Dissimilarity Metric Learning in the Belief Function Framework

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 datasets. It consistently led to comparable performance with regard to testing accuracy and class structure visualization.