decision function

Decision rules for evidential classifiers

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

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

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'.

Returns

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

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.

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

References

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

See Also

EkNNval, proDSval

Author(s)

Thierry Denoeux.