DeepAI

# A Well-Tempered Landscape for Non-convex Robust Subspace Recovery

We present a mathematical analysis of a non-convex energy landscape for Robust Subspace Recovery. We prove that an underlying subspace is the only stationary point and local minimizer in a large neighborhood if a generic condition holds for a dataset. We further show that if the generic condition is satisfied, a geodesic gradient descent method over the Grassmannian manifold can exactly recover the underlying subspace with proper initialization. The condition is shown to hold with high probability for a certain model of data.

• 12 publications
• 44 publications
• 42 publications
06/24/2014

### Fast, Robust and Non-convex Subspace Recovery

This work presents a fast and non-convex algorithm for robust subspace r...
10/01/2016

### Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation From Undersampled Data

Subspace learning and matrix factorization problems have a great many ap...
12/20/2011

### A Novel M-Estimator for Robust PCA

We study the basic problem of robust subspace recovery. That is, we assu...
05/04/2020

### High-Dimensional Robust Mean Estimation via Gradient Descent

We study the problem of high-dimensional robust mean estimation in the p...
06/11/2020

### Randomized Fast Subspace Descent Methods

Randomized Fast Subspace Descent (RFASD) Methods are developed and analy...
06/11/2022

### Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering

The K-subspaces (KSS) method is a generalization of the K-means method f...
01/22/2022

### Implicit Bias of Projected Subgradient Method Gives Provable Robust Recovery of Subspaces of Unknown Codimension

Robust subspace recovery (RSR) is a fundamental problem in robust repres...