Testing modified confusion entropy as split criterion for decision trees

In 2010, a new performance measure to evaluate the results obtained by algorithms of data classification was presented, Confusion Entropy (CEN). This render measure is able to achieve a greater discrimination than Accuracy focusing on the distribution across different classes of both correctly and wrongly classified instances, but it is not able to work correctly in cases of binary classification. Recently, an enhancement has been proposed to correct its behaviour in those cases, the Modified Confusion Entropy (MCEN). In this work, we propose a new algorithm, MCENTree. This algorithm uses MCEN as splitting criterion to build a decision tree model instead of CEN, as proposed in the CENTree algorithm in the literature. We make a comparison among a classic J48, CENTree and the new algorithm MCENTree in terms of Accuracy, CEN and MCEN performance measures, and we analyze how the undesired behaviour of CEN affects the results of the algorithms and how MCEN shows a good behaviour in terms of results: while MCENTree gives correct results in a statistical range [0,1], CENTree sometimes gives non monotonous and out of range results in binary class classification

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.This work was supported by Ministerio de Economía y Competitividad, Gobierno de España, MTM2015 67802-P to R.D. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript