Accelerating the k-Means++ Algorithm by Using Geometric Information

Clustering is a fundamental task in data analysis with applications across a wide range of fields, such as computer vision, pattern recognition, and data mining. Real-world use cases include social network analysis, medical imaging, market segmentation, and anomaly detection, to name a few. In this...

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Published in:IEEE access Vol. 13; pp. 67693 - 67717
Main Authors: Rodriguez Corominas, Guillem, Blesa, Maria J., Blum, Christian
Format: Journal Article
Language:English
Published: IEEE 2025
Subjects:
Approximation algorithms
Clustering
Clustering algorithms
Computational efficiency
D² sampling
Filters
k-means
Machine learning algorithms
Measurement
norm
Prediction algorithms
Scalability
triangle inequality
Vectors
ISSN:2169-3536, 2169-3536
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Abstract Clustering is a fundamental task in data analysis with applications across a wide range of fields, such as computer vision, pattern recognition, and data mining. Real-world use cases include social network analysis, medical imaging, market segmentation, and anomaly detection, to name a few. In this paper, we propose an acceleration of the exact k-means++ algorithm using geometric information, specifically the Triangle Inequality and additional norm filters, along with a two-step sampling procedure. Our experiments demonstrate that the accelerated version outperforms the standard k-means++ version in terms of the number of visited points and distance calculations, achieving greater speedup as the number of clusters increases. The version utilizing the Triangle Inequality is particularly effective for low-dimensional data, while the additional norm-based filter enhances performance in high-dimensional instances with greater norm variance among points. Additional experiments show the behavior of our algorithms when executed concurrently across multiple jobs and examine how memory performance impacts practical speedup.
AbstractList Clustering is a fundamental task in data analysis with applications across a wide range of fields, such as computer vision, pattern recognition, and data mining. Real-world use cases include social network analysis, medical imaging, market segmentation, and anomaly detection, to name a few. In this paper, we propose an acceleration of the exact k-means++ algorithm using geometric information, specifically the Triangle Inequality and additional norm filters, along with a two-step sampling procedure. Our experiments demonstrate that the accelerated version outperforms the standard k-means++ version in terms of the number of visited points and distance calculations, achieving greater speedup as the number of clusters increases. The version utilizing the Triangle Inequality is particularly effective for low-dimensional data, while the additional norm-based filter enhances performance in high-dimensional instances with greater norm variance among points. Additional experiments show the behavior of our algorithms when executed concurrently across multiple jobs and examine how memory performance impacts practical speedup.
Author Blesa, Maria J.
Rodriguez Corominas, Guillem
Blum, Christian
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10.3390/app11156963
10.3844/jcssp.2014.1197.1206
10.1609/aaai.v30i1.10259
10.1186/1471-2105-7-173
10.1007/s10115-007-0114-2
10.3390/a14010006
10.1007/978-3-642-32512-0_50
10.24963/ijcai.2021/403
10.1049/el:19901037
10.1007/978-3-031-30678-5_11
10.1109/5.726791
10.1016/j.snb.2012.01.074
10.3390/s23052368
10.1109/MDM.2013.24
10.1007/s10994-009-5103-0
10.1137/1.9781611974348.37
10.3390/app11031043
10.2307/3001968
10.1016/j.ins.2022.11.139
10.1016/j.eswa.2015.03.013
10.1016/j.petrol.2021.109681
10.1016/j.patcog.2019.04.014
10.14778/2180912.2180915
10.1038/ncomms5308
10.1137/1.9781611972801.12
10.1137/1.9781611974973.32
10.1109/TPDS.2014.2306193
10.1109/76.825859
10.1609/icwsm.v2i1.18651
10.1145/1046456.1046470
10.1007/978-3-319-09259-1_2
10.1155/2021/9982484
10.1016/j.snb.2015.03.028
10.1002/9781118032794
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References ref13
ref15
ref14
ref58
ref53
ref52
ref11
ref55
ref10
ref54
Dau (ref56) 2018
ref17
Kaul (ref42) 2013
Logacjov (ref46) 2023
ref16
ref19
ref18
Heck (ref37) 1998
Elkan (ref36)
Lattanzi (ref25)
Krizhevsky (ref57) 2009
Bachem (ref23); 29
ref47
ref44
ref43
(ref50) 2024
Bhatt (ref41) 2009
ref49
ref8
ref7
ref9
Vergara (ref51) 2012
ref4
ref3
ref6
Bachem (ref12); 37
Liang (ref26) 2022
ref35
ref34
ref31
Whiteson (ref62) 2014
ref30
Xia (ref33) 2022; 44
ref2
ref1
Bock (ref38) 2004
Anagnostopoulos (ref40) 2018
Newling (ref32); 48
Arthur (ref5)
ref20
ref63
ref22
ref21
Fonollosa (ref48) 2015
ref28
ref27
ref29
Hebrail (ref45) 2006
Cohen-Addad (ref24); 33
ref61
Ortega-Binderberger (ref39) 1998
Bertin-Mahieux (ref60) 2011
Bertin-Mahieux (ref59)
References_xml – ident: ref2
  doi: 10.1109/TIT.1982.1056489
– ident: ref21
