[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123552-en":3,"doc-seo-123552-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},123552,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Accelerating Spectral Clustering under Fairness Constraints - Abstract and Introduction","Fairness of decision-making algorithms is addressed through spectral clustering with group fairness constraints, requiring each demographic group to appear in every cluster proportionally to its presence in the overall population. The work proposes an efficient fair spectral clustering method (Fair SC) by reformulating the problem within the differences of convex functions (DC) framework. A novel variable augmentation and a DC-adapted ADMM-type algorithm enable efficient solution of each subproblem, avoiding expensive eigendecomposition. Experiments on synthetic and real-world benchmarks confirm significant computational speedups, especially as problem size increases.","Accelerating Spectral Clustering under Fairness Constraints  \nFrancesco Tonin 1 Alex Lambert 2 Johan A.K. Suykens 2 Volkan Cevher 1  \nAbstract  \nFairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the general population. We present a new efficient method for fair spectral clustering (Fair SC) by casting the Fair SC problem within the difference of convex functions (DC) framework. To this end, we introduce a novel variable augmentation strategy and employ an alternating direction method of multipliers type of algorithm adapted to DC problems. We show that each associated subproblem can be solved efficiently, resulting in higher computational efficiency compared to prior work, which required a computationally expensive eigendecomposition. Numerical experiments demonstrate the effectiveness of our approach on both synthetic and real-world benchmarks, showing significant speedups in computation time over prior art, especially as the problem size grows.  \nThis work thus represents a considerable step forward towards the adoption of fair clustering in real-world applications.  \n1. Introduction  \nAlgorithmic decision-making systems leveraging machine learning (ML) are increasingly being used in critical domains such as healthcare, social policy, and education, raising concerns about the potential for these algorithms to exhibit unfair behavior towards certain demographic groups (Hardt et al., 2016 ; Buolamwini & Gebru, 2018 ; Chouldechova & Roth, 2020) . In response to these concerns, the field of fair ML has proposed mathematical fairness formulations for various ML tasks, e.g., (Dwork et al., 2012 ; Zafar et al., 2017 ; Samadi et al., 2018 ; Donini et al., 2018 ;  \n1LIONS, EPFL, Switzerland 2ESAT-STADIUS, KU Leuven, Belgium. Correspondence to: Francesco Tonin \u003C[francesco.tonin@epfl.ch](francesco.tonin@epfl.ch)>.  \nProceedings of the 42 nd International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025 . Copyright 2025 by the author(s) .  \nAgarwal et al., 2019 ; Aghaei et al., 2019 ; Amini et al., 2019 ; Davidson & Ravi, 2020 ; Celis et al., 2018 ; Singh et al., 2023 ; Ali et al., 2023) .  \nIn clustering research, Chierichetti et al. (2017) introduced demographic fairness by imposing fairness constraints to ensure balanced representation across protected groups in clusters. Initially applied to two groups in Chierichetti et al.(2017), this concept was expanded to multiple groups (Rösner & Schmidt, 2018 ; Bera et al., 2019a) and primarily explored in prototype-based clustering (Chierichetti et al., 2017 ; Carreira-Perpinán & Wang, 2013 ; Bera et al., 2019a) . Kleindessner et al. (2019) adapted this notion of fairness to spectral clustering (Shi & Malik, 2000 ; Von Luxburg, 2007) and is known as fair spectral clustering (Fair SC) . Although recent advances (Wang et al., 2023) have sped up the computation of Fair SC, the reliance on the computationally expensive eigendecomposition of the fairness-constrained graph Laplacian still limits the application of Fair SC to real-world problems.  \nFrom an optimization standpoint, SC can be cast as atrace maximization problem with orthonormality constraints (Bach & Jordan, 2003), falling into the differences of convex functions (DC) framework. This problem class has spurred substantial interest (Tao et al., 1986 ; Le Thi & Pham Dinh, 2018), and efficient DC-based algorithms have been developed for various ML tasks including feature selection (Le Thi et al., 2015), reinforcement learning (Piot et al., 2014) and (kernel) PCA (Beck & Teboulle, 2021 ; Toninet al., 2023) . However, these algorithms do not extend directly to Fair SC due to their lack of consideration for the fairness constraints, the integration of which within the DC framework remains unexplored in the existing literature.  \nIn this wor","cbCailIA6xZVEIbF","https://ap.wps.com/l/cbCailIA6xZVEIbF","pdf",597116,1,21,"English","en",105,"# Abstract\n# Introduction\n## Fairness in algorithmic decision-making\n## Fair spectral clustering and its computational bottleneck\n## DC reformulation and the proposed ADMM-type method\n# Problem Formulation","[{\"question\":\"What fairness requirement does the proposed spectral clustering method enforce?\",\"answer\":\"It enforces group fairness by ensuring every demographic group is represented in each cluster proportionally to the group’s representation in the overall population.\"},{\"question\":\"How does the paper improve the computational efficiency of fair spectral clustering?\",\"answer\":\"It reformulates Fair SC within the differences of convex functions (DC) framework and uses a DC-adapted ADMM-type algorithm with a novel variable augmentation, which allows efficient subproblem solutions without costly eigendecomposition.\"},{\"question\":\"What evidence supports the effectiveness of the proposed approach?\",\"answer\":\"Numerical experiments on both synthetic and real-world benchmarks show significant speedups in computation time compared with prior methods, especially as problem size grows.\"}]","Accelerating Spectral Clustering under Fairness Constraints - Abstract and Introduction | PDF",1785817272,53,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"accelerating-spectral-clustering-under-fairness-constraints-abstract-and-introduction","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/accelerating-spectral-clustering-under-fairness-constraints-abstract-and-introduction/123552/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What fairness requirement does the proposed spectral clustering method enforce?","Question",{"text":75,"@type":76},"It enforces group fairness by ensuring every demographic group is represented in each cluster proportionally to the group’s representation in the overall population.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper improve the computational efficiency of fair spectral clustering?",{"text":80,"@type":76},"It reformulates Fair SC within the differences of convex functions (DC) framework and uses a DC-adapted ADMM-type algorithm with a novel variable augmentation, which allows efficient subproblem solutions without costly eigendecomposition.",{"name":82,"@type":73,"acceptedAnswer":83},"What evidence supports the effectiveness of the proposed approach?",{"text":84,"@type":76},"Numerical experiments on both synthetic and real-world benchmarks show significant speedups in computation time compared with prior methods, especially as problem size grows.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]