Mathematical Analysis on Information-Theoretic Metric Learning With Application to Supervised Learning

This article presents a concrete mathematical analysis on Information-Theoretic Metric Learning (ITML). The analysis provides a theoretical foundation for ITML, by supplying well-posedness, strong duality, and convergence. Our analysis suggests the correction of a typo in the original ITML article that may lead to the loss of accuracy in the metric learning. The necessity of this correction is confirmed by several numerical experiments on supervised learning.