Anomalous Neighborhood Selection

We propose a method to extract row/column-wise heterogeneous elements between two precision matrices for an anomaly localization. We formulate the task as a convex optimization problem using a regularization term that penalizes row/column-wise differences between two matrices. The fundamental difficulties of the problem are that the proposed regularization term (1) is a sum of group-wise regularizations with overlapping supports between the groups, (2) penalizes matrices in a symmetric manner. Our proposed algorithm with an alternating direction method of multipliers can deal with these two difficulties efficiently resulting in a very simple formulation with each updating step computed analytically. We also show the validity of the proposed method through an anomaly localization simulation using a real world data.