Resample and combine: an approach to improving uncertainty representation in evidential pattern classification

Abstract Uncertainty representation is a major issue in pattern recognition. In many applications, the outputs of a classifier do not lead directly to a final decision, but are used in combination with other systems, or as input to an interactive decision process. In such contexts, it may be advantageous to resort to rich and flexible formalisms for representing and manipulating uncertain information. This paper addresses the issue of uncertainty representation in pattern classification, in the framework of the Dempster–Shafer theory of evidence. It is shown that the quality and reliability of the outputs of a classifier may be improved using a variant of bagging, a resample-and-combine approach introduced by Breiman in a conventional statistical context. This technique is explained and studied experimentally on simulated data and on a character recognition application. In particular, results show that bagging improves classification accuracy and limits the influence of outliers and ambiguous training patterns.

[1]  Philippe Smets,et al.  The Transferable Belief Model for Quantified Belief Representation , 1998 .

[2]  Dov M. Gabbay,et al.  Handbook of defeasible reasoning and uncertainty management systems: volume 2: reasoning with actual and potential contradictions , 1998 .

[3]  Ethem Alpaydin,et al.  Cascading classifiers , 1998, Kybernetika.

[4]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[5]  J. Kacprzyk,et al.  Aggregation and Fusion of Imperfect Information , 2001 .

[6]  Philippe Smets,et al.  Resolving misunderstandings about belief functions , 1992, Int. J. Approx. Reason..

[7]  Thierry Denoeux,et al.  Reasoning with imprecise belief structures , 1999, Int. J. Approx. Reason..

[8]  Adam Krzyżak,et al.  Methods of combining multiple classifiers and their applications to handwriting recognition , 1992, IEEE Trans. Syst. Man Cybern..

[9]  Thomas G. Dietterich.  An Experimental Comparison of Three Methods for Constructing Ensembles of Decision Trees: Bagging, Boosting, and Randomization , 2000, Machine Learning.

[10]  E. Mandler,et al.  Combining the Classification Results of Independent Classifiers Based on the Dempster/Shafer Theory of Evidence , 1988 .

[11]  Thierry Denoeux,et al.  Modeling vague beliefs using fuzzy-valued belief structures , 2000, Fuzzy Sets Syst..

[12]  Thierry Denoeux,et al.  A k-nearest neighbor classification rule based on Dempster-Shafer theory , 1995, IEEE Trans. Syst. Man Cybern..

[13]  P. Smets.  Application of the transferable belief model to diagnostic problems , 1998 .

[14]  Catherine Blake,et al.  UCI Repository of machine learning databases , 1998 .

[15]  Thierry Denux.  Reasoning with imprecise belief structures , 1999 .

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

[17]  Alain Appriou,et al.  Uncertain Data Aggregation in Classification and Tracking Processes , 1998 .

[18]  Glenn Shafer,et al.  Perspectives on the theory and practice of belief functions , 1990, Int. J. Approx. Reason..

[19]  Thierry Denoeux,et al.  An evidence-theoretic k-NN rule with parameter optimization , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[20]  Nikhil R. Pal,et al.  Some classification algorithms integrating Dempster-Shafer theory of evidence with the rank nearest neighbor rules , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[21]  Ch Chen,et al.  Pattern recognition and artificial intelligence , 1976 .

[22]  Thierry Denoeux,et al.  A neural network classifier based on Dempster-Shafer theory , 2000, IEEE Trans. Syst. Man Cybern. Part A.

[23]  Xavier Briottet,et al.  Presentation and description of two classification methods using data fusion based on sensor management , 2001, Inf. Fusion.

[24]  Jürg Kohlas,et al.  Handbook of Defeasible Reasoning and Uncertainty Management Systems , 2000 .

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

[26]  Pedro M. Domingos.  Why Does Bagging Work? A Bayesian Account and its Implications , 1997, KDD.

[27]  R. Tibshirani,et al.  An introduction to the bootstrap , 1993 .

[28]  J. Kacprzyk,et al.  Advances in the Dempster-Shafer theory of evidence , 1994 .

[29]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[30]  Philippe Smets,et al.  What is Dempster-Shafer's model? , 1994 .

[31]  Philippe Smets,et al.  Practical Uses of Belief Functions , 1999, UAI.

[32]  Galina L. Rogova,et al.  Combining the results of several neural network classifiers , 1994, Neural Networks.

[33]  Thierry Denoeux,et al.  Analysis of evidence-theoretic decision rules for pattern classification , 1997, Pattern Recognit..