# Efficient Sparse Clustering of High-Dimensional Non-spherical Gaussian Mixtures

arXiv: https://arxiv.org/abs/1406.2206 · HTML: https://mlsanity.com/paper/1406.2206/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2014.

## Built on by (most cited first, 6 of 6)

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- [Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap](https://mlsanity.com/paper/2205.13527/) (2022)
- [Mixture-Models: a one-stop Python Library for Model-based Clustering using various Mixture Models](https://mlsanity.com/paper/2402.10229/) (2024)
- [Discourse vs emissions: Analysis of corporate narratives, symbolic practices, and mimicry through LLMs](https://mlsanity.com/paper/2510.01222/) (2025)
- [A Data-Informed Variational Clustering Framework for Noisy High-Dimensional Data](https://mlsanity.com/paper/2604.06864/) (2026)

## Abstract (arXiv)

We consider the problem of clustering data points in high dimensions, i.e. when the number of data points may be much smaller than the number of dimensions. Specifically, we consider a Gaussian mixture model (GMM) with non-spherical Gaussian components, where the clusters are distinguished by only a few relevant dimensions. The method we propose is a combination of a recent approach for learning parameters of a Gaussian mixture model and sparse linear discriminant analysis (LDA). In addition to cluster assignments, the method returns an estimate of the set of features relevant for clustering. Our results indicate that the sample complexity of clustering depends on the sparsity of the relevant feature set, while only scaling logarithmically with the ambient dimension. Additionally, we require much milder assumptions than existing work on clustering in high dimensions. In particular, we do not require spherical clusters nor necessitate mean separation along relevant dimensions.