A modified entropy-based performance criterion for class-modelling with multiple classes

Abstract

The paper presents a new proposal for a single overall measure, the diagonal modified confusion entropy (DMCEN), to assess the performance of class-models jointly computed for several classes, a versatile index regarding sensitivity and specificity, and that supports class weighting.

The characteristics of the proposed figure of merit are illustrated as against other usual performance measures and show how the index is more sensitive to the variations in the class-models than similar published indexes.

Besides, a benchmark value representing a random modelling is also defined for DMCEN to be used as initial level to assess the quality of the built class-models.

Furthermore, systematic comparisons have been conducted by using the degree of consistency C and the degree of discriminancy D when comparing the proposed DMCEN to the usual total efficiency (a geometric mean between sensitivity and specificity).

Simulations show that, for a hundred thousand sensitivity/specificity matrices with four categories, C is almost 0.7 on average, well above the needed 0.5, and there is more than 62% probability that DMCEN detects differences when the total efficiency does not.

Illustration of the application of the index is shown with an experimental data set with four categories.