In evidential clustering, cluster-membership uncertainty is represented by Dempster-Shafer mass functions. The notion of evidential partition generalizes other soft clustering structures such as fuzzy, possibilistic or rough partitions. In this paper, we propose two extensions of the Rand index for evaluating and comparing evidential partitions, called similarity and consistency indices. The similarity index is suitable for measuring the closeness of two soft partitions, while the consistency index allows one to assess the agreement, or lack of conflict, between a soft partition and the true hard partition. Simulation experiments illustrate some applications of these indices.

A new approach to nonlinear state estimation based on belief-function theory and interval analysis is presented. This method uses belief structures composed of a finite number of axis-aligned boxes with associated masses. Such belief structures can represent partial information on model and measurement uncertainties more accurately than can the bounded-error approach alone. Focal sets are propagated in system equations using interval arithmetics and constraint-satisfaction techniques, thus generalizing pure interval analysis. This model was used to locate a land vehicle using a dynamic fusion of Global Positioning System measurements with dead reckoning sensors. The method has been shown to provide more accurate estimates of vehicle position than does the bounded-error method while retaining what is essential: providing guaranteed computations. The performances of our method were also slightly better than those of a particle filter, with comparable running time. These results suggest that our method is a viable alternative to both bounded-error and probabilistic Monte Carlo approaches for vehicle-localization applications.

While the accurate delineation of tumor volumes in FDG-positron emission tomography (PET) is a vital task for diverse objectives in clinical oncology, noise and blur due to the imaging system make it a challenging work. In this paper, we propose to address the imprecision and noise inherent in PET using Dempster-Shafer theory, a powerful tool for modeling and reasoning with uncertain and/or imprecise information. Based on Dempster-Shafer theory, a novel evidential clustering algorithm is proposed and tailored for the tumor segmentation task in three-dimensional. For accurate clustering of PET voxels, each voxel is described not only by the single intensity value but also complementarily by textural features extracted from a patch surrounding the voxel. Considering that there are a large amount of textures without consensus regarding the most informative ones, and some of the extracted features are even unreliable due to the low-quality PET images, a specific procedure is included in the proposed clustering algorithm to adapt distance metric for properly representing the clustering distortions and the similarities between neighboring voxels. This integrated metric adaptation procedure will realize a low-dimensional transformation from the original space, and will limit the influence of unreliable inputs via feature selection. A Dempster-Shafer-theory-based spatial regularization is also proposed and included in the clustering algorithm, so as to effectively quantify the local homogeneity. The proposed method has been compared with other methods on the real-patient FDG-PET images, showing good performance.

The Evidential K-Nearest-Neighbor (EK-NN) method provided a global treatment of imperfect knowledge regarding the class membership of training patterns. It has outperformed traditional K-NN rules in many applications, but still shares some of their basic limitations, e.g., 1) classification accuracy depends heavily on how to quantify the dissimilarity between different patterns and 2) no guarantee for satisfactory performance when training patterns contain unreliable (imprecise and/or uncertain) input features. In this paper, we propose to address these issues by learning a suitable metric, using a low-dimensional transformation of the input space, so as to maximize both the accuracy and efficiency of the EK-NN classification. To this end, a novel loss function to learn the dissimilarity metric is constructed. It consists of two terms: the first one quantifies the imprecision regarding the class membership of each training pattern; while, by means of feature selection, the second one controls the influence of unreliable input features on the output linear transformation. The proposed method has been compared with some other metric learning methods on several synthetic and real data sets. It consistently led to comparable performance with regard to testing accuracy and class structure visualization.