\(M\) given by Hand and Till (2001) defines a multiple class
version of the area under curve of the receiver operating characteristic.
References
David J. Hand and Robert J. Till (2001). A Simple
Generalisation of the Area Under the ROC Curve for Multiple Class
Classification Problems. Machine Learning45(2), p. 171--186.
DOI:
tools:::Rd_expr_doi("10.1023/A:1010920819831").
See Also
help(package="HandTill2001"), especially
?HandTill2001::auc; various packages that calculate
binary class AUC (ROCR) or multiple class AUC
(pROC, caTools).