Set Analysis of Coincident Errors and Its Applications for Combining Classifiers

Although addressed in many papers, classifier dependency is still not well defined. Continuously being described by variety of statistical models from conditional probability to diversity measures, dependency among classifier outputs was recently shown to have a crucial impact on the performance of multiple classifier system. However, individual classifier performances still represent competitive and simple information clearly related to the performance of the combined system. In this work we show that all the measures related to classifier outputs can be reformulated to represent just different forms of the same information of error coincidences. Applying set analysis for the representation and description of error coincidences we define collection of classifier sets decomposed into two complementary types of coincidence levels. Furthermore we illustrate a high flexibility of using the coincidence levels, which supported be a simple algebra cover many established dependency measures including combining error in case of majority voting. Moreover we show that in the setscollection representation of error coincidences a specific inclusion relation results in a quicker and more effective handling of dependency information under different complexity conditions. In the experimental section we examine relations of the introduced error coincidence levels with majority voting combiner using real datasets and classifiers and indicate further potential applications of the presented concepts.