A Robust Approach for Image Clustering with Outliers via Tensor Low-Rank Representation

Abstract

Recently, low-rank tensor analysis has received widespread attention, due to its effectiveness in many applications in computer vision and pattern recognition. However, existing methods mainly focus on recovering tensor data contaminated by Gaussian or gross sparse noise, which leads to unsatisfactory results when handling outliers or sample-specific corruptions. In this regard, this paper proposes an outlier-robust tensor low-rank representation (OR-TLRR) method that can perform outlier detection and clustering of two-dimensional data simultaneously based on the t-SVD framework. In particular, for tensor observations with arbitrary outlier corruptions, OR-TLRR has provable performance guarantees for exactly recovering the row space of clean data and detecting outliers under mild conditions. This paper also introduces a divide-and-conquer algorithm that can substantially accelerate OR-TLRR without performance drop, while maintaining OR-TLRR’s strong recovery guarantees. Furthermore, it extends OR-TLRR to the case when parts of the data are missing. Finally, it reports the outcomes of a series of numerical experiments involving both synthetic and real data that demonstrate the superiority of the proposed algorithms over existing approaches in the literature.