Enhancing Confusion Entropy (CEN) for binary and multiclass classification

Different performance measures are used to assess the behaviour, and to carry out the comparison, of classifiers in Machine Learning. Many measures have been defined on the literature, and among them, a measure inspired by Shannon's entropy named the Confusion Entropy (CEN). In this work we introduce a new measure, MCEN, by modifying CEN to avoid its unwanted behaviour in the binary case, that disables it as a suitable performance measure in classification. We compare MCEN with CEN and other performance measures, presenting analytical results in some particularly interesting cases, as well as some heuristic computational experimentation.