Cayley- Klein Metric Learning with Shrinkage-Expansion Constraints

Cayley-Klein metric is a specific kind of non-Euclidean metric in projective space. Recently, it has been introduced into metric learning with encouraging performance when dealing with computer vision tasks. However, the original Cayley-Klein metric learning methods with conventional pairwise and triplet-wise constraints, which are fixed bound based constraints, may not perform well when the intra-and inter-class variations of data distribution become complex. Pairwise constraints restrict the distance between samples of a similar pair to be lower than a fixed upper bound, and the distance between samples of a dissimilar pair higher than a fixed lower bound. Triplet-wise constraints restrict the distance between samples of a similar pair to be smaller than that between a pair of samples from different classes. In this paper, we propose a novel Cayley-Klein metric learning method (CKseML) with adaptive shrinkage-expansion pairwise constraints. CKseML is very effective in learning metric from data with complex distributions. Our experimental results demonstrate that CKseML achieves better performance than the original Cayley-Klein metric learning methods.