  We propose a novel Riemannian method for solving the Extreme multi-label
classification problem that exploits the geometric structure of the sparse
low-dimensional local embedding models. A constrained optimization problem is
formulated as an optimization problem on matrix manifold and solved using a
Riemannian optimization method. The proposed approach is tested on several real
world large scale multi-label datasets and its usefulness is demonstrated
through numerical experiments. The numerical experiments suggest that the
proposed method is fastest to train and has least model size among the
embedding-based methods. An outline of the proof of convergence for the
proposed Riemannian optimization method is also stated.
