Robust Manifold Learning via Conformity Pursuit

• Published in: IEEE signal processing letters 2019-03, Vol.26 (3), p.425-429
• Main Authors: Sedghi, Mahlagha, Atia, George, Georgiopoulos, Michael
• Format: Article
• Language: English
• Subjects: Anomaly detection; Chaos theory; Data analysis; Data models; Data points; Global conformity; Indexes; Inliers (landforms); Kernel; Machine learning; manifold learning; Manifolds; Manifolds (mathematics); Noise sensitivity; outlier detection; Outliers (statistics); Principal component analysis; reproducing kernel; Signal processing algorithms
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2019.2893064

This letter presents an effective and simple method, termed Global Conformity Pursuit (GCP), for robust manifold learning. Data points lying on a union of low-dimensional nonlinear manifolds are expected to be highly conforming. On the other hand, outliers do not typically adhere to low-dimensional structures or otherwise do not exist in large numbers. Hence, they can be identified by their low overall resemblance to the rest of the data. Our kernel-based setting allows us to capture the underlying nonlinear structure of the manifold data, while avoiding the construction of local neighborhood regions which typically causes extreme sensitivity to noise and outliers. Aside from its significantly simple structure-involving only a matrix evaluation and multiplication-GCP is the first manifold learning approach that is simultaneously noniterative and capable of tolerating a large number of outliers, dependent outliers, and noise components. Theoretical analysis guarantees a large gap between conformity values of inliers and outliers. Experimental results showcase potential uses of the proposed framework on benchmark datasets.