Toward a generic representation of random variables for machine learning

A global relative similarity for inferring interactions of multi-agent systems

Interactions and dynamics are critical mechanisms for multi-agent systems to achieve complex intelligence through the cooperation of simple agents. Yet, inferring interactions of the multi-agent system is still a common and open problem. A new method named K-similarity is designed to measure the global relative similarities for inferring the interactions among multiple agents in this paper. K-similarity is defined to be a synthetic measure of relative similarity on each observation snapshot where regular distances are nonlinearly mapped into a network. Therefore, K-similarity contains the global relative similarity information, and the interaction topology can be inferred from the similarity matrix. It has the potential to transform into distance strictly and detect multi-scale information with various K strategies. Therefore, K-similarity can be flexibly applied to various synchronized dynamical systems with fixed, switching, and time-varying topologies. In the experiments, K-similarity outperforms four benchmark methods in accuracy in most scenarios on both simulated and real datasets, and shows strong stability towards outliers. Furthermore, according to the property of K-similarity we develop a Gaussian Mixture Model (GMM)-based threshold to select probable interactions. Our method contributes to not only similarity measurement in multi-agent systems, but also other global similarity measurement problems.