The Computational Complexity of Concise Hypersphere Classification

Eduard Eiben, Robert Ganian, Iyad A. Kanj, Sebastian Ordyniak, Stefan Szeider
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:9060-9070, 2023.

Abstract

Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued as well as binary data. However, obtaining an (ideally concise) explanation via hypersphere classification is much more difficult when dealing with binary data as opposed to real-valued data. In this paper, we perform the first complexity-theoretic study of the hypersphere classification problem for binary data. We use the fine-grained parameterized complexity paradigm to analyze the impact of structural properties that may be present in the input data as well as potential conciseness constraints. Our results include not only stronger lower bounds but also a number of new fixed-parameter algorithms for hypersphere classification of binary data, which can find an exact and concise explanation when one exists.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-eiben23a, title = {The Computational Complexity of Concise Hypersphere Classification}, author = {Eiben, Eduard and Ganian, Robert and Kanj, Iyad A. and Ordyniak, Sebastian and Szeider, Stefan}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {9060--9070}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/eiben23a/eiben23a.pdf}, url = {https://proceedings.mlr.press/v202/eiben23a.html}, abstract = {Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued as well as binary data. However, obtaining an (ideally concise) explanation via hypersphere classification is much more difficult when dealing with binary data as opposed to real-valued data. In this paper, we perform the first complexity-theoretic study of the hypersphere classification problem for binary data. We use the fine-grained parameterized complexity paradigm to analyze the impact of structural properties that may be present in the input data as well as potential conciseness constraints. Our results include not only stronger lower bounds but also a number of new fixed-parameter algorithms for hypersphere classification of binary data, which can find an exact and concise explanation when one exists.} }
Endnote
%0 Conference Paper %T The Computational Complexity of Concise Hypersphere Classification %A Eduard Eiben %A Robert Ganian %A Iyad A. Kanj %A Sebastian Ordyniak %A Stefan Szeider %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-eiben23a %I PMLR %P 9060--9070 %U https://proceedings.mlr.press/v202/eiben23a.html %V 202 %X Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued as well as binary data. However, obtaining an (ideally concise) explanation via hypersphere classification is much more difficult when dealing with binary data as opposed to real-valued data. In this paper, we perform the first complexity-theoretic study of the hypersphere classification problem for binary data. We use the fine-grained parameterized complexity paradigm to analyze the impact of structural properties that may be present in the input data as well as potential conciseness constraints. Our results include not only stronger lower bounds but also a number of new fixed-parameter algorithms for hypersphere classification of binary data, which can find an exact and concise explanation when one exists.
APA
Eiben, E., Ganian, R., Kanj, I.A., Ordyniak, S. & Szeider, S.. (2023). The Computational Complexity of Concise Hypersphere Classification. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:9060-9070 Available from https://proceedings.mlr.press/v202/eiben23a.html.

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