# On Riemannian Approach for Constrained Optimization Model in Extreme Classification Problems

arXiv: https://arxiv.org/abs/2109.15021 · HTML: https://mlsanity.com/paper/2109.15021/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 30 Sep 2021.

## Builds on (most cited first, 10 of 10)

- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [AttentionXML: Label Tree-based Attention-Aware Deep Model for High-Performance Extreme Multi-Label Text Classification](https://mlsanity.com/paper/1811.01727/) (2018)
- [DiSMEC - Distributed Sparse Machines for Extreme Multi-label Classification](https://mlsanity.com/paper/1609.02521/) (2016)
- [Bonsai -- Diverse and Shallow Trees for Extreme Multi-label Classification](https://mlsanity.com/paper/1904.08249/) (2019)
- [LightXML: Transformer with Dynamic Negative Sampling for High-Performance Extreme Multi-label Text Classification](https://mlsanity.com/paper/2101.03305/) (2021)
- [Large-scale Multi-label Learning with Missing Labels](https://mlsanity.com/paper/1307.5101/) (2013)
- [Extreme Classification in Log Memory using Count-Min Sketch: A Case Study of Amazon Search with 50M Products](https://mlsanity.com/paper/1910.13830/) (2019)
- [DECAF: Deep Extreme Classification with Label Features](https://mlsanity.com/paper/2108.00368/) (2021)
- [Deep Extreme Multi-label Learning](https://mlsanity.com/paper/1704.03718/) (2017)
- [Fast Label Embeddings for Extremely Large Output Spaces](https://mlsanity.com/paper/1503.08873/) (2015)

## Built on by (most cited first, 1 of 1)

- [DXML: Distributed Extreme Multilabel Classification](https://mlsanity.com/paper/2112.10297/) (2021)

## Abstract (arXiv)

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.