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Learning the similarity between structured data, especially the graphs, isone of the essential problems. Besides the approach like graph kernels,Gromov-Wasserstein (GW) distance recently draws big attention due to itsflexibility to capture both topological and feature characteristics, as well ashandling the permutation invariance. However, structured data are widelydistributed for different data mining and machine learning applications. Withprivacy concerns, accessing the decentralized data is limited to eitherindividual clients or different silos. To tackle these issues, we propose aprivacy-preserving framework to analyze the GW discrepancy of node embeddinglearned locally from graph neural networks in a federated flavor, and thenexplicitly place local differential privacy (LDP) based on Multi-bit Encoder toprotect sensitive information. Our experiments show that, with strong privacyprotections guaranteed by the $\varepsilon$-LDP algorithm, the proposedframework not only preserves privacy in graph learning but also presents anoised structural metric under GW distance, resulting in comparable and evenbetter performance in classification and clustering tasks. Moreover, we reasonthe rationale behind the LDP-based GW distance analytically and empirically.

Gromov-Wasserstein Discrepancy with Local Differential Privacy for Distributed Structural Graphs