Geometric Mean Metric Learning
This work provides a more efficient and interpretable method for metric learning, which is important for tasks like classification in machine learning, though it appears incremental as it builds on existing metric learning approaches.
The authors tackled the problem of learning a Euclidean metric from data by formulating it as a simple optimization problem with a closed-form solution, which achieved higher classification accuracy on standard benchmarks and was computationally much faster than existing methods like LMNN and ITML.
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.