# Gradient-based Sparse Principal Component Analysis with Extensions to Online Learning

arXiv: https://arxiv.org/abs/1911.08048 · HTML: https://mlsanity.com/paper/1911.08048/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2019.

## Built on by (most cited first, 5 of 5)

- [Oja's Algorithm for Streaming Sparse PCA](https://mlsanity.com/paper/2402.07240/) (2024)
- [On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA](https://mlsanity.com/paper/2606.21951/) (2026)
- [Simultaneous Best Subset Selection and Dimension Reduction via Primal-Dual Iterations](https://mlsanity.com/paper/2211.15889/) (2022)
- [Enhancing Blind Source Separation with Dissociative Principal Component Analysis](https://mlsanity.com/paper/2411.12321/) (2024)
- [Combinatorial Sparse PCA Beyond the Spiked Identity Model](https://mlsanity.com/paper/2603.02607/) (2026)

## Abstract (arXiv)

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on the global convergence. Sparse PCA algorithms based on a convex formulation, for example the Fantope projection and selection (FPS), overcome this difficulty, but are computationally expensive. In this work we study sparse PCA based on the convex FPS formulation, and propose a new algorithm that is computationally efficient and applicable to large and high-dimensional data sets. Nonasymptotic and explicit bounds are derived for both the optimization error and the statistical accuracy, which can be used for testing and inference problems. We also extend our algorithm to online learning problems, where data are obtained in a streaming fashion. The proposed algorithm is applied to high-dimensional gene expression data for the detection of functional gene groups.