Robust Pca With Concurrent Column And Element-Wise Outliers

To date, existing robust PCA algorithms have only considered settings where the data is corrupted with one type of outliers at a time, but a mechanism to handle simultaneous types of outliers has been lacking. This paper proposes a low rank matrix recovery algorithm that is robust to concurrent presence of column-wise and sparse element-wise outliers. The underpinning of our approach is a sparse approximation of a sparsely corrupted column whereby we set apart an inlier column with sparse corruption from an outlying data point. The core idea of sparse approximation is analyzed analytically where we show that the underlying-norm minimization can obtain the representation of an inlier in presence of sparse corruptions