Inthispaper,wepropose a tractable algorithm that estimates the probabilistic aggregation map from the system'strajectory.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states

We thank three reviewers for the constructive comments. In what follows we make a few clarifications and itemized responses. We are the first to bring the perspective of NMF/topic modeling to Markov state aggregation. We hope our work would inspire future work and more efficient methods may be developed. Making this idea work, both in theory and in applications, requires substantial efforts and nontrivial analysis.