Angular Embedding: A New Angular Robust Principal Component Analysis
This work provides a non-iterative and robust dimensionality reduction method for machine learning practitioners dealing with outlier-corrupted data.
This paper introduces Angular Embedding (AE), a non-iterative Robust Principal Component Analysis (RPCA) method that uses angular density to handle outliers. An extension, Trimmed AE (TAE), is proposed for datasets with large-scale outliers. Experiments show AE/TAE outperforms existing RPCA methods on synthetic and real-world datasets with various outlier types.
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.