Shapley Values of Reconstruction Errors of PCA for Explaining Anomaly Detection We present a method to compute the Shapley values of reconstruction errors of principal component analysis (PCA), which is particularly useful in explaining the results of anomaly detection based on PCA. Because features are usually correlated when PCAbased anomaly detection is applied, care must be taken in computing a value function for the Shapley values. We utilize the probabilistic view of PCA, particularly its conditional distribution, to exactly compute a value function for the Shapely values. We also present numerical examples, which imply that the Shapley values are advantageous for explaining detected anomalies than raw reconstruction errors of each feature.

Stochastic Principal Component Analysis Via Mean Absolute Projection Maximization PrincipalComponent Analysis (PCA) is a data processing method with numerous applications in signal processing and machine learning. At the same time, standard PCA has been shown to be very sensitive against faultyoutlying data. On the other hand, L1normbased PCA (L1PCA), seeking to maximize the aggregate absolute projections of the processed data, has demonstrated sturdy corruption resistance. At the same time, in our big data era, there is a need for online (stochastic) algorithms for data analysis with limited storage and computation requirements. To this end, in this paper we extend batch L1PCA and propose a novel algorithm for stochastic PC calculation based on mean absolute projection maximization, with formal convergence guarantees. Our numerical studies demonstrate the convergence and corroborate the corruption resistance of the proposed method.