The Eigenvalues Entropy as a Classifier Evaluation Measure

TL;DR

This paper introduces the eigenvalues entropy as a novel evaluation measure for classifiers, especially effective with imbalanced datasets, providing better performance than traditional measures.

Contribution

The paper proposes using eigenvalues entropy as an evaluation metric for classification, establishing relations with standard measures and estimating confusion matrices for imbalanced data.

Findings

Eigenvalues entropy correlates with sensitivity, specificity, AUC, and Gini index.

It provides more accurate evaluation for imbalanced datasets.

Demonstrates improved performance over standard measures on various datasets.

Abstract

Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A classifier prediction results and training set information are often used to get a contingency table which is used to quantify the method quality through an evaluation measure. Such measure, typically a numerical value, allows to choose a suitable method among several. Many evaluation measures available in the literature are less accurate for a dataset with imbalanced classes. In this paper, the eigenvalues entropy is used as an evaluation measure for a binary or a multi-class problem. For a binary problem, relations are given between the eigenvalues and some commonly used measures, the sensitivity, the specificity, the area under the operating receiver characteristic curve and the Gini index. A by-product result of this paper is an estimate of the confusion matrix to deal with the curse of the imbalanced classes. Various data examples are used to show the better performance of the proposed evaluation measure over the gold standard measures available in the literature.