# Sparse and geometry-aware generalisation of the mutual information for joint discriminative clustering and feature selection

arXiv: https://arxiv.org/abs/2302.03391 · HTML: https://mlsanity.com/paper/2302.03391/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 59 references that are in the map.
- First posted on arXiv 7 Feb 2023.

## Builds on (most cited first, 5 of 5)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [LassoNet: A Neural Network with Feature Sparsity](https://mlsanity.com/paper/1907.12207/) (2019)
- [Kernel k-Groups via Hartigan's Method](https://mlsanity.com/paper/1710.09859/) (2017)
- [Variable Selection Methods for Model-based Clustering](https://mlsanity.com/paper/1707.00306/) (2017)
- [Generalised Mutual Information for Discriminative Clustering](https://mlsanity.com/paper/2210.06300/) (2022)

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

- [A Tutorial on Discriminative Clustering and Mutual Information](https://mlsanity.com/paper/2505.04484/) (2025)

## Abstract (arXiv)

Feature selection in clustering is a hard task which involves simultaneously the discovery of relevant clusters as well as relevant variables with respect to these clusters. While feature selection algorithms are often model-based through optimised model selection or strong assumptions on the data distribution, we introduce a discriminative clustering model trying to maximise a geometry-aware generalisation of the mutual information called GEMINI with a simple l1 penalty: the Sparse GEMINI. This algorithm avoids the burden of combinatorial feature subset exploration and is easily scalable to high-dimensional data and large amounts of samples while only designing a discriminative clustering model. We demonstrate the performances of Sparse GEMINI on synthetic datasets and large-scale datasets. Our results show that Sparse GEMINI is a competitive algorithm and has the ability to select relevant subsets of variables with respect to the clustering without using relevance criteria or prior hypotheses.