Hierarchical Quasi-Clustering Methods for Asymmetric Networks

Gunnar Carlsson, Facundo Mémoli, Alejandro Ribeiro, Santiago Segarra
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):352-360, 2014.

Abstract

This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-carlsson14, title = {Hierarchical Quasi-Clustering Methods for Asymmetric Networks}, author = {Carlsson, Gunnar and Mémoli, Facundo and Ribeiro, Alejandro and Segarra, Santiago}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {352--360}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/carlsson14.pdf}, url = {https://proceedings.mlr.press/v32/carlsson14.html}, abstract = {This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.} }
Endnote
%0 Conference Paper %T Hierarchical Quasi-Clustering Methods for Asymmetric Networks %A Gunnar Carlsson %A Facundo Mémoli %A Alejandro Ribeiro %A Santiago Segarra %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-carlsson14 %I PMLR %P 352--360 %U https://proceedings.mlr.press/v32/carlsson14.html %V 32 %N 2 %X This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.
RIS
TY - CPAPER TI - Hierarchical Quasi-Clustering Methods for Asymmetric Networks AU - Gunnar Carlsson AU - Facundo Mémoli AU - Alejandro Ribeiro AU - Santiago Segarra BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-carlsson14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 352 EP - 360 L1 - http://proceedings.mlr.press/v32/carlsson14.pdf UR - https://proceedings.mlr.press/v32/carlsson14.html AB - This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States. ER -
APA
Carlsson, G., Mémoli, F., Ribeiro, A. & Segarra, S.. (2014). Hierarchical Quasi-Clustering Methods for Asymmetric Networks. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):352-360 Available from https://proceedings.mlr.press/v32/carlsson14.html.

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