Change point detection in multi-agent systems based on higher-order features

Change point detection (CPD) for multi-agent systems helps one to evaluate the state and better control the system. Multivariate CPD methods solve the d × T time series well; however, the multi-agent systems often produce the N × d × T dimensional data, where d is the dimension of multivariate observations, T is the total observation time, and N is the number of agents. In this paper, we propose two valid approaches based on higher-order features, namely, the Betti number feature extraction and the Persistence feature extraction, to compress the d-dimensional features into one dimension so that general CPD methods can be applied to higher-dimensional data. First, a topological structure based on the Vietoris-Rips complex is constructed on each time-slice snapshot. Then, the Betti number and persistence of the topological structures are obtained to separately constitute two feature matrices for change point estimates. Higher-order features primarily describe the data distribution on each snapshot and are, therefore, independent of the node correspondence cross snapshots, which gives our methods unique advantages in processing missing data. Experiments in multi-agent systems demonstrate the significant performance of our methods. We believe that our methods not only provide a new tool for dimensionality reduction and missing data in multi-agent systems but also have the potential to be applied to a wider range of fields, such as complex networks.