Fusion of multi-level decision systems using the Transferable Belief Model David Mercier Universit´ e de Technologie de Compi` egne / SOLYSTIC UMR CNRS 6599 Heudiasyc, BP20529 F-60205 Compi` egne Cedex, France Email: dmercier@hds.utc.fr david.mercier@solystic.com Genevi` eve Cron SOLYSTIC 14 avenue Raspail F-94257 Gentilly Cedex, France Email: genevieve.cron@solystic.com Thierry Denoeux Universit´ e de Technologie de Compi` egne UMR CNRS 6599 Heudiasyc, BP20529 F-60205 Compi` egne Cedex, France Email: tdenoeux@hds.utc.fr Myl` ene Masson Universit´ e de Picardie Jules Verne UMR CNRS 6599 Heudiasyc, BP20529 F-60205 Compi` egne Cedex, France Email: mmasson@hds.utc.fr Abstract—In this paper, we are interested in the fusion of classifiers providing decisions which are organized in a hierarchy, i.e., for each pattern to classify, each classifier has the possibility to choose a class, a set of classes, or a reject option. We present a method to combine these decisions based on the Transferable Belief Model (TBM), an interpretation of the Dempster-Shafer theory of evidence. The TBM is shown to provide a powerful and flexible framework, well suited to this problem. Special emphasis is put on the construction of basic be- lief assignments, an important issue which has not yet been fully explored in the literature. We propose an approach extending a former proposal made by Xu, Krzyzak and Suen (1992) in a simpler context. A rational decision modelling allowing different levels of decision is also presented. Finally, the proposed combination is compared experimentally to several simpler alternatives. Index Terms— Decision Fusion, multi-level decisions, belief functions, Dempster-Shafer theory, Evidence theory, classifica- tion. I. I NTRODUCTION Building highly reliable classifiers is an important objective in pattern recognition. An interesting way to achieve this goal consists in the combination of already existing classifiers. Indeed, experimental results ([1], [2]) show that methods based on multiple classifiers generally outperform each individual classifier. As explained by Xu, Krzyzak and Suen in [3], the combination of multiple classifiers includes several problems: selecting the classifiers to combine (types, algorithms, number, . . . ), choosing an architecture for the combination (parallel, cascade, mixtures of both, . . . ), and combining the classifier outputs in order to achieve better performance than each classifier individually. In this paper 1 , we focus on the problem of combining clas- 1 This work is the result of a cooperation agreement between the Heudiasyc laboratory at the Universit´ e de Technologie de Compi` egne and the SOLYSTIC company. sifiers providing decisions which are organized as a hierarchy: decisions can be expressed at different levels. For each pattern to classify, each classifier has the possibility to choose either a class, or a set of classes, or rejection. We assume that the decisions are not associated with any scoring vector, or posterior probabilities. It is a common situation in real world applications. Classifiers providing only class labels are called abstract level classifiers or classifiers of Type 1 in [3]. To combine such classifiers, various combination techniques were pro- posed such as voting-based systems [3], [4], [5], plurality [6], Bayesian theory [3], Dempster-Shafer theory [3], [7] or classifier local accuracy [8]. Inspired by a former proposal by Xu, Krzyzak and Suen (1992) [3], a combination of these decisions based on the Transferable Belief Model (TBM) ([9], [10]) is proposed. Like all Dempster-Shafer approaches, the assignment of masses is an important task which often determines the success of the combination. Therefore, different assignments are discussed. A decision process allowing different levels of decision is also presented. This paper is organized as follows. The key points of the TBM, an interpretation of the Dempster-Shafer theory of evidence [11] well suited to information fusion, are recalled in Section II. In Section III, we come back to an existing method for combining belief functions in the case of non hierarchical decisions. Then, in Section IV, a model based on the TBM is presented for the combination of multi-level decisions. Finally, Section V describes experimental results and compares the proposed combination with voting-based schemes. 0-7803-9286-8/05/$20.00 © 2005 IEEE