Robust Low-Complexity Randomized Methods for Locating Outliers in Large Matrices
This work addresses outlier detection in large-scale matrix data, which is incremental as it builds on existing methods with a focus on robustness and efficiency.
The paper tackles the problem of locating outlier columns in large, low-rank matrices with noise or missing data, proposing a randomized two-step inference framework that achieves accurate outlier detection with high probability, as verified by numerical experiments showing computational efficiency.
This paper examines the problem of locating outlier columns in a large, otherwise low-rank matrix, in settings where {}{the data} are noisy, or where the overall matrix has missing elements. We propose a randomized two-step inference framework, and establish sufficient conditions on the required sample complexities under which these methods succeed (with high probability) in accurately locating the outliers for each task. Comprehensive numerical experimental results are provided to verify the theoretical bounds and demonstrate the computational efficiency of the proposed algorithm.