Fusion of Classifiers based on Centrality Measures Ronan A. Silva 1,4 , Alceu S. Britto Jr. 1,5 , Fabricio Enembreck 1 , Robert Sabourin 2 , and Luis S. Oliveira 3 1 Pontifical Catholic University of Parana (PUCPR), Curitiba, PR, Brazil 2 ´ Ecole de Technologie Sup´ erieure ( ´ ETS), Montreal, QC, Canada 3 Federal University of Parana (UFPR), Curitiba, PR, Brazil 4 Federal Institute of Parana (IFPR), Telemaco Borba, PR, Brazil 5 State University of Ponta Grossa (UEPG), Ponta Grossa, PR, Brazil Email: {ronan.silva}@pucpr.edu.br Abstract—This paper presents the Centrality Based Fusion (CBF) method for ensemble fusion which is based on the centrality measures in the context of complex network theory. Such a concept has been applied in Social Network Analysis to measure the importance of each person inside of a social network. We hypothesized that the centrality of each classifier inside of an ensemble represented as a complex network could be combined with accuracy to provide the weight for its decision during the ensemble fusion. The main idea is to derive the weight considering the classifier importance inside the ensemble network which reflects the classifiers’ diversity. A robust experimental protocol based on 30 datasets has confirmed that the notion of prominence provided employing centrality measures is a promising strategy to weight the classifiers of an ensemble. When compared with 9 fusion methods of the literature, the proposed fusion method won in 189 out of 270 experiments (70%), lost in 61 cases (22.59%) and tied in 20 cases (7.41%). Index Terms—Fusion methods, Diversity, Centrality Measures, Ensemble of Classifiers, Multiple Classifier Systems. I. I NTRODUCTION Ensembles have been used as an attractive alternative to avoid the risk of selecting a single classifier as the solution for a pattern recognition problem. So, covering the entire problem space is a responsibility divided among the members of a team composed of diverse and accurate classifiers. This diversity derives from the fact that the members should make different errors, and as a result, merging their decisions may lead to an improvement in classification performance. The literature presents different approaches to generate an ensemble, categorized as heterogeneous or homogeneous. The former uses different base classifiers to achieve diversity. The later uses the same base classifier, but vary the data used for training the elements which will constitute the ensemble. Bagging [1], Boosting [2] and Random Subspaces [3] are classical pool generators. No matter the generation method used, in an ensemble of classifiers C = {c 1 ,c 2 ,...,c T }, every member represents an independent function c t : R n → W that assigns a class label w i ∈ W to x ∈ R n , where W = {w 1 ,w 2 ,...,w M }. Fusion methods are applied to the decisions of all the classifiers in the ensemble, or on the decisions of a subset of classifiers selected statically or dynamically [4] producing the ensemble’s final decision. The literature provides a variety of fusion methods as seen in [5], and in [6]. The most used, and perhaps the simplest fusion method is the majority vote (also known as plurality vote). It considers each classifier as equal concerning their influence and assigns the class label w i to x if the majority of classifiers support the decision. However, this technique can sometimes perform worse than an individual classifier in the ensemble. The most interesting alternative has been to weight the vote of the classifiers while assuming that they compete with one another in assigning the correct class label [6]. The competition among the classifiers in the ensemble through the use of weights has been shown to be very promising. The literature thus supports a wide variety of static and dynamic strategies for weighting the decision of each classifier in an ensemble. A static weighting strategy estimates the ensemble member’s influence during the training phase of a classification system and the weights obtained remain the same during the test phase, while in a dynamic strategy, each classifier receives a different weight for each test instance. In the present context, the challenge, irrespective of the weighting strategy (static or dynamic), is how to combine di- verse classifiers, considering not only their competence based on accuracy individually but also their competence working together. Therefore, a thorough analysis is needed to evaluate the classifiers and their interactions, after which a proper fusion procedure defines how the ensemble vote. In fact, most of the combination methods do not explore the classifier interactions properly. They usually ignore interactions and are only based on the classifiers’ performance or confidence. While the fusion methods continue ignoring the relationship between classifiers, it inspired a variety of different classifier selection schemes [4], [7], in which is found, e.g., static selection based on diversity and accuracy information. This paper presents a novel approach for combining clas- sifiers, a static method for classifier decision fusion based on centrality measures computed on complex networks con- structed from a given ensemble. Social Network Analysis (SNA) employs centrality measures to understand a variety of problems, due to the ability to estimate the importance of each member (vertex), by measuring his influence based on the network relations. The hypothesis is that the centrality of each classifier within an ensemble represented as a complex