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DOI: 10.4230/LIPIcs.ISAAC.2021.46
URN: urn:nbn:de:0030-drops-154794
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15479/
Cho, Kyungjin ; Oh, Eunjin
Linear-Time Approximation Scheme for k-Means Clustering of Axis-Parallel Affine Subspaces
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Abstract
In this paper, we present a linear-time approximation scheme for k-means clustering of incomplete data points in d-dimensional Euclidean space. An incomplete data point with Δ > 0 unspecified entries is represented as an axis-parallel affine subspace of dimension Δ. The distance between two incomplete data points is defined as the Euclidean distance between two closest points in the axis-parallel affine subspaces corresponding to the data points. We present an algorithm for k-means clustering of axis-parallel affine subspaces of dimension Δ that yields an (1+ε)-approximate solution in O(nd) time. The constants hidden behind O(⋅) depend only on Δ, ε and k. This improves the O(n² d)-time algorithm by Eiben et al. [SODA'21] by a factor of n.
BibTeX - Entry
@InProceedings{cho_et_al:LIPIcs.ISAAC.2021.46,
author = {Cho, Kyungjin and Oh, Eunjin},
title = {{Linear-Time Approximation Scheme for k-Means Clustering of Axis-Parallel Affine Subspaces}},
booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
pages = {46:1--46:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-214-3},
ISSN = {1868-8969},
year = {2021},
volume = {212},
editor = {Ahn, Hee-Kap and Sadakane, Kunihiko},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15479},
URN = {urn:nbn:de:0030-drops-154794},
doi = {10.4230/LIPIcs.ISAAC.2021.46},
annote = {Keywords: k-means clustering, affine subspaces}
}
| Keywords: | k-means clustering, affine subspaces | |
| Seminar: | 32nd International Symposium on Algorithms and Computation (ISAAC 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 30.11.2021 |
