Geometric Mean Metric Learning

Pourya Zadeh, Reshad Hosseini, Suvrit Sra
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:2464-2471, 2016.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Geometric Mean Metric Learning %A Pourya Zadeh %A Reshad Hosseini %A Suvrit Sra %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-zadeh16 %I PMLR %P 2464--2471 %U https://proceedings.mlr.press/v48/zadeh16.html %V 48 %X 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.
RIS
TY - CPAPER TI - Geometric Mean Metric Learning AU - Pourya Zadeh AU - Reshad Hosseini AU - Suvrit Sra BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-zadeh16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 2464 EP - 2471 L1 - http://proceedings.mlr.press/v48/zadeh16.pdf UR - https://proceedings.mlr.press/v48/zadeh16.html AB - 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. ER -
APA
Zadeh, P., Hosseini, R. & Sra, S.. (2016). Geometric Mean Metric Learning. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:2464-2471 Available from https://proceedings.mlr.press/v48/zadeh16.html.

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