Alpha-integration of multiple evidence

In pattern recognition, data integration is a processing method to combine multiple sources so that the combined result can be more accurate than a single source. Evidence theory is one of the methods that have been successfully applied to the data integration task. Since Dempster-Shafer theory as the first evidence theory can be against our intuitive reasoning with some data sets, many researchers have proposed different rules for evidence theory. Among all these rules, the averaging rule is known to be better than others. On the other hand, a-integration was proposed by Amari as a principled way of blending multiple positive measures. It is a generalized averaging algorithm including arithmetic, geometric and harmonic means as its special case. In this paper, we generalize evidence theory with α-integration. Our experimental results show how our proposed methods work.

[1]  Geoffrey E. Hinton,et al.  Adaptive Mixtures of Local Experts , 1991, Neural Computation.

[2]  Qi Liu,et al.  Combining belief functions based on distance of evidence , 2004, Decis. Support Syst..

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

[4]  Weifeng Tian,et al.  A novel conflict reassignment method based on grey relational analysis (GRA) , 2007, Pattern Recognit. Lett..

[5]  Yoonsuck Choe,et al.  Manifold Integration with Markov Random Walks , 2008, AAAI.

[6]  Kari Sentz,et al.  Combination of Evidence in Dempster-Shafer Theory , 2002 .

[7]  Nello Cristianini,et al.  Kernel-Based Data Fusion and Its Application to Protein Function Prediction in Yeast , 2003, Pacific Symposium on Biocomputing.

[8]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[9]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[10]  Geoffrey E. Hinton.  Training Products of Experts by Minimizing Contrastive Divergence , 2002, Neural Computation.

[11]  Yoonsuck Choe,et al.  Probabilistic Combination of Multiple Evidence , 2009, ICONIP.

[12]  Nir Friedman,et al.  Bayesian Network Classifiers , 1997, Machine Learning.

[13]  Catherine K. Murphy.  Combining belief functions when evidence conflicts , 2000, Decis. Support Syst..

[14]  Pascal Vasseur,et al.  Introduction to Multisensor Data Fusion , 2005, The Industrial Information Technology Handbook.

[15]  S. Amari.  Integration of Stochastic Models by Minimizing -Divergence , 2007, Neural Computation.