# Sparse Principal Component Analysis via Variable Projection

arXiv: https://arxiv.org/abs/1804.00341 · HTML: https://mlsanity.com/paper/1804.00341/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2018.

## Built on by (most cited first, 9 of 9)

- [Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks](https://mlsanity.com/paper/2201.09989/) (2022)
- [Spike and slab Bayesian sparse principal component analysis](https://mlsanity.com/paper/2102.00305/) (2021)
- [Spherical Rotation Dimension Reduction with Geometric Loss Functions](https://mlsanity.com/paper/2204.10975/) (2022)
- [Feature Grouping and Sparse Principal Component Analysis with Truncated Regularization](https://mlsanity.com/paper/2106.13685/) (2021)
- [Do algorithms and barriers for sparse principal component analysis extend to other structured settings?](https://mlsanity.com/paper/2307.13535/) (2023)
- [Analysis of Truncated Orthogonal Iteration for Sparse Eigenvector Problems](https://mlsanity.com/paper/2103.13523/) (2021)
- [Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures](https://mlsanity.com/paper/2507.19787/) (2025)
- [Rethinking PCA Through Duality](https://mlsanity.com/paper/2510.18130/) (2025)
- [Video-based detection of cessation of breathing in pre-term infants using machine learning](https://mlsanity.com/paper/2607.05230/) (2026)

## Abstract (arXiv)

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales. We demonstrate a robust and scalable SPCA algorithm by formulating it as a value-function optimization problem. This viewpoint leads to a flexible and computationally efficient algorithm. Further, we can leverage randomized methods from linear algebra to extend the approach to the large-scale (big data) setting. Our proposed innovation also allows for a robust SPCA formulation which obtains meaningful sparse principal components in spite of grossly corrupted input data. The proposed algorithms are demonstrated using both synthetic and real world data, and show exceptional computational efficiency and diagnostic performance.