Geometric Mean Metric Learning

2016/07/18 by Pourya Habib Zadeh, Zadeh, Pourya Habib, Reshad Hosseini +3 · 2 citations
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1607.05002

7 pages, 4 figures

arxiv created 2016/07/18 · arxiv updated 2016/07/19

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.

Cited by

• Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspective
• On the computation of tensor functions under tensor-tensor multiplications with linear maps

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