Initialization of Masses by the Okm for the Belief Function Theory: Application to System Biology

In this paper we present a method of initialization of the masses for the belief function theory using the method of the Overlapping k-means (Okm). The Okm enables to create masses from union of singletons. The technic is presented with first experimental results on bioprocesses are presented.

[1]  Lotfi A. Zadeh,et al.  Review of A Mathematical Theory of Evidence , 1984 .

[2]  J. Steyer,et al.  Sur une approche qualitative des systemes physiques. Aide en temps reel a la conduite des proceds fermentaires , 1991 .

[3]  Thierry Denoeux A k -Nearest Neighbor Classification Rule Based on Dempster-Shafer Theory , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[4]  Guillaume Cleuziou OKM : une extension des k-moyennes pour la recherche de classes recouvrantes , 2007, EGC.

[5]  J. A. Roels,et al.  Energetics and Kinetics in Biotechnology , 1983 .

[6]  Henri Prade,et al.  Representation and combination of uncertainty with belief functions and possibility measures , 1988, Comput. Intell..

[7]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[8]  Philippe Smets,et al.  The Combination of Evidence in the Transferable Belief Model , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Philippe Smets,et al.  Belief functions: The disjunctive rule of combination and the generalized Bayesian theorem , 1993, Int. J. Approx. Reason..

[10]  Laurent Lardon,et al.  On-line diagnosis and uncertainty management using evidence theory––experimental illustration to anaerobic digestion processes , 2004 .

[11]  Guillaume Cleuziou,et al.  An extended version of the k-means method for overlapping clustering , 2008, 2008 19th International Conference on Pattern Recognition.

[12]  P. Vannoorenberghe,et al.  Handling uncertain labels in multiclass problems using belief decision trees , 2002 .

[13]  Eric Lefevre,et al.  Belief function combination and conflict management , 2002, Inf. Fusion.

[14]  Sébastien Régis Segmentation, classification et fusion de séries temporelles multi-sources : application à des signaux dans un bio-procédé , 2004 .