  Properties of data are frequently seen to vary depending on the sampled
situations, which usually changes along a time evolution or owing to
environmental effects. One way to analyze such data is to find invariances, or
representative features kept constant over changes. The aim of this paper is to
identify one such feature, namely interactions or dependencies among variables
that are common across multiple datasets collected under different conditions.
To that end, we propose a common substructure learning (CSSL) framework based
on a graphical Gaussian model. We further present a simple learning algorithm
based on the Dual Augmented Lagrangian and the Alternating Direction Method of
Multipliers. We confirm the performance of CSSL over other existing techniques
in finding unchanging dependency structures in multiple datasets through
numerical simulations on synthetic data and through a real world application to
anomaly detection in automobile sensors.
