6d0f846348a856321729a2f36734d1a7-Reviews.html

This equation, and others, probably overlap quite substantially with the approaches taken in e.g. "Optimization Algorithms on Matrix Manifolds" by Absil, P., Mahony, R., Sepulchre, R. ( this reference also addresses more general gradient flows, stepsize, retraction ("projection"), and convergence issues). S. Bonnabel, "Stochastic gradient descent on Riemannian manifolds" (arXiv) A. Edelman et al. "THE GEOMETRY OF ALGORITHMS WITH ORTHOGONALITY CONSTRAINTS" - The perspective of gradient descent on matrix manifolds is, to this reviewer, a major omission. The paper could greatly benefit from a discussion as to how this slice of the literature fits in to the picture, in terms of both practical algorithms and theory. I understand that space is a constraint. But if the authors decide to ultimately write a journal version of the submission, careful, considered inclusion of the above would make for a fantastic, authoritative paper bridging all of the major points of view on the topic.