# Individual-heterogeneous sub-Gaussian Mixture Models

arXiv: https://arxiv.org/abs/2604.05337 · HTML: https://mlsanity.com/paper/2604.05337/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 20 of 20)

- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Community detection in networks: A user guide](https://mlsanity.com/paper/1608.00163/) (2016)
- [Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants](https://mlsanity.com/paper/1612.02099/) (2016)
- [Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel](https://mlsanity.com/paper/1309.4111/) (2013)
- [Optimality of Spectral Clustering in the Gaussian Mixture Model](https://mlsanity.com/paper/1911.00538/) (2019)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [Global analysis of Expectation Maximization for mixtures of two Gaussians](https://mlsanity.com/paper/1608.07630/) (2016)
- [Partial recovery bounds for clustering with the relaxed Kmeans](https://mlsanity.com/paper/1807.07547/) (2018)
- [Mixed Membership Estimation for Social Networks](https://mlsanity.com/paper/1708.07852/) (2017)
- [Spectral Algorithms for Community Detection in Directed Networks](https://mlsanity.com/paper/2008.03820/) (2020)
- [Leave-one-out Singular Subspace Perturbation Analysis for Spectral Clustering](https://mlsanity.com/paper/2205.14855/) (2022)
- [Determining the Number of Communities in Degree-corrected Stochastic Block Models](https://mlsanity.com/paper/1809.01028/) (2018)
- [A Robust Spectral Clustering Algorithm for Sub-Gaussian Mixture Models with Outliers](https://mlsanity.com/paper/1912.07546/) (2019)
- [Adjusted chi-square test for degree-corrected block models](https://mlsanity.com/paper/2012.15047/) (2020)
- [Adversarially robust clustering with optimality guarantees](https://mlsanity.com/paper/2306.09977/) (2023)
- [Exact Recovery of Community Detection in k-Community Gaussian Mixture Model](https://mlsanity.com/paper/2009.01185/) (2020)
- [Community detection by spectral methods in multi-layer networks](https://mlsanity.com/paper/2403.12540/) (2024)
- [Strong Consistency of Spectral Clustering for the Sparse Degree-Corrected Hypergraph Stochastic Block Model](https://mlsanity.com/paper/2309.10416/) (2023)

## Abstract (arXiv)

The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the individual-heterogeneous sub-Gaussian mixture model, a flexible framework that assigns each observation its own heterogeneity parameter, thereby explicitly capturing the heterogeneity inherent in practical applications. Built upon this model, we propose an efficient spectral method that provably achieves exact recovery of the true cluster labels under mild separation conditions, even in high-dimensional settings where the number of features far exceeds the number of samples. Numerical experiments on both synthetic and real data demonstrate that our method consistently outperforms existing clustering algorithms, including those designed for classical Gaussian mixture models.