Constrained Clustering: General Pairwise and Cardinality Constraints

In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Adel Bibi [verfasserIn] Ali Alqahtani [verfasserIn] Bernard Ghanem [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Constrained clustering K-means pairwise cardinality constraints

Übergeordnetes Werk:	In: IEEE Access - IEEE, 2014, 11(2023), Seite 5824-5836
Übergeordnetes Werk:	volume:11 ; year:2023 ; pages:5824-5836

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1109/ACCESS.2023.3236608

Katalog-ID:	DOAJ086270028

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allfields	10.1109/ACCESS.2023.3236608 doi (DE-627)DOAJ086270028 (DE-599)DOAJ97bf3ee149864caeb81906d8dbc4193f DE-627 ger DE-627 rakwb eng TK1-9971 Adel Bibi verfasserin aut Constrained Clustering: General Pairwise and Cardinality Constraints 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization. Constrained clustering K-means pairwise cardinality constraints Electrical engineering. Electronics. Nuclear engineering Ali Alqahtani verfasserin aut Bernard Ghanem verfasserin aut In IEEE Access IEEE, 2014 11(2023), Seite 5824-5836 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:11 year:2023 pages:5824-5836 https://doi.org/10.1109/ACCESS.2023.3236608 kostenfrei https://doaj.org/article/97bf3ee149864caeb81906d8dbc4193f kostenfrei https://ieeexplore.ieee.org/document/10015761/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 5824-5836
spelling	10.1109/ACCESS.2023.3236608 doi (DE-627)DOAJ086270028 (DE-599)DOAJ97bf3ee149864caeb81906d8dbc4193f DE-627 ger DE-627 rakwb eng TK1-9971 Adel Bibi verfasserin aut Constrained Clustering: General Pairwise and Cardinality Constraints 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization. Constrained clustering K-means pairwise cardinality constraints Electrical engineering. Electronics. Nuclear engineering Ali Alqahtani verfasserin aut Bernard Ghanem verfasserin aut In IEEE Access IEEE, 2014 11(2023), Seite 5824-5836 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:11 year:2023 pages:5824-5836 https://doi.org/10.1109/ACCESS.2023.3236608 kostenfrei https://doaj.org/article/97bf3ee149864caeb81906d8dbc4193f kostenfrei https://ieeexplore.ieee.org/document/10015761/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 5824-5836
allfields_unstemmed	10.1109/ACCESS.2023.3236608 doi (DE-627)DOAJ086270028 (DE-599)DOAJ97bf3ee149864caeb81906d8dbc4193f DE-627 ger DE-627 rakwb eng TK1-9971 Adel Bibi verfasserin aut Constrained Clustering: General Pairwise and Cardinality Constraints 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization. Constrained clustering K-means pairwise cardinality constraints Electrical engineering. Electronics. Nuclear engineering Ali Alqahtani verfasserin aut Bernard Ghanem verfasserin aut In IEEE Access IEEE, 2014 11(2023), Seite 5824-5836 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:11 year:2023 pages:5824-5836 https://doi.org/10.1109/ACCESS.2023.3236608 kostenfrei https://doaj.org/article/97bf3ee149864caeb81906d8dbc4193f kostenfrei https://ieeexplore.ieee.org/document/10015761/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 5824-5836
allfieldsGer	10.1109/ACCESS.2023.3236608 doi (DE-627)DOAJ086270028 (DE-599)DOAJ97bf3ee149864caeb81906d8dbc4193f DE-627 ger DE-627 rakwb eng TK1-9971 Adel Bibi verfasserin aut Constrained Clustering: General Pairwise and Cardinality Constraints 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization. Constrained clustering K-means pairwise cardinality constraints Electrical engineering. Electronics. Nuclear engineering Ali Alqahtani verfasserin aut Bernard Ghanem verfasserin aut In IEEE Access IEEE, 2014 11(2023), Seite 5824-5836 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:11 year:2023 pages:5824-5836 https://doi.org/10.1109/ACCESS.2023.3236608 kostenfrei https://doaj.org/article/97bf3ee149864caeb81906d8dbc4193f kostenfrei https://ieeexplore.ieee.org/document/10015761/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 5824-5836
allfieldsSound	10.1109/ACCESS.2023.3236608 doi (DE-627)DOAJ086270028 (DE-599)DOAJ97bf3ee149864caeb81906d8dbc4193f DE-627 ger DE-627 rakwb eng TK1-9971 Adel Bibi verfasserin aut Constrained Clustering: General Pairwise and Cardinality Constraints 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization. Constrained clustering K-means pairwise cardinality constraints Electrical engineering. Electronics. Nuclear engineering Ali Alqahtani verfasserin aut Bernard Ghanem verfasserin aut In IEEE Access IEEE, 2014 11(2023), Seite 5824-5836 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:11 year:2023 pages:5824-5836 https://doi.org/10.1109/ACCESS.2023.3236608 kostenfrei https://doaj.org/article/97bf3ee149864caeb81906d8dbc4193f kostenfrei https://ieeexplore.ieee.org/document/10015761/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 11 2023 5824-5836
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callnumber-first	T - Technology
author	Adel Bibi
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topic_title	TK1-9971 Constrained Clustering: General Pairwise and Cardinality Constraints Constrained clustering K-means pairwise cardinality constraints
topic	misc TK1-9971 misc Constrained clustering misc K-means misc pairwise misc cardinality constraints misc Electrical engineering. Electronics. Nuclear engineering
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title	Constrained Clustering: General Pairwise and Cardinality Constraints
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title_full	Constrained Clustering: General Pairwise and Cardinality Constraints
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title_sort	constrained clustering: general pairwise and cardinality constraints
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title_auth	Constrained Clustering: General Pairwise and Cardinality Constraints
abstract	In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization.
abstractGer	In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization.
abstract_unstemmed	In this work, we study constrained clustering, where constraints are utilized to guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the cluster labels of two instances to be the same (must-link constraints) or different (cannot-link constraints). Cardinality constraints encourage cluster sizes to satisfy a user-specified distribution. However, most existing constrained clustering models can only utilize one category of constraints at a time. In this paper, we enforce the above two categories into a unified clustering model starting with the integer program formulation of the standard K-means. As these two categories provide useful information at different levels, utilizing both of them is expected to allow for better clustering performance. However, the optimization is difficult due to the binary and quadratic constraints in the proposed unified formulation. To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization.
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title_short	Constrained Clustering: General Pairwise and Cardinality Constraints
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To alleviate this difficulty, we utilize two techniques: equivalently replacing the binary constraints by the intersection of two continuous constraints; the other is transforming the quadratic constraints into bi-linear constraints by introducing extra variables. Then we derive an equivalent continuous reformulation with simple constraints, which can be efficiently solved by Alternating Direction Method of Multipliers (ADMM) algorithm. Extensive experiments on both synthetic and real data demonstrate: 1) when utilizing a single category of constraint, the proposed model is superior to or competitive with state-of-the-art constrained clustering models, and 2) when utilizing both categories of constraints jointly, the proposed model shows better performance than the case of the single category. The experimental results show that the proposed method exploits the constraints to achieve perfect clustering performance with improved clustering to <inline-formula< <tex-math notation="LaTeX"<$2-5$ </tex-math<</inline-formula<% in classical clustering metrics, e.g., Adjusted Random Index (ARI), Mirkin’s Index (MI), and Huber’s Index (HI), outerperfomring all compared-againts methods across the board. Moreover, we show that our method is robust to initialization.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Constrained clustering</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">K-means</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">pairwise</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">cardinality constraints</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Electrical engineering. Electronics. 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