The Complexity of k-Means Clustering when Little is Known
Robert Ganian, Thekla Hamm, Viktoriia Korchemna, Karolina Okrasa, Kirill Simonov
Abstract
In the area of data analysis and arguably even in machine learning as a whole, few approaches have been as impactful as the classical k-means clustering. Here, we study the complexity of k-means clustering in settings where most of the data is not known or simply irrelevant. To obtain a more fine-grained understanding of the tractability of this clustering problem, we apply the parameterized complexity paradigm and obtain three new algorithms for k-means clustering of incomplete data: one for the clustering of bounded-domain (i.e., integer) data, and two incomparable algorithms that target real-valued data. Our approach is based on exploiting structural properties of a graphical encoding of the missing entries, and we show that tractability can be achieved using significantly less restrictive parameterizations than in the complementary case of few missing entries.
BibTeX
@InProceedings{pmlr-v162-ganian22a,
title = {The Complexity of k-Means Clustering when Little is Known},
author = {Ganian, Robert and Hamm, Thekla and Korchemna, Viktoriia and Okrasa, Karolina and Simonov, Kirill},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {6960--6987},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/ganian22a/ganian22a.pdf},
url = {https://proceedings.mlr.press/v162/ganian22a.html},
abstract = {In the area of data analysis and arguably even in machine learning as a whole, few approaches have been as impactful as the classical k-means clustering. Here, we study the complexity of k-means clustering in settings where most of the data is not known or simply irrelevant. To obtain a more fine-grained understanding of the tractability of this clustering problem, we apply the parameterized complexity paradigm and obtain three new algorithms for k-means clustering of incomplete data: one for the clustering of bounded-domain (i.e., integer) data, and two incomparable algorithms that target real-valued data. Our approach is based on exploiting structural properties of a graphical encoding of the missing entries, and we show that tractability can be achieved using significantly less restrictive parameterizations than in the complementary case of few missing entries.}
}