# Support Recovery in Sparse PCA with Incomplete Data

arXiv: https://arxiv.org/abs/2205.15215 · HTML: https://mlsanity.com/paper/2205.15215/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 24 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 3 of 3)

- [Scalable Semidefinite Programming](https://mlsanity.com/paper/1912.02949/) (2019)
- [Sparsistency and agnostic inference in sparse PCA](https://mlsanity.com/paper/1401.6978/) (2014)
- [Approximating Sparse PCA from Incomplete Data](https://mlsanity.com/paper/1503.03903/) (2015)

## Built on by (most cited first, 2 of 2)

- [Oja's Algorithm for Streaming Sparse PCA](https://mlsanity.com/paper/2402.07240/) (2024)
- [Support Recovery in Sparse PCA with Non-Random Missing Data](https://mlsanity.com/paper/2302.01535/) (2023)

## Abstract (arXiv)

We study a practical algorithm for sparse principal component analysis (PCA) of incomplete and noisy data. Our algorithm is based on the semidefinite program (SDP) relaxation of the non-convex l1-regularized PCA problem. We provide theoretical and experimental evidence that SDP enables us to exactly recover the true support of the sparse leading eigenvector of the unknown true matrix, despite only observing an incomplete (missing uniformly at random) and noisy version of it. We derive sufficient conditions for exact recovery, which involve matrix incoherence, the spectral gap between the largest and second-largest eigenvalues, the observation probability and the noise variance. We validate our theoretical results with incomplete synthetic data, and show encouraging and meaningful results on a gene expression dataset.