The sources of evidence may have different reliability and importance in real applications for decision making. The estimation of the discounting (weighting) factors when the prior knowledge is unknown have been regularly studied until recently. In the past, the determination of the weighting factors focused only on reliability discounting rule and it was mainly dependent on the dissimilarity measure between basic belief assignments (bba's) represented by an evidential distance. Nevertheless, it is very difficult to characterize efficiently the dissimilarity only through an evidential distance. Thus, both a distance and a conflict coefficient based on probabilistic transformations BetP are proposed to characterize the dissimilarity. The distance represents the difference between bba's, whereas the conflict coefficient reveals the divergence degree of the hypotheses that two belief functions strongly support. These two aspects of dissimilarity are complementary in a certain sense, and their fusion is used as the dissimilarity measure. Then, a new estimation method of weighting factors is presented by using the proposed dissimilarity measure. In the evaluation of weight of a source, both its dissimilarity with other sources and their weighting factors are considered. The weighting factors can be applied in the both importance and reliability discounting rules, but the selection of the adapted discounting rule should depend on the actual application. Simple numerical examples are given to illustrate the interest of the proposed approach.

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.

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The change detection in heterogeneous remote sensing images remains an important and open problem for damage assessment. We propose a new change detection method for heterogeneous images (i.e., SAR and optical images) based on homogeneous pixel transformation (HPT). HPT transfers one image from its original feature space (e.g., gray space) to another space (e.g., spectral space) in pixel-level to make the pre-event and post-event images represented in a common space for the convenience of change detection. HPT consists of two operations, i.e., the forward transformation and the backward transformation. In forward transformation, for each pixel of pre-event image in the first feature space, we will estimate its mapping pixel in the second space corresponding to post-event image based on the known unchanged pixels. A multi-value estimation method with noise tolerance is introduced to determine the mapping pixel using -nearest neighbors technique. Once the mapping pixels of pre-event image are available, the difference values between the mapping image and the post-event image can be directly calculated. After that, we will similarly do the backward transformation to associate the post-event image with the first space, and one more difference value for each pixel will be obtained. Then, the two difference values are combined to improve the robustness of detection with respect to the noise and heterogeneousness (modality difference) of images. Fuzzy-c means clustering algorithm is employed to divide the integrated difference values into two clusters: changed pixels and unchanged pixels. This detection results may contain some noisy regions (i.e., small error detections), and we develop a spatial-neighbor-based noise filter to further reduce the false alarms and missing detections using belief functions theory. The experiments for change detection with real images (e.g., SPOT, ERS, and NDVI) during a flood in U.K. are given to validate the effectiveness of the proposed method.

Classifier fusion is an efficient strategy to improve the classification performance for the complex pattern recognition problem. In practice, the multiple classifiers to combine can have different reliabilities and the proper reliability evaluation plays an important role in the fusion process for getting the best classification performance. We propose a new method for classifier fusion with contextual reliability evaluation (CF-CRE) based on inner reliability and relative reliability concepts. The inner reliability, represented by a matrix, characterizes the probability of the object belonging to one class when it is classified to another class. The elements of this matrix are estimated from the -nearest neighbors of the object. A cautious discounting rule is developed under belief functions framework to revise the classification result according to the inner reliability. The relative reliability is evaluated based on a new incompatibility measure which allows to reduce the level of conflict between the classifiers by applying the classical evidence discounting rule to each classifier before their combination. The inner reliability and relative reliability capture different aspects of the classification reliability. The discounted classification results are combined with Dempster-Shafer's rule for the final class decision making support. The performance of CF-CRE have been evaluated and compared with those of main classical fusion methods using real data sets. The experimental results show that CF-CRE can produce substantially higher accuracy than other fusion methods in general. Moreover, CF-CRE is robust to the changes of the number of nearest neighbors chosen for estimating the reliability matrix, which is appealing for the applications.

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International audienceIn this paper we present a new credal classification rule (CCR) based on belief functions to deal with the uncertain data. CCR allows the objects to belong (with different masses of belief) not only to the specific classes, but also to the sets of classes called meta-classes which correspond to the disjunction of several specific classes. Each specific class is characterized by a class center (i.e. prototype), and consists of all the objects that are sufficiently close to the center. The belief of the assignment of a given object to classify with a specific class is determined from the Mahalanobis distance between the object and the center of the corresponding class. The meta-classes are used to capture the imprecision in the classification of the objects when they are difficult to correctly classify because of the poor quality of available attributes. The selection of meta-classes depends on the application and the context, and a measure of the degree of indistinguishability between classes is introduced. In this new CCR approach, the objects assigned to a meta-class should be close to the center of this meta-class having similar distances to all the involved specific classes' centers, and the objects too far from the others will be considered as outliers (noise). CCR provides robust credal classification results with a relatively low computational burden. Several experiments using both artificial and real data sets are presented at the end of this paper to evaluate and compare the performances of this CCR method with respect to other classification methods