The seeding algorithm for spherical k-means clustering with penalties

Ji, Sai; Xu, Donghao; Guo, Longkun; Li, Min; Zhang, Dongmei

doi:10.1007/s10878-020-00569-1

Cited by 12 publications

(5 citation statements)

References 18 publications

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“…Ji et al. (2020) propose a new approximation cluster initialization (ACI) method for spherical KM using a 2 max{2,m}(1 + m ) ( ln K+2) approximation algorithm.…”

Section: Related Work Of Initialization Methodsmentioning

confidence: 99%

“…The EI method has lower computation costs, but requires a large amount of memory and time on a large scale data due to multiple timedistance computations. Ji et al (2020) propose a new approximation cluster initialization (ACI) method for spherical KM using a 2 max{2,m}(1 þ m) (ln Kþ2) approximation algorithm. The proposed algorithm employs a high probability approach with a 2 max{3,Mþ1} approximation ratio.…”

Section: Reviews Of the Existing Km Initialization Algorithmsmentioning

confidence: 99%

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NDPD: an improved initial centroid method of partitional clustering for big data mining

Pandey

Shukla

2022

JAMR

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PurposeThe K-means (KM) clustering algorithm is extremely responsive to the selection of initial centroids since the initial centroid of clusters determines computational effectiveness, efficiency and local optima issues. Numerous initialization strategies are to overcome these problems through the random and deterministic selection of initial centroids. The random initialization strategy suffers from local optimization issues with the worst clustering performance, while the deterministic initialization strategy achieves high computational cost. Big data clustering aims to reduce computation costs and improve cluster efficiency. The objective of this study is to achieve a better initial centroid for big data clustering on business management data without using random and deterministic initialization that avoids local optima and improves clustering efficiency with effectiveness in terms of cluster quality, computation cost, data comparisons and iterations on a single machine.Design/methodology/approachThis study presents the Normal Distribution Probability Density (NDPD) algorithm for big data clustering on a single machine to solve business management-related clustering issues. The NDPDKM algorithm resolves the KM clustering problem by probability density of each data point. The NDPDKM algorithm first identifies the most probable density data points by using the mean and standard deviation of the datasets through normal probability density. Thereafter, the NDPDKM determines K initial centroid by using sorting and linear systematic sampling heuristics.FindingsThe performance of the proposed algorithm is compared with KM, KM++, Var-Part, Murat-KM, Mean-KM and Sort-KM algorithms through Davies Bouldin score, Silhouette coefficient, SD Validity, S_Dbw Validity, Number of Iterations and CPU time validation indices on eight real business datasets. The experimental evaluation demonstrates that the NDPDKM algorithm reduces iterations, local optima, computing costs, and improves cluster performance, effectiveness, efficiency with stable convergence as compared to other algorithms. The NDPDKM algorithm minimizes the average computing time up to 34.83%, 90.28%, 71.83%, 92.67%, 69.53% and 76.03%, and reduces the average iterations up to 40.32%, 44.06%, 32.02%, 62.78%, 19.07% and 36.74% with reference to KM, KM++, Var-Part, Murat-KM, Mean-KM and Sort-KM algorithms.Originality/valueThe KM algorithm is the most widely used partitional clustering approach in data mining techniques that extract hidden knowledge, patterns and trends for decision-making strategies in business data. Business analytics is one of the applications of big data clustering where KM clustering is useful for the various subcategories of business analytics such as customer segmentation analysis, employee salary and performance analysis, document searching, delivery optimization, discount and offer analysis, chaplain management, manufacturing analysis, productivity analysis, specialized employee and investor searching and other decision-making strategies in business.

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“…Ji et al. (2020) propose a new approximation cluster initialization (ACI) method for spherical KM using a 2 max{2,m}(1 + m ) ( ln K+2) approximation algorithm.…”

Section: Related Work Of Initialization Methodsmentioning

confidence: 99%

Section: Reviews Of the Existing Km Initialization Algorithmsmentioning

confidence: 99%

NDPD: an improved initial centroid method of partitional clustering for big data mining

Pandey

Shukla

2022

JAMR

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“…Such a variant of k-means suffers dependence on initialization, thus further improvements are proposed, e.g. [19], [20], [21] and [22].…”

Section: B Spherical K-meansmentioning

confidence: 99%

Hashtag Discernability - Competitiveness Study of Graph Spectral and Other Clustering Methods

Starosta,

Kłopotek,

Wierzchon

et al. 2023

Annals of Computer Science and Information Systems

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“…The k-means problem is the most representative problem in clustering. It has been widely studied in the fields of operations research, management, and computer science (Charikar et al, 2001;Friggstad et al, 2019;Ji et al, 2020;Kanungo et al, 2004;Makarychev et al, 2019;Vazirani, 2001;Williamson and Shmoys, 2011). A standard k-means problem is described as follows.…”

Section: Introductionmentioning

confidence: 99%

An improved primal-dual approximation algorithm for the k-means problem with penalties

Ren

et al. 2021

Math. Struct. Comp. Sci.

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In the k-means problem with penalties, we are given a data set ${\cal D} \subseteq \mathbb{R}^\ell $ of n points where each point $j \in {\cal D}$ is associated with a penalty cost p j and an integer k. The goal is to choose a set ${\rm{C}}S \subseteq {{\cal R}^\ell }$ with |CS| ≤ k and a penalized subset ${{\cal D}_p} \subseteq {\cal D}$ to minimize the sum of the total squared distance from the points in D / D p to CS and the total penalty cost of points in D p , namely $\sum\nolimits_{j \in {\cal D}\backslash {{\cal D}_p}} {d^2}(j,{\rm{C}}S) + \sum\nolimits_{j \in {{\cal D}_p}} {p_j}$ . We employ the primal-dual technique to give a pseudo-polynomial time algorithm with an approximation ratio of (6.357+ε) for the k-means problem with penalties, improving the previous best approximation ratio 19.849+∊ for this problem given by Feng et al. in Proceedings of FAW (2019).

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The seeding algorithm for spherical k-means clustering with penalties

Cited by 12 publications

References 18 publications

NDPD: an improved initial centroid method of partitional clustering for big data mining

NDPD: an improved initial centroid method of partitional clustering for big data mining

Hashtag Discernability - Competitiveness Study of Graph Spectral and Other Clustering Methods

An improved primal-dual approximation algorithm