Latent Low-Rank Representation for subspace segmentation and feature extraction

TLDR

Low‑Rank Representation (LRR) is an effective method for uncovering multiple subspace structures, but using the data matrix as the dictionary can degrade performance when observations are limited or corrupted. This study proposes building the dictionary from both observed and hidden data to improve LRR. LatLRR recovers hidden data through convex nuclear‑norm minimization and unifies subspace segmentation with feature extraction in a single framework. LatLRR outperforms state‑of‑the‑art subspace segmentation algorithms, extracts robust features from corrupted data better than benchmarks, and is more noise‑robust than dimensionality‑reduction methods.

Abstract

Low-Rank Representation (LRR) [16, 17] is an effective method for exploring the multiple subspace structures of data. Usually, the observed data matrix itself is chosen as the dictionary, which is a key aspect of LRR. However, such a strategy may depress the performance, especially when the observations are insufficient and/or grossly corrupted. In this paper we therefore propose to construct the dictionary by using both observed and unobserved, hidden data. We show that the effects of the hidden data can be approximately recovered by solving a nuclear norm minimization problem, which is convex and can be solved efficiently. The formulation of the proposed method, called Latent Low-Rank Representation (LatLRR), seamlessly integrates subspace segmentation and feature extraction into a unified framework, and thus provides us with a solution for both subspace segmentation and feature extraction. As a subspace segmentation algorithm, LatLRR is an enhanced version of LRR and outperforms the state-of-the-art algorithms. Being an unsupervised feature extraction algorithm, LatLRR is able to robustly extract salient features from corrupted data, and thus can work much better than the benchmark that utilizes the original data vectors as features for classification. Compared to dimension reduction based methods, LatLRR is more robust to noise.