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FAST TOPOLOGICAL CLUSTERING WITH WASSERSTEIN DISTANCE

Publication ,  Conference
Songdechakraiwut, T; Krause, BM; Banks, MI; Nourski, KV; Van Veen, BD
Published in: ICLR 2022 - 10th International Conference on Learning Representations
January 1, 2022

The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and dense networks whose node degrees range over multiple orders of magnitude. In this paper, we propose a novel and computationally practical topological clustering method that clusters complex networks with intricate topology using principled theory from persistent homology and optimal transport. Such networks are aggregated into clusters through a centroid-based clustering strategy based on both their topological and geometric structure, preserving correspondence between nodes in different networks. The notions of topological proximity and centroid are characterized using a novel and efficient approach to computation of the Wasserstein distance and barycenter for persistence barcodes associated with connected components and cycles. The proposed method is demonstrated to be effective using both simulated networks and measured functional brain networks.

Duke Scholars

Published In

ICLR 2022 - 10th International Conference on Learning Representations

Publication Date

January 1, 2022
 

Citation

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Songdechakraiwut, T., Krause, B. M., Banks, M. I., Nourski, K. V., & Van Veen, B. D. (2022). FAST TOPOLOGICAL CLUSTERING WITH WASSERSTEIN DISTANCE. In ICLR 2022 - 10th International Conference on Learning Representations.
Songdechakraiwut, T., B. M. Krause, M. I. Banks, K. V. Nourski, and B. D. Van Veen. “FAST TOPOLOGICAL CLUSTERING WITH WASSERSTEIN DISTANCE.” In ICLR 2022 - 10th International Conference on Learning Representations, 2022.
Songdechakraiwut T, Krause BM, Banks MI, Nourski KV, Van Veen BD. FAST TOPOLOGICAL CLUSTERING WITH WASSERSTEIN DISTANCE. In: ICLR 2022 - 10th International Conference on Learning Representations. 2022.
Songdechakraiwut, T., et al. “FAST TOPOLOGICAL CLUSTERING WITH WASSERSTEIN DISTANCE.” ICLR 2022 - 10th International Conference on Learning Representations, 2022.
Songdechakraiwut T, Krause BM, Banks MI, Nourski KV, Van Veen BD. FAST TOPOLOGICAL CLUSTERING WITH WASSERSTEIN DISTANCE. ICLR 2022 - 10th International Conference on Learning Representations. 2022.

Published In

ICLR 2022 - 10th International Conference on Learning Representations

Publication Date

January 1, 2022