In many applications non-metric distances are better than metric distances in reflecting the perceptual distances of human beings. Previous studies on non-metric distances mainly focused on supervised setting and did not consider the usefulness of unlabeled data. In this paper, we present probably the first study of label propagation on graphs induced from non-metric distances. The challenge here lies in the fact that the triangular inequality does not hold for non-metric distances and therefore, a direct application of existing label propagation methods will lead to inconsistency and conflict. We show that by applying spectrum transformation, non-metric distances can be converted into metric ones, and thus label propagation can be executed. Such methods, however, suffer from the change of original semantic relations. As a main result of this paper, we prove that any non-metric distance matrix can be decomposed into two metric distance matrices containing different information of the data. Based on this recognition, our proposed *NMLP* method derives two graphs from the original non-metric distance and performs a joint label propagation on the joint graph. Experiments validate the effectiveness of the proposed *NMLP *method.

Yin Zhang, Zhi-Hua Zhou