# Factor Adjusted Spectral Clustering for Mixture Models

arXiv: https://arxiv.org/abs/2408.12564 · HTML: https://mlsanity.com/paper/2408.12564/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 70 references that are in the map.
- First posted on arXiv 22 Aug 2024.

## Builds on (most cited first, 29 of 29)

- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm](https://mlsanity.com/paper/1902.03736/) (2019)
- [Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants](https://mlsanity.com/paper/1612.02099/) (2016)
- [Challenges of Big Data Analysis](https://mlsanity.com/paper/1308.1479/) (2013)
- [Optimality of Spectral Clustering in the Gaussian Mixture Model](https://mlsanity.com/paper/1911.00538/) (2019)
- [Ten Steps of EM Suffice for Mixtures of Two Gaussians](https://mlsanity.com/paper/1609.00368/) (2016)
- [Settling the Robust Learnability of Mixtures of Gaussians](https://mlsanity.com/paper/2011.03622/) (2020)
- [Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression](https://mlsanity.com/paper/2210.02002/) (2022)
- [Learning Mixtures of Gaussians in High Dimensions](https://mlsanity.com/paper/1503.00424/) (2015)
- [Randomly initialized EM algorithm for two-component Gaussian mixture achieves near optimality in O(√n) iterations](https://mlsanity.com/paper/1908.10935/) (2019)
- [Optimal estimation of high-dimensional location Gaussian mixtures](https://mlsanity.com/paper/2002.05818/) (2020)
- [Leave-one-out Singular Subspace Perturbation Analysis for Spectral Clustering](https://mlsanity.com/paper/2205.14855/) (2022)
- [Estimating Number of Factors by Adjusted Eigenvalues Thresholding](https://mlsanity.com/paper/1909.10710/) (2019)
- [Clustering a Mixture of Gaussians with Unknown Covariance](https://mlsanity.com/paper/2110.01602/) (2021)
- [Robust high dimensional factor models with applications to statistical machine learning](https://mlsanity.com/paper/1808.03889/) (2018)
- [Learning GMMs with Nearly Optimal Robustness Guarantees](https://mlsanity.com/paper/2104.09665/) (2021)
- [Factor-Adjusted Regularized Model Selection](https://mlsanity.com/paper/1612.08490/) (2016)
- [Statistical Guarantees for Estimating the Centers of a Two-component Gaussian Mixture by EM](https://mlsanity.com/paper/1608.02280/) (2016)
- [Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors](https://mlsanity.com/paper/1908.01252/) (2019)
- [CAST: A Correlation-based Adaptive Spectral Clustering Algorithm on Multi-scale Data](https://mlsanity.com/paper/2006.04435/) (2020)
- [Optimal Clustering in Anisotropic Gaussian Mixture Models](https://mlsanity.com/paper/2101.05402/) (2021)
- [Phase Transitions for High Dimensional Clustering and Related Problems](https://mlsanity.com/paper/1502.06952/) (2015)
- [FarmTest: Factor-Adjusted Robust Multiple Testing with Approximate False Discovery Control](https://mlsanity.com/paper/1711.05386/) (2017)
- [Projected principal component analysis in factor models](https://mlsanity.com/paper/1406.3836/) (2014)
- [Adversarially robust clustering with optimality guarantees](https://mlsanity.com/paper/2306.09977/) (2023)
- [Asymptotics of Empirical Eigen-structure for Ultra-high Dimensional Spiked Covariance Model](https://mlsanity.com/paper/1502.04733/) (2015)
- [On the best approximation by finite Gaussian mixtures](https://mlsanity.com/paper/2404.08913/) (2024)
- [A provable initialization and robust clustering method for general mixture models](https://mlsanity.com/paper/2401.05574/) (2024)

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

- [Factor Informed Double Deep Learning For Average Treatment Effect Estimation](https://mlsanity.com/paper/2508.17136/) (2025)

## Abstract (arXiv)

This paper studies a factor modeling-based approach for clustering high-dimensional data generated from a mixture of strongly correlated variables. Statistical modeling with correlated structures pervades modern applications in economics, finance, genomics, wireless sensing, etc., with factor modeling being one of the popular techniques for explaining the common dependence. Standard techniques for clustering high-dimensional data, e.g., naive spectral clustering, often fail to yield insightful results as their performances heavily depend on the mixture components having a weakly correlated structure. To address the clustering problem in the presence of a latent factor model, we propose the Factor Adjusted Spectral Clustering (FASC) algorithm, which uses an additional data denoising step via eliminating the factor component to cope with the data dependency. We prove this method achieves an exponentially low mislabeling rate, with respect to the signal to noise ratio under a general set of assumptions. Our assumption bridges many classical factor models in the literature, such as the pervasive factor model, the weak factor model, and the sparse factor model. The FASC algorithm is also computationally efficient, requiring only near-linear sample complexity with respect to the data dimension. We also show the applicability of the FASC algorithm with real data experiments and numerical studies, and establish that FASC provides significant results in many cases where traditional spectral clustering fails.