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arXiv · 1607.05002

Geometric Mean Metric Learning

Pourya Habib Zadeh·Reshad Hosseini·Suvrit Sra
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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.

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Pourya Habib Zadeh, Reshad Hosseini, Suvrit Sra. 2016-07-18. Geometric Mean Metric Learning. https://arxiv.org/abs/1607.05002

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