  doi: 10.1145/2133803.2184450
– ident: ref53
  doi: 10.1016/j.chemolab.2013.10.012
– volume-title: R6A—Yahoo! Front Page Today Module User Click Log Dataset, Version 1.0
  year: 2024
  ident: ref50
– ident: ref20
  doi: 10.1145/1327452.1327492
– volume-title: Year Prediction MSD Dataset
  year: 2011
  ident: ref60
– ident: ref27
  doi: 10.3390/app11156963
– ident: ref7
  doi: 10.3844/jcssp.2014.1197.1206
– start-page: 1027
  volume-title: Proc. 18th Annu. ACM-SIAM Symp. Discrete Algorithms (SODA)
  ident: ref5
  article-title: K-means++: The advantages of careful seeding
– ident: ref22
  doi: 10.1609/aaai.v30i1.10259
– ident: ref44
  doi: 10.1186/1471-2105-7-173
– ident: ref3
  doi: 10.1007/s10115-007-0114-2
– volume: 37
  start-page: 209
  volume-title: Proc. 32nd Int. Conf. Mach. Learn. (ICML)
  ident: ref12
  article-title: Coresets for nonparametric estimation—The case of DP-means
– ident: ref18
  doi: 10.3390/a14010006
– ident: ref13
  doi: 10.1007/978-3-642-32512-0_50
– volume-title: Gas Sensor Array Drift Dataset
  year: 2012
  ident: ref51
– start-page: 1
  year: 1998
  ident: ref37
  article-title: CORSIKA: A Monte Carlo code to simulate extensive air showers
  publication-title: Forschungszentrum Karlsruhe
– volume-title: Road Network Dataset
  year: 2013
  ident: ref42
– ident: ref15
  doi: 10.24963/ijcai.2021/403
– ident: ref30
  doi: 10.1049/el:19901037
– ident: ref16
  doi: 10.1007/978-3-031-30678-5_11
– volume-title: The UCR Time Series Classification Archive
  year: 2018
  ident: ref56
– ident: ref58
  doi: 10.1109/5.726791
– ident: ref52
  doi: 10.1016/j.snb.2012.01.074
– volume-title: Query Analytics Workloads Dataset
  year: 2018
  ident: ref40
– ident: ref47
  doi: 10.3390/s23052368
– ident: ref43
  doi: 10.1109/MDM.2013.24
– ident: ref1
  doi: 10.1007/s10994-009-5103-0
– ident: ref14
  doi: 10.1137/1.9781611974348.37
– ident: ref35
  doi: 10.3390/app11031043
– ident: ref63
  doi: 10.2307/3001968
– ident: ref4
  doi: 10.1016/j.ins.2022.11.139
– ident: ref8
  doi: 10.1016/j.eswa.2015.03.013
– ident: ref11
  doi: 10.1016/j.petrol.2021.109681
– ident: ref6
  doi: 10.1016/j.patcog.2019.04.014
– volume-title: Skin Segmentation Dataset
  year: 2009
  ident: ref41
– volume-title: Individual Household Electric Power Consumption Dataset
  year: 2006
  ident: ref45
– start-page: 591
  volume-title: Proc. 12th Int. Conf. Music Inf. Retr. (ISMIR)
  ident: ref59
  article-title: The million song dataset
– ident: ref17
  doi: 10.14778/2180912.2180915
– ident: ref61
  doi: 10.1038/ncomms5308
– volume: 29
  start-page: 55
  volume-title: Proc. Adv. Neural Inf. Process. Syst.
  ident: ref23
  article-title: Fast and provably good seedings for k-means
– ident: ref29
  doi: 10.1137/1.9781611972801.12
– volume-title: Corel Image Features Dataset
  year: 1998
  ident: ref39
– volume-title: Dataset
  year: 2023
  ident: ref46
– volume-title: MAGIC Gamma Telescope Dataset
  year: 2004
  ident: ref38
– volume: 33
  start-page: 16235
  volume-title: Proc. Adv. Neural Inf. Process. Syst.
  ident: ref24
  article-title: Fast and accurate k-means++ via rejection sampling
– ident: ref55
  doi: 10.1137/1.9781611974973.32
– start-page: 3662
  volume-title: Proc. 36th Int. Conf. Mach. Learn. (ICML)
  ident: ref25
  article-title: A better k-means++ algorithm via local search
– ident: ref19
  doi: 10.1109/TPDS.2014.2306193
– volume: 48
  start-page: 936
  volume-title: Proc. 33rd Int. Conf. Mach. Learn.
  ident: ref32
  article-title: Fast k-means with accurate bounds
– ident: ref34
  doi: 10.1109/76.825859
– ident: ref10
  doi: 10.1609/icwsm.v2i1.18651
– volume-title: Learning Multiple Layers of Features From Tiny Images
  year: 2009
  ident: ref57
– ident: ref54
  doi: 10.1145/1046456.1046470
– volume: 44
  start-page: 87
  issue: 1
  year: 2022
  ident: ref33
  article-title: Ball k-means: Fast adaptive clustering with no bounds
  publication-title: IEEE Trans. Pattern Anal. Mach. Intell.
– start-page: 147
  volume-title: Proc. 20th Int. Conf. Int. Conf. Mach. Learn. (ICML)
  ident: ref36
  article-title: Using the triangle inequality to accelerate k-means
– ident: ref31
  doi: 10.1007/978-3-319-09259-1_2
– volume-title: Gas Sensor Array Under Dynamic Gas Mixtures Dataset
  year: 2015
  ident: ref48
– ident: ref9
  doi: 10.1155/2021/9982484
– year: 2022
  ident: ref26
  article-title: A faster k-means++ algorithm
  publication-title: arXiv:2211.15118
– ident: ref49
  doi: 10.1016/j.snb.2015.03.028
– volume-title: Dataset
  year: 2014
  ident: ref62
– ident: ref28
  doi: 10.1002/9781118032794
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StartPage 67693
SubjectTerms Approximation algorithms
Clustering
Clustering algorithms
Computational efficiency
D² sampling
Filters
k-means
Machine learning algorithms
Measurement
norm
Prediction algorithms
Scalability
triangle inequality
Vectors
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Title Accelerating the k-Means++ Algorithm by Using Geometric Information
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