Evidence theory, also called belief functions theory, provides an efficient tool to represent and combine uncertain information for pattern classification. Evidence combination can be interpreted, in some applications, as classifier fusion. The sources of evidence corresponding to multiple classifiers usually exhibit different classification qualities, and they are often discounted using different weights before combination. In order to achieve the best possible fusion performance, a new Credal Belief Redistribution (CBR) method is proposed to revise such evidence. The rationale of CBR consists in transferring belief from one class not just to other classes but also to the associated disjunctions of classes (i.e., meta-classes). As classification accuracy for different objects in a given classifier can also vary, the evidence is revised according to prior knowledge mined from its training neighbors. If the selected neighbors are relatively close to the evidence, a large amount of belief will be discounted for redistribution. Otherwise, only a small fraction of belief will enter the redistribution procedure. An imprecision matrix estimated based on these neighbors is employed to specifically redistribute the discounted beliefs. This matrix expresses the likelihood of misclassification (i.e., the probability of a test pattern belonging to a class different from the one assigned to it by the classifier). In CBR, the discounted beliefs are divided into two parts. One part is transferred between singleton classes, whereas the other is cautiously committed to the associated meta-classes. By doing this, one can efficiently reduce the chance of misclassification by modeling partial imprecision. The multiple revised pieces of evidence are finally combined by Dempster-Shafer rule to reduce uncertainty and further improve classification accuracy. The effectiveness of CBR is extensively validated on several real datasets from the UCI repository, and critically compared with that of other related fusion methods.

Classifier fusion remains an effective method to improve classification performance. In applications, the classifiers learnt using different attributes may work with various frames of discernment (FoD) of classification. There generally exist more or less complementary knowledge among these classifiers. However, how to efficiently combine such classifiers under different FoD is a challenging problem. In this paper, we propose a new method for classifier fusion with different FoD based on the belief functions (BF), which allow to well represent and deal with uncertain information. The credal transformation rules are developed to map the various FoD into a common one. It allows to transfer the probability (or mass of belief) of one class in the given FoD not only to several singleton classes but also to the meta-classes (i.e. disjunction of several classes) and the ignorance in other chosen FoD according to a transformation matrix, which is estimated based on the training (pair wise) data by minimizing a certain error criteria. Thus, we can well characterize the uncertainty and imprecision during the transformation of FoD. After that, the outputs of different classifiers represented by Basic Belief Assignments (BBA) can be transformed to a common FoD. Then the well-known Dempster's rule is employed to combine these transformed BBA to obtain final classification result under the chosen FoD. Several real data sets are used in the experiment to evaluate the performance of the proposed method. Our experimental results show that this new method can efficiently improve the classification accuracy with respect to other related methods.

Multi-sensor fusion strategies have been widely applied in Human Activity Recognition (HAR) in Body Sensor Networks (BSNs). However, the sensory data collected by BSNs systems are often uncertain or even incomplete. Thus, designing a robust and intelligent sensor fusion strategy is necessary for high-quality activity recognition. In this paper, Dezert-Smarandache Theory (DSmT) is used to develop a novel sensor fusion strategy for HAR in BSNs, which can effectively improve the accuracy of recognition. Specifically, in the training stage, the Kernel Density Estimation (KDE) based models are first built and then precisely selected for each specific activity according to the proposed discriminative functions. After that, a structure of Basic Belief Assignment (BBA) can be constructed, using the relationship between the test data of unknown class and the selected KDE models of all considered types of activities. In order to deal with the conflict between the obtained BBAs, Proportional Conflict Redistribution-6 (PCR6) is applied to fuse the acquired BBAs. Moreover, the missing data of the involved sensors are addressed as ignorance in the framework of the DSmT without manual interpolation or intervention. Experimental studies on two real-world activity recognition datasets (The OPPORTUNITY dataset; Daily and Sports Activity Dataset (DSAD)) were conducted, and the results showed the superiority of our proposed method over some state-of-the-art approaches proposed in the literature.

In the original belief function (BF) theory, a precise-valued belief structure has been widely used to represent uncertain information. However, this mentioned belief structure is difficult to effectively measure the specific hesitant situation, especially when decision makers have a set of possible values for the belief assignments of focal elements. In order to model the hesitant nature of the behavior of people to make a decision under uncertainty, we propose a hesitant fuzzy belief structure (HFBS) that is based on the BF theory and the recent hesitant fuzzy set theory. We also present the novel rule of combination of HFBS that is used and evaluated in a wearable human activity recognition (HAR) system coupled with an extreme learning machine. The evaluation of this new HFBS approach is done from two benchmark datasets. We clearly show its effectiveness and its superiority compared to various methods used classically for the wearable HAR.

In pattern classification, there may not exist labeled patterns in the target domain to train a classifier. Domain adaptation (DA) techniques can transfer the knowledge from the source domain with massive labeled patterns to the target domain for learning a classification model. In practice, some objects in the target domain are easily classified by this classification model, and these objects usually can provide more or less useful information for classifying the other objects in the target domain. So a new method called distribution adaptation based on evidence theory (DAET) is proposed to improve the classification accuracy by combining the complementary information derived from both the source and target domains. In DAET, the objects that are easy to classify are first selected as easy-target objects, and the other objects are regarded as hard-target objects. For each hard-target object, we can obtain one classification result with the assistance of massive labeled patterns in the source domain, and another classification result can be acquired based on the easy-target objects with confidently predicted (pseudo) labels. However, the weights of these classification results may vary because the reliabilities of the used information sources are different. The weights are estimated by mean difference reflecting the information source quality. Then, we discount the classification results with the corresponding weights under the framework of the evidence theory, which is expert at dealing with uncertain information. These discounted classification results are combined by an evidential combination rule for making the final class decision. The effectiveness of DAET for cross-domain pattern classification is evaluated with respect to some advanced DA methods, and the experiment results show DAET can significantly improve the classification accuracy.