Breaking Ties of Plurality Voting in Ensembles of Distributed Neural Network Classifiers Using Soft Max Accumulations

Abstract

Part 2: Learning-Ensemble LearningInternational audienceAn ensemble of distributed neural network classifiers is composed when several different individual neural networks are trained based on their local training data. These classifiers can provide either a single class label prediction, or the normalized via the soft max real value class-outputs that represent posterior probabilities which give the confidence levels. To form the ensemble decision the individual classifier decisions can be combined via the well known majority (or plurality) voting that sums the votes for each class and selects the class that receives most of the votes. While the majority voting is the most popular combination rule many ties in votes can occur, especially in multi-class problems. Ties are usually broken either randomly where the unknown instance is assigned randomly to one of the tied classes or using the class proportions where the tied class with the largest proportion wins. We present a tie breaking strategy that uses soft max confidence accumulations. Every class accumulates a vote and a confidence for this vote. If a tie occurs then the tied class with the maximum confidence sum wins. The proposed tie breaking in the voting process performs very well in all cases of different data distributions on various benchmark datasets

Patch-Based CNN Evaluation for Bark Classification

“…Nevertheless, we decided to include this comparison to demonstrate the difficulties of encountering ties in majority voting for patch-based CNN and investigate existing strategies to overcome this. It is interesting to observe (in table 3) that for patches extracted from non-scaled original Bark-101 (where there is a higher number of ties), the best tie-breaking strategy is the maximum confidence sum, as affirmed in [22] where the authors had tested it on simpler datasets (having a maximum of 26 classes in the Letter dataset) taken from the UCI repository [14]. To summarise, we present few important insights.…”

“…multiple classes can have the highest count of votes. In our study, we examine few tiebreaking strategies from existing literature in majority voting [22][23] [26][34] [35].…”

“…Second, using Class Accuracy (given by F1-score), the tie goes in favor of the class having a better F1-score. Outside of these standard methods, more particular to neural network classifiers is the breaking of ties in ensembles by using Soft Max Accumulations [22]. Neural network classifiers output, by default, the class label prediction accompanied by a confidence of prediction (by using soft max function) and this information is leveraged to resolve ties in [22].…”

“…Outside of these standard methods, more particular to neural network classifiers is the breaking of ties in ensembles by using Soft Max Accumulations [22]. Neural network classifiers output, by default, the class label prediction accompanied by a confidence of prediction (by using soft max function) and this information is leveraged to resolve ties in [22]. In case of a tie in the voting process, the confidences for the received votes of the tied classes, are summed up.…”

“…more than one class could get the largest count of votes, and it can be challenging when a considerable number of ties occur. In our study, we apply concepts of ensemble-based classi-fiers and investigate various tie-breaking strategies [22][23] [26][34] [35] of majority voting. We validated our approach on three pre-trained CNNs -Squeezenet [20], MobileNetV2 [28] and VGG16 [30], of which the first two are compact and light-weight models that could be used for applications on mobile devices in the future.…”