The paper Comparing Clusterings - An Overview has a good view of different metrics for comparing the similarity of 2 clusterings. Overall, Normalized Mutual Information sounds like a good one. It is implemented in sklearn as sklearn.metrics.normalized_mutual_info_score . Of course, there are many more metrics for measuring similarity of 2 clusters (e.g., Adjusted Rand Index) implemented in sklearn. For more details, please refer to Clustering Metrics.

References

• Comparing Clusterings - An Overview

• https://hal.inria.fr/hal-01514872/document