Combining Classifiers through Triplet-Based Belief Functions

Classifier outputs in the form of continuous values have often been combined using linear sum or stacking, but little is generally known about evidential reasoning methods for combining truncated lists of ordered decisions. In this paper we introduce a novel class-indifferent method for combining such a kind of classifier decisions. Specifically we model each output given by classifiers on new instances as a list of ranked decisions that is divided into 2 subsets of decisions, which are represented by triplet-based belief functions and then are combined using Dempster’s rule of combination. We present a formalism for triplet-based belief functions and establish a range of general formulae for combining these beliefs in order to arrive at a consensus decision. In addition we carry out a comparative analysis with an alternative representation dichotomous belief functions on the UCI benchmark data. We also compare our combination method with the popular methods of stacking, boosting, linear sum and majority voting over the same benchmark data to demonstrate the advantage of our approach.