The Combination of Evidence in the Transferable Belief Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering interval-valued proximity data using belief functions
Pattern Recognition Letters
ECM: An evidential version of the fuzzy c-means algorithm
Pattern Recognition
Decision making in the TBM: the necessity of the pignistic transformation
International Journal of Approximate Reasoning
IEEE Transactions on Pattern Analysis and Machine Intelligence
The possibilistic C-means algorithm: insights and recommendations
IEEE Transactions on Fuzzy Systems
Least squares quantization in PCM
IEEE Transactions on Information Theory
A new belief-based K-nearest neighbor classification method
Pattern Recognition
Soft clustering -- Fuzzy and rough approaches and their extensions and derivatives
International Journal of Approximate Reasoning
Evidential classifier for imprecise data based on belief functions
Knowledge-Based Systems
Enhanced interval type-2 fuzzy c-means algorithm with improved initial center
Pattern Recognition Letters
A belief classification rule for imprecise data
Applied Intelligence
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The well-known Fuzzy C-Means (FCM) algorithm for data clustering has been extended to Evidential C-Means (ECM) algorithm in order to work in the belief functions framework with credal partitions of the data. Depending on data clustering problems, some barycenters of clusters given by ECM can become very close to each other in some cases, and this can cause serious troubles in the performance of ECM for the data clustering. To circumvent this problem, we introduce the notion of imprecise cluster in this paper. The principle of our approach is to consider that objects lying in the middle of specific classes (clusters) barycenters must be committed with equal belief to each specific cluster instead of belonging to an imprecise meta-cluster as done classically in ECM algorithm. Outliers object far away of the centers of two (or more) specific clusters that are hard to be distinguished, will be committed to the imprecise cluster (a disjunctive meta-cluster) composed by these specific clusters. The new Belief C-Means (BCM) algorithm proposed in this paper follows this very simple principle. In BCM, the mass of belief of specific cluster for each object is computed according to distance between object and the center of the cluster it may belong to. The distances between object and centers of the specific clusters and the distances among these centers will be both taken into account in the determination of the mass of belief of the meta-cluster. We do not use the barycenter of the meta-cluster in BCM algorithm contrariwise to what is done with ECM. In this paper we also present several examples to illustrate the interest of BCM, and to show its main differences with respect to clustering techniques based on FCM and ECM.