Angular Embedding: A New Angular Robust Principal Component Analysis

TL;DR

This paper introduces Angular Embedding (AE), a novel non-iterative robust PCA method based on angular density, and its trimmed version (TAE), which effectively handles outliers in high-dimensional data, outperforming existing methods.

Contribution

The paper presents a new angular density-based RPCA approach and a trimmed version for large outliers, improving robustness and scalability over prior methods.

Findings

AE/TAE outperform state-of-the-art RPCA methods on synthetic and real datasets.

AE/TAE effectively handle vector-level and pixel-level outliers.

Proposed methods are suitable for large-scale and high-dimensional data.

Abstract

As a widely used method in machine learning, principal component analysis (PCA) shows excellent properties for dimensionality reduction. It is a serious problem that PCA is sensitive to outliers, which has been improved by numerous Robust PCA (RPCA) versions. However, the existing state-of-the-art RPCA approaches cannot easily remove or tolerate outliers by a non-iterative manner. To tackle this issue, this paper proposes Angular Embedding (AE) to formulate a straightforward RPCA approach based on angular density, which is improved for large scale or high-dimensional data. Furthermore, a trimmed AE (TAE) is introduced to deal with data with large scale outliers. Extensive experiments on both synthetic and real-world datasets with vector-level or pixel-level outliers demonstrate that the proposed AE/TAE outperforms the state-of-the-art RPCA based methods.