Measure Specific Mixture Model (MSM2) for Change Detection

• Activity Number: 630 - Uncertainty Quantification, Reliability and Robust Inference
• Type: Contributed
• Date/Time: Thursday, August 2, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Defense and National Security
• Author(s): Fairul Mohd-Zaid* and Christine Schubert Kabban
• Companies: Air Force Research Lab and Air Force Institute of Technology
• Keywords: Bayesian; Mixture Model; Topology; Graph; Change Detection

Abstract

We propose a change detection method, for any arbitrary system, that is driven by the characterized topological representation of the system via the system measures. Current state-of-the-art approaches rely on analyses of the raw system measurements which may lack discernible structure. By utilizing the topological structure of the data, one is able to consider the relationships within the dataset instead of the state of each datum thereby providing information about the system that is more robust against small and uninformative perturbations. This is performed by 1) characterizing the distribution of graphical measures of the topological representation and 2) detecting any changes that are present within the system through deviations from the characterized model. Since the network measures are empirical, finite mixture modeling is used to model the graphical measures which combines the measure specific properties as well as noise for characterizing the topological structure. This is performed using an MCMC approach for Bayesian analysis to obtain the posterior distributions of the mixture model which are then compared to the prior to determine whether the system has changed.