# Distributed Robust Subspace Recovery

## TL;DR

This paper introduces distributed algorithms for Robust Subspace Recovery that operate efficiently over large datasets in decentralized networks, avoiding data transfer and ensuring convergence.

## Contribution

It develops novel distributed implementations of RSR algorithms, including Consensus-Based Gradient, Reaper, and Fast Median Subspace, with proven convergence properties.

## Key findings

- Algorithms perform competitively on synthetic data.
- Algorithms demonstrate effectiveness on real datasets.
- Distributed methods achieve accurate subspace recovery without data centralization.

## Abstract

We propose distributed solutions to the problem of Robust Subspace Recovery (RSR). Our setting assumes a huge dataset in an ad hoc network without a central processor, where each node has access only to one chunk of the dataset. Furthermore, part of the whole dataset lies around a low-dimensional subspace and the other part is composed of outliers that lie away from that subspace. The goal is to recover the underlying subspace for the whole dataset, without transferring the data itself between the nodes. We first apply the Consensus-Based Gradient method to the Geometric Median Subspace algorithm for RSR. For this purpose, we propose an iterative solution for the local dual minimization problem and establish its r-linear convergence. We then explain how to distributedly implement the Reaper and Fast Median Subspace algorithms for RSR. The proposed algorithms display competitive performance on both synthetic and real data.