# Stay on path: PCA along graph paths

arXiv: https://arxiv.org/abs/1506.02344 · HTML: https://mlsanity.com/paper/1506.02344/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2015.

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

- [Network Representation Learning: From Traditional Feature Learning to Deep Learning](https://mlsanity.com/paper/2103.04339/) (2021)
- [Do algorithms and barriers for sparse principal component analysis extend to other structured settings?](https://mlsanity.com/paper/2307.13535/) (2023)

## Abstract (arXiv)

We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph G on p vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with vertices lying along a path in G. From a statistical perspective, information on the underlying network may potentially reduce the number of observations required to recover the population principal component. We consider the canonical estimator which optimally exploits the prior knowledge by solving a non-convex quadratic maximization on the empirical covariance. We introduce a simple network and analyze the estimator under the spiked covariance model. We show that side information potentially improves the statistical complexity. We propose two algorithms to approximate the solution of the constrained quadratic maximization, and recover a component with the desired properties. We empirically evaluate our schemes on synthetic and real datasets.