# Graph Regularized PCA

arXiv: https://arxiv.org/abs/2601.10199 · HTML: https://mlsanity.com/paper/2601.10199/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 33 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Builds on (most cited first, 8 of 8)

- [Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updates](https://mlsanity.com/paper/2102.03646/) (2021)
- [Learning Some Popular Gaussian Graphical Models without Condition Number Bounds](https://mlsanity.com/paper/1905.01282/) (2019)
- [Parsimonious modeling with Information Filtering Networks](https://mlsanity.com/paper/1602.07349/) (2016)
- [Robust Principal Component Analysis on Graphs](https://mlsanity.com/paper/1504.06151/) (2015)
- [HLOB -- Information Persistence and Structure in Limit Order Books](https://mlsanity.com/paper/2405.18938/) (2024)
- [Learning Clique Forests](https://mlsanity.com/paper/1905.02266/) (2019)
- [Effective Resistance for Pandemics: Mobility Network Sparsification for High-Fidelity Epidemic Simulation](https://mlsanity.com/paper/2111.02449/) (2021)
- [Anomaly Detection in California Electricity Price Forecasting: Enhancing Accuracy and Reliability Using Principal Component Analysis](https://mlsanity.com/paper/2412.07787/) (2024)

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

- [Are Whitepaper Claims Reflected in Market Structure? A Contamination-Aware Pipeline and a Power-Limited Null](https://mlsanity.com/paper/2601.20336/) (2026)

## Abstract (arXiv)

Multivariate data often exhibit complex dependencies that violate the assumption of isotropic residual noise. For such cases, we introduce Graph Regularized PCA (GR-PCA). It is a graph-based regularization of PCA that incorporates the dependency structure of the data features by learning a sparse precision graph and biasing loadings toward the low-frequency Fourier modes of the corresponding graph Laplacian. Consequently, high-frequency signals are suppressed, while graph-coherent low-frequency ones are preserved, yielding interpretable principal components aligned with conditional relationships. We evaluate GR-PCA on synthetic data spanning diverse graph topologies, signal-to-noise ratios, and sparsity levels. Compared to mainstream alternatives, it concentrates variance on the intended support, produces loadings with lower graph-Laplacian energy, and remains competitive in out-of-sample reconstruction. When high-frequency signals are present, the graph Laplacian penalty prevents overfitting, reducing the reconstruction accuracy but improving structural fidelity. The advantage over PCA is most pronounced when high-frequency signals are graph-correlated, whereas PCA remains competitive when such signals are nearly rotationally invariant. The procedure is simple to implement, modular with respect to the precision estimator, and scalable, providing a practical route to structure-aware dimensionality reduction that improves structural fidelity without sacrificing predictive performance.