A New Kind of Nonparametric Test for Statistical Comparison of Multiple Classifiers over Multiple Datasets

Nonparametric statistical analysis, such as the Friedman test (FT), is gaining more and more attention due to its useful applications in a lot of experimental studies. However, traditional FT for the comparison of multiple learning algorithms on different datasets adopts the naive ranking approach. The ranking is based on the average accuracy values obtained by the set of learning algorithms on the datasets, which neither considers the differences of the results obtained by the learning algorithms on each dataset nor takes into account the performance of the learning algorithms in each run. In this paper, we will first propose three kinds of ranking approaches, which are the weighted ranking approach, the global ranking approach (GRA), and the weighted GRA. Then, a theoretical analysis is performed to explore the properties of the proposed ranking approaches. Next, a set of the modified FTs based on the proposed ranking approaches are designed for the comparison of the learning algorithms. Finally, the modified FTs are evaluated through six classifier ensemble approaches on 34 real-world datasets. The experiments show the effectiveness of the modified FTs.