of evidence-theoretic decision rules for pattern classification. Pattern Recognition, 30(7):1095--1107, 1997.

See Also

EkNNval, proDSval

Examples

## Example with M=2 classes
m<-matrix(c(0.9,0.1,0,0.4,0.6,0,0.1,0.1,0.8),3,3,byrow=TRUE)
## Loss matrix with na=4 acts: assignment to class 1, assignment to class2,
# rejection, and assignment to the unknown class.
L<-matrix(c(0,1,1,1,0,1,0.2,0.2,0.2,0.25,0.25,0),3,4)
d<-decision(m,L,'upper') ## instances 2 and 3 are rejected
d<-decision(m,L,'lower') ## instance 2 is rejected, instance 3 is
# assigned to the unknown class