Distributed Low-rank Subspace Segmentation

TL;DR

This paper introduces a scalable divide-and-conquer algorithm for low-rank subspace segmentation that maintains strong theoretical guarantees and demonstrates significant improvements in large-scale vision and multimedia tasks.

Contribution

It proposes a novel divide-and-conquer method for LRR-based subspace segmentation that scales to large datasets while preserving accuracy and recovery guarantees.

Findings

Demonstrates scalability on large face recognition datasets.

Achieves state-of-the-art results in multimedia event detection.

Provides order-of-magnitude speedups over previous methods.

Abstract

Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subspace segmentation problem, is provably and empirically accurate on small problems but does not scale to the massive sizes of modern vision datasets. Moreover, past work aimed at scaling up low-rank matrix factorization is not applicable to LRR given its non-decomposable constraints. In this work, we propose a novel divide-and-conquer algorithm for large-scale subspace segmentation that can cope with LRR's non-decomposable constraints and maintains LRR's strong recovery guarantees. This has immediate implications for the scalability of subspace segmentation, which we demonstrate on a benchmark face recognition dataset and in simulations. We then introduce novel applications of LRR-based subspace segmentation to large-scale semi-supervised learning for multimedia event detection, concept detection, and image tagging. In each case, we obtain state-of-the-art results and order-of-magnitude speed ups.