Academic Journal
An Exact Solution Approach for Hierarchical Clustering.
| Title: | An Exact Solution Approach for Hierarchical Clustering. |
|---|---|
| Authors: | Willemsen, Rick1 (AUTHOR) willemsen@ese.eur.nl, Cavicchia, Carlo1 (AUTHOR) cavicchia@ese.eur.nl, van den Heuvel, Wilco1 (AUTHOR) wvandenheuvel@ese.eur.nl, van de Velden, Michel1 (AUTHOR) vandevelden@ese.eur.nl |
| Source: | INFORMS Journal on Computing. Mar/Apr2026, Vol. 38 Issue 2, p447-462. 16p. |
| Subject Terms: | *Mathematical programming, *Mathematical optimization, Hierarchical clustering (Cluster analysis), Mixed integer linear programming, Analytical solutions, Cost functions, Clustering algorithms |
| Abstract: | In hierarchical clustering, a hierarchy of nested data partitions is obtained. Commonly used agglomerative and divisive heuristics do not optimize over a global objective function. Although several objective functions and approximation algorithms have been proposed, exact methods that find optimal solutions based on these objective functions have received little attention. In this paper, we consider an objective function involving a sum of partitional clustering objectives over each level. We introduce two compact mixed-integer linear programming formulations as well as a set-covering formulation that can handle various objective functions. In addition, we provide a branch-and-price framework to solve the set-covering formulation. We apply our branch-and-price approach to real-world data instances containing up to 200 observations compared with 15 in the literature. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0903) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2024.0903). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR] |
| Copyright of INFORMS Journal on Computing is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Business Source Index |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: bsx DbLabel: Business Source Index An: 192991003 RelevancyScore: 1492 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1491.61413574219 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: An Exact Solution Approach for Hierarchical Clustering. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Willemsen%2C+Rick%22">Willemsen, Rick</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> willemsen@ese.eur.nl</i><br /><searchLink fieldCode="AR" term="%22Cavicchia%2C+Carlo%22">Cavicchia, Carlo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cavicchia@ese.eur.nl</i><br /><searchLink fieldCode="AR" term="%22van+den+Heuvel%2C+Wilco%22">van den Heuvel, Wilco</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> wvandenheuvel@ese.eur.nl</i><br /><searchLink fieldCode="AR" term="%22van+de+Velden%2C+Michel%22">van de Velden, Michel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> vandevelden@ese.eur.nl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22INFORMS+Journal+on+Computing%22">INFORMS Journal on Computing</searchLink>. Mar/Apr2026, Vol. 38 Issue 2, p447-462. 16p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Mathematical+programming%22">Mathematical programming</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Hierarchical+clustering+%28Cluster+analysis%29%22">Hierarchical clustering (Cluster analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Mixed+integer+linear+programming%22">Mixed integer linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+functions%22">Cost functions</searchLink><br /><searchLink fieldCode="DE" term="%22Clustering+algorithms%22">Clustering algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In hierarchical clustering, a hierarchy of nested data partitions is obtained. Commonly used agglomerative and divisive heuristics do not optimize over a global objective function. Although several objective functions and approximation algorithms have been proposed, exact methods that find optimal solutions based on these objective functions have received little attention. In this paper, we consider an objective function involving a sum of partitional clustering objectives over each level. We introduce two compact mixed-integer linear programming formulations as well as a set-covering formulation that can handle various objective functions. In addition, we provide a branch-and-price framework to solve the set-covering formulation. We apply our branch-and-price approach to real-world data instances containing up to 200 observations compared with 15 in the literature. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0903) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2024.0903). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of INFORMS Journal on Computing is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=bsx&AN=192991003 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1287/ijoc.2024.0903 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 447 Subjects: – SubjectFull: Mathematical programming Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Hierarchical clustering (Cluster analysis) Type: general – SubjectFull: Mixed integer linear programming Type: general – SubjectFull: Analytical solutions Type: general – SubjectFull: Cost functions Type: general – SubjectFull: Clustering algorithms Type: general Titles: – TitleFull: An Exact Solution Approach for Hierarchical Clustering. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Willemsen, Rick – PersonEntity: Name: NameFull: Cavicchia, Carlo – PersonEntity: Name: NameFull: van den Heuvel, Wilco – PersonEntity: Name: NameFull: van de Velden, Michel IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar/Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10919856 Numbering: – Type: volume Value: 38 – Type: issue Value: 2 Titles: – TitleFull: INFORMS Journal on Computing Type: main |
| ResultId | 1 |