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.

On Riemannian Approach for Constrained Optimization Model in Extreme Classification Problems