ICML 2016poster232 citations
Geometric Mean Metric Learning
Pourya Zadeh, Reshad Hosseini, Suvrit Sra
Abstract
We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric appeal through the Riemannian geometry of positive definite matrices; (ii) ease of interpretability; and (iii) computational speed several orders of magnitude faster than the widely used LMNN and ITML methods. Furthermore, on standard benchmark datasets, our closed-form solution consistently attains higher classification accuracy.
BibTeX
@InProceedings{pmlr-v48-zadeh16,
title = {Geometric Mean Metric Learning},
author = {Zadeh, Pourya and Hosseini, Reshad and Sra, Suvrit},
booktitle = {Proceedings of The 33rd International Conference on Machine Learning},
pages = {2464--2471},
year = {2016},
editor = {Balcan, Maria Florina and Weinberger, Kilian Q.},
volume = {48},
series = {Proceedings of Machine Learning Research},
address = {New York, New York, USA},
month = {20--22 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v48/zadeh16.pdf},
url = {https://proceedings.mlr.press/v48/zadeh16.html},
abstract = {We revisit the task of learning a Euclidean metric from data. We approach this problem from first principles and formulate it as a surprisingly simple optimization problem. Indeed, our formulation even admits a closed form solution. This solution possesses several very attractive properties: (i) an innate geometric appeal through the Riemannian geometry of positive definite matrices; (ii) ease of interpretability; and (iii) computational speed several orders of magnitude faster than the widely used LMNN and ITML methods. Furthermore, on standard benchmark datasets, our closed-form solution consistently attains higher classification accuracy.}
}