TY - GEN
T1 - Variational wasserstein clustering
AU - Mi, Liang
AU - Zhang, Wen
AU - Gu, Xianfeng
AU - Wang, Yalin
N1 - Funding Information:
Acknowledgments. The research is partially supported by National Institutes of Health (R21AG043760, RF1AG051710, and R01EB025032), and National Science Foundation (DMS-1413417 and IIS-1421165).
Publisher Copyright:
© Springer Nature Switzerland AG 2018.
PY - 2018
Y1 - 2018
N2 - We propose a new clustering method based on optimal transportation. We discuss the connection between optimal transportation and k-means clustering, solve optimal transportation with the variational principle, and investigate the use of power diagrams as transportation plans for aggregating arbitrary domains into a fixed number of clusters. We drive cluster centroids through the target domain while maintaining the minimum clustering energy by adjusting the power diagram. Thus, we simultaneously pursue clustering and the Wasserstein distance between the centroids and the target domain, resulting in a measure-preserving mapping. We demonstrate the use of our method in domain adaptation, remeshing, and learning representations on synthetic and real data.
AB - We propose a new clustering method based on optimal transportation. We discuss the connection between optimal transportation and k-means clustering, solve optimal transportation with the variational principle, and investigate the use of power diagrams as transportation plans for aggregating arbitrary domains into a fixed number of clusters. We drive cluster centroids through the target domain while maintaining the minimum clustering energy by adjusting the power diagram. Thus, we simultaneously pursue clustering and the Wasserstein distance between the centroids and the target domain, resulting in a measure-preserving mapping. We demonstrate the use of our method in domain adaptation, remeshing, and learning representations on synthetic and real data.
KW - Clustering
KW - Discrete distribution
KW - K-means
KW - Measure preserving
KW - Optimal transportation
KW - Wasserstein distance
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U2 - 10.1007/978-3-030-01267-0_20
DO - 10.1007/978-3-030-01267-0_20
M3 - Conference contribution
AN - SCOPUS:85055425376
SN - 9783030012663
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 336
EP - 352
BT - Computer Vision – ECCV 2018 - 15th European Conference, 2018, Proceedings
A2 - Weiss, Yair
A2 - Ferrari, Vittorio
A2 - Sminchisescu, Cristian
A2 - Hebert, Martial
PB - Springer Verlag
T2 - 15th European Conference on Computer Vision, ECCV 2018
Y2 - 8 September 2018 through 14 September 2018
ER -