Uncertain Data Classification And Decision Fusion Based On The Theory Of Belief Functions

In complicated battlefields,affected by external interferences,electronic countermeasures or inherent limitations of sensors,the available information is usually uncertain.For example,the information may be incomplete,which refers to cases where the value of a variable is missing.Sometimes,the information may be imprecise,when the value of a variable is given,but not with enough precision.In addition,the data may be unreliable,i.e.,the obtained values might be wrong.These widely existed uncertainties in target recognition and threat assessment applications present great challenges to traditional data classification and decision fusion methods.As a generalization of probability theory,the theory of belief functions offers a well-founded and workable framework to represent and combine a large variety of uncertain information.In this thesis,we use this theory to address the uncertain data classification and decision fusion problems as follows.1.An evidential editing k-nearest neighbor(EEk NN)classifier is developed for dealing with imprecise training data set,in which samples from different classes strongly overlap.The proposed classifier contains two stages: evidential editing and classification.First,an evidential editing procedure reassigns the original training samples with new labels represented by an evidential membership structure,which provides more expressiveness to characterize the imprecision for those samples in overlapping regions.After evidential editing,a classification procedure is developed to classify a query pattern based on the edited training samples.Experiments have shown that the proposed classifier can achieve better performance than other considered nearest-neighbor-based methods,especially for data sets with high overlapping ratios.2.A multi-hypothesis k-nearest neighbor(MHk NN)classifier is developed for dealing with incomplete training data set,in which case the real class-conditional probability distributions cannot be well characterized using the limited training samples.The scheme of the proposed classifier is to classify the query pattern under multiple hypotheses,in which the k-nearest neighbor sub-classifiers can be implemented based on the proposed class-conditional weighted distance metric.Then the classification results of multiple sub-classifiers are combined in the framework of belief functions to get the final result.The reported results have shown that the proposed technique can achieve a uniformly good performance when applied to a variety of classification tasks,especially for those with high dimensionality and sparse samples.3.A belief rule-based classification system(BRBCS)is developed by extending the traditional fuzzy rule-based classification system in the framework of belief functions to address unreliable training samples in complex classification problems.The proposed BRBCS is composed of two components: the belief rule base,which establishes an association between the feature space and the class space,and the belief reasoning method which provides a mechanism to classify a query pattern.These two components have been designed specifically by taking into account the possible pattern noise in many real-world applications.The delivered experiments have shown that the proposed method can get better classification accuracy and robustness than other rule-based methods for a variety of real-world classification problems.4.A hybrid belief rule-based classification system(HBRBCS)is developed in order to make use of the information from both uncertain training data and expert knowledge jointly for classification.The belief rule structure is used as a common model to represent both uncertain training data and expert knowledge.In the fusion process,the weights of these two types of information are taken into account to get an adaptively optimized fusion model.The HBRBCS can inherit the complementary advantages from data-driven models and knowledge-driven models.We have studied an airborne target classification problem,in which both training data collected by sensors and expert knowledge are available.The experiment results have shown that the HBRBCS can make good use of these two types of independent and complementary information and achieve better performance.5.The combination of sources of evidence with reliability has been widely studied within the framework of belief functions.By the fact that sources of evidence may also be different in importance,we propose an importance discounting and combination operation.Based on these theoretical foundations,two popular decision fusion algorithms,i.e.,original ER(OER)and modified ER(MER),are analyzed in the framework of belief functions.We find that the OER algorithm actually follows the reliability discounting and combination scheme,while the MER algorithm follows the importance discounting and combination scheme.Based on these findings,we have developed an generalized ER(GER)algorithm to consider both reliability and importance for decision fusion.We have studied a target threat assessment problem and the experiment results have shown that the GER algorithm can obtain a more comprehensive and reasonable decision.