mlsanityData to 7 Oct 2026

Geometric Mean Metric Learning

arXiv 1607.05002 ↗First posted 18 Jul 2016stat.ML cs.LGcited by 22

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Abstract (arXiv)

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.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jul 2016.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 6; 2023: 3; 2024: 5; 2025: 1; 2026: 1.

22 papers.

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  1. 2021Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometrycited by 10
  2. 2022Spectral, Probabilistic, and Deep Metric Learning: Tutorial and Surveycited by 9
  3. 2023Differential geometry with extreme eigenvalues in the positive semidefinite conecited by 5
  4. 2021Efficient Hierarchical Bayesian Inference for Spatio-temporal Regression Models in Neuroimagingcited by 3
  5. 2022Adaptive neighborhood Metric learningcited by 3
  6. 2022Robust Geometric Metric Learningcited by 3
  7. 2024A Framework for Bilevel Optimization on Riemannian Manifoldscited by 3
  8. 2024A Riemannian Approach to Ground Metric Learning for Optimal Transportcited by 3
  9. 2021Learning Log-Determinant Divergences for Positive Definite Matricescited by 2
  10. 2023Multi-Fidelity Covariance Estimation in the Log-Euclidean Geometrycited by 2
  11. 2021Vector Transport Free Riemannian LBFGS for Optimization on Symmetric Positive Definite Matrix Manifoldscited by 1
  12. 2022On a class of geodesically convex optimization problems solved via Euclidean MM methodscited by 1
10 more
  1. 2023Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matricescited by 1
  2. 2024Random matrix theory improved Fr'echet mean of symmetric positive definite matricescited by 1
  3. 2024Learning-Rate-Free Stochastic Optimization over Riemannian Manifoldscited by 1
  4. 2021Multimodal-Aware Weakly Supervised Metric Learning with Self-weighting Triplet Losscited by 0
  5. 2021Hierarchical Relationship Alignment Metric Learningcited by 0
  6. 2022A Novel Splitting Criterion Inspired by Geometric Mean Metric Learning for Decision Treecited by 0
  7. 2022Principal Component Classificationcited by 0
  8. 2024Semantic-Enhanced Relational Metric Learning for Recommender Systemscited by 0
  9. 2025Kolmogorov Arnold Networks (KANs) for Imbalanced Data -- An Empirical Perspectivecited by 0
  10. 2026A Generalized Parallelogram Rule for Proportional Analogies on Riemannian Manifoldscited by 0