Abstract
In 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.
Highlights
The classical methods of classification have been developed at first in the probability theory framework
An Evidential C-Means (ECM) [9] clustering method inspired from the Fuzzy C-Means (FCM) [23], and a Noise-Clustering algorithm [24] have been proposed for the credal partition of object data
The model-based classifiers [15] have been proposed by Denœux and Smets based on Smets' transfer belief model (TBM) [6,7,8]
Summary
The classical methods of classification have been developed at first in the probability theory framework. An evidential version of K-nearest neighbors rule (EK-NN) is proposed in [13], and a neural network classifier based on DST is presented in [26]. All these evidential classifiers consider only as possible assignment solution the specific classes, and one extra class (i.e. the ignorant class) which is defined by the disjunction of all the specific classes. In these supervised methods, the meta-classes (i.e. the partially ignorant classes) are not considered as useful solutions of the credal classification
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