Hierarchical Clustering of Data Streams: Scalable Algorithms and Approximation Guarantees
Anand Rajagopalan, Fabio Vitale, Danny Vainstein, Gui Citovsky, Cecilia M Procopiuc, Claudio Gentile
Abstract
We investigate the problem of hierarchically clustering data streams containing metric data in R^d. We introduce a desirable invariance property for such algorithms, describe a general family of hyperplane-based methods enjoying this property, and analyze two scalable instances of this general family against recently popularized similarity/dissimilarity-based metrics for hierarchical clustering. We prove a number of new results related to the approximation ratios of these algorithms, improving in various ways over the literature on this subject. Finally, since our algorithms are principled but also very practical, we carry out an experimental comparison on both synthetic and real-world datasets showing competitive results against known baselines.
BibTeX
@InProceedings{pmlr-v139-rajagopalan21a,
title = {Hierarchical Clustering of Data Streams: Scalable Algorithms and Approximation Guarantees},
author = {Rajagopalan, Anand and Vitale, Fabio and Vainstein, Danny and Citovsky, Gui and Procopiuc, Cecilia M and Gentile, Claudio},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {8799--8809},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/rajagopalan21a/rajagopalan21a.pdf},
url = {https://proceedings.mlr.press/v139/rajagopalan21a.html},
abstract = {We investigate the problem of hierarchically clustering data streams containing metric data in R^d. We introduce a desirable invariance property for such algorithms, describe a general family of hyperplane-based methods enjoying this property, and analyze two scalable instances of this general family against recently popularized similarity/dissimilarity-based metrics for hierarchical clustering. We prove a number of new results related to the approximation ratios of these algorithms, improving in various ways over the literature on this subject. Finally, since our algorithms are principled but also very practical, we carry out an experimental comparison on both synthetic and real-world datasets showing competitive results against known baselines.}
}