Reviews: Curvilinear Distance Metric Learning

Originality: The method is new and provides a direct generalization of the Linear Distance Metric learning. Quality: Theorems are clearly interesting to validate the methodology. Fitting capacity result (Theorem 2) ensures that there exists a curvilinear metric that can well separate the data. The Generalization bound ensures empirical loss converges to the expected loss. However, it is unclear whether this ensures that the algorithm converges to the/a Distance introduced by Theorem 2 (the distance well separating the data).