Beyond Mahalanobis Metric: Cayley-Klein Metric Learning

Yanhong Bi, Bin Fan, Fuchao Wu; The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015, pp. 2339-2347


Cayley-Klein metric is a kind of non-Euclidean metric suitable for projective space. In this paper, we introduce it into the computer vision community as a powerful metric and an alternative to the widely studied Mahalanobis metric. We show that besides its good characteristic in non-Euclidean space, it is a generalization of Mahalanobis metric in some specific cases. Furthermore, as many Mahalanobis metric learning, we give two kinds of Cayley-Klein metric learning methods: MMC Cayley-Klein metric learning and LMNN Cayley-Klein metric learning. Experiments have shown the superiority of Cayley-Klein metric over Mahalanobis ones and the effectiveness of our Cayley-Klein metric learning methods.

Related Material

author = {Bi, Yanhong and Fan, Bin and Wu, Fuchao},
title = {Beyond Mahalanobis Metric: Cayley-Klein Metric Learning},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2015}