The art of centering without centering for robust principal component analysis

Many robust variants of Principal Component Analysis remove outliers from the data and compute the principal components of the remaining data. The robust centered variant requires knowledge of the center of the non-outliers. Unfortunately, the center of non-outliers is unknown until after the outliers are determined, and using an inaccurate center may lead to the detection of wrong outliers. We demonstrate this problem in several known robust PCA algorithms. We describe a method that implicitly centers the non-outliers, implemented by appending a constant value (bias) to each data point. This bias method can be used with "black box" robust PCA algorithms by augmenting their input with minimal change to the algorithm itself.