Angular Embedding: A Robust Quadratic Criterion

Abstract—Given the size and confidence of pairwise local orderings, angular embedding (AE) finds a global ordering with a nearglobal optimal eigensolution. As a quadratic criterion in the complex domain, AE is remarkably robust to outliers, unlike its real domain counterpart LS, the least squares embedding. Our comparative study of LS and AE reveals that AE’s robustness is due not to the particular choice of the criterion, but to the choice of representation in the complex domain. When the embedding is encoded in the angular space, we not only have a non-convex error function that delivers robustness, but also have a Hermitian graph Laplacian that completely determines the optimum and delivers efficiency. The high quality of embedding by AE in the presence of outliers can hardly be matched by LS, its corresponding L1 norm formulation, or their bounded versions. These results suggest that the key to overcoming outliers lies not with additionally imposing constraints on the embedd...

• Type: Journal
• Year: 2012
• Where: PAMI
• Authors: Stella Yu
• Keywords: Cluster Organization, Least Squares, Measurement Space, PAMI 2012, Software Engineering