[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83872-en":3,"doc-seo-83872-105":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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83872,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Sensitivity Sampling with Predictions for k-Means Clustering","Sensitivity Sampling with Predictions for k-Means Clustering研究k-means在大规模数据集上的聚类难题。现有基于coresets的前沿方法可用小型加权摘要近似聚类目标并给出严格质量保证，其中灵敏度采样需要计算每个点相对全数据、对所有中心选择的精确重要性。该工作证明：在coresets构造中使用更粗的灵敏度近似仍能保持理论结果，并提出利用预测来加速灵敏度采样的自然预测器。通过序列数据共享未知分布，低误差的中心可作为后续数据的灵敏度采样预测，且实验显示在聚类代价与运行时间上优于均匀采样与现有方法。","arXiv :2607 .04949v 1 [ cs .LG] 6 Jul 2026  \nSensitivity Sampling with Predictions fork-Means Clustering  \nCristian Boldrin and Fabio Vandin (􀀀)  \nUniversity of Padova, Padova, Italy [boldrincri@dei.unipd.it](boldrincri@dei.unipd.it), [fabio.vandin@unipd.it](fabio.vandin@unipd.it)  \nAbstract. We study the problem of k-means clustering on large datasets.  \nThe state-of-the-art for the problem is given by coresets-based approaches, which build small weighted summaries of the input and derive approximate solutions with rigorous quality guarantees from them. One of the most popular and advanced approaches to derive coresets for k-means is sensitivity sampling. However, sensitivity sampling requires to compute the importance of each input point with respect to the whole dataset over all possible choices of centers. Since the exact computation of such quantities is unfeasible, current approaches work by approximating the sensitivity values. Nevertheless, the runtime of such approaches is still impractical for large datasets.  \nIn this work, we propose to reduce the runtime of sensitivity-based approaches for k-means by leveraging predictions to approximate the importance of input points. We first formally prove that current theoretical results on coresets construction via sensitivity sampling hold for coarser approximations of sensitivities compared to the one required by existing approaches. This implies that even fairly noisy predictors can be leveraged for sensitivity-sampling approaches. We then propose a natural predictor, which applies to the common scenario where clustering is performed (over time) on a sequence of datasets from the same problem.  \nWe prove that when the datasets in the sequence come from the same (unknown) distribution, centers resulting in a low error on one dataset can be used as predictions for sensitivity sampling in subsequent datasets, with guarantees on their quality. We perform an extensive experimental evaluation showing that our approach significantly improves, in terms of clustering cost vs runtime, over uniform sampling and state-of-the-art sensitivity sampling approaches when applied to sequences of datasets.  \nKeywords: k-means clustering · algorithms with predictions · sensitivity sampling · coresets  \n1 Introduction  \nClustering is a fundamental task for data mining and machine learning, with applications in several domains [25] . One of the most popular variants is kmeans clustering: given a set P of n points in d-dimensional Euclidean space, the goal is to find a set S of k points of the Euclidean space, called centers, which  \n2 C. Boldrin and F. Vandin  \npartitions P into clusters minimizing the k-means cost, defined as the sum of squared distances between points in P and their nearest center in S. Finding the optimal set of centers is known to be NP-hard even for k = 2 [16], and even finding an approximation to the optimal objective value within a factor of 1.07 is known to be NP-hard [12] .  \nThe most popular heuristic for solving the k-means problem in Euclidean spaces is Lloyd’s algorithm [31], which uses iterative improvements to find a locally optimal k-means clustering. Each iteration of Lloyd’s algorithm requires O (nkd) time, and in the worst case the number of iterations required to converge is 2Ω (√n) [2], leading to superpolynomial worst-case time complexity. Moreover, the quality of the final solution depends heavily on the centers’ initialization.  \nAs modern datasets continue to grow, a natural approach to scale the computation is to derive compressed representations of the input (e.g., by sampling) . For clustering, a common approach is to use coresets, where the input data Pis replaced by a small set of weighted points, which provably approximates the k-means cost function with respect to any set of centers. Running optimization algorithms (e.g., Lloyd’s algorithm) on coresets then produces results close to the solution obtained from running the same algorithms on the ori","cbCaiosotJ62XD8C","https://ap.wps.com/l/cbCaiosotJ62XD8C","pdf",3268337,3,1,52,"English","en",105,"# Introduction\n## Problem setting and NP-hardness\n## Coresets and sensitivity sampling\n## Bi-criteria approximations and coreset construction","[{\"question\":\"为什么灵敏度采样在大规模k-means中计算开销很高？\",\"answer\":\"灵敏度采样需要为每个输入点计算其相对整个数据集、在所有可能中心集合上的重要性（精确灵敏度）。由于要在无穷多个中心选择上评估聚类成本，这种精确计算不可行，从而导致现有方法仍然难以在大规模场景下达到可接受运行时间。\"},{\"question\":\"该论文如何降低灵敏度采样方法的运行时间？\",\"answer\":\"论文提出利用预测来近似各点的重要性，从而不必逐点计算精确灵敏度。研究首先证明：即使灵敏度近似更粗于现有方法所需的精度，coresets构造的理论质量保证仍然成立，从而允许更可计算、也更快的近似过程。\"},{\"question\":\"当数据按时间序列变化时，如何利用前一次结果预测后续数据的采样重要性？\",\"answer\":\"论文在“序列数据来自同一未知分布”的条件下证明：在某一时刻获得低误差的中心，可用作后续数据进行灵敏度采样的预测来源，并带来质量保证。\"}]",1784191121,131,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"sensitivity-sampling-with-predictions-for-k-means-clustering","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"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":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/sensitivity-sampling-with-predictions-for-k-means-clustering/83872/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"为什么灵敏度采样在大规模k-means中计算开销很高？","Question",{"text":75,"@type":76},"灵敏度采样需要为每个输入点计算其相对整个数据集、在所有可能中心集合上的重要性（精确灵敏度）。由于要在无穷多个中心选择上评估聚类成本，这种精确计算不可行，从而导致现有方法仍然难以在大规模场景下达到可接受运行时间。","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"该论文如何降低灵敏度采样方法的运行时间？",{"text":80,"@type":76},"论文提出利用预测来近似各点的重要性，从而不必逐点计算精确灵敏度。研究首先证明：即使灵敏度近似更粗于现有方法所需的精度，coresets构造的理论质量保证仍然成立，从而允许更可计算、也更快的近似过程。",{"name":82,"@type":73,"acceptedAnswer":83},"当数据按时间序列变化时，如何利用前一次结果预测后续数据的采样重要性？",{"text":84,"@type":76},"论文在“序列数据来自同一未知分布”的条件下证明：在某一时刻获得低误差的中心，可用作后续数据进行灵敏度采样的预测来源，并带来质量保证。","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":21,"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":52,"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"]