Subspace Segmentation by Successive Approximations: A Method for Low-Rank and High-Rank Data with Missing Entries

TL;DR

This paper introduces an iterative method for reconstructing and clustering incomplete high-dimensional data in multiple subspaces, leveraging sparse representations to improve accuracy and robustness over existing techniques.

Contribution

It presents a novel iterative approach that jointly reconstructs missing data and estimates subspace structures, outperforming current methods in accuracy and robustness.

Findings

Achieves higher reconstruction accuracy than existing methods.

Improves clustering performance on synthetic and real data.

Effective for both low-rank and high-rank data.

Abstract

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic subspace structure. Since we have a non-convex problem, we propose an iterative method to reconstruct the data and provide a sparse similarity affinity matrix. This method is robust to initialization and achieves greater reconstruction accuracy than current methods, which dramatically improves clustering performance. Extensive experiments with synthetic and real data show that our approach leads to significant improvements in the reconstruction and segmentation, outperforming current state of the art for both low and high-rank data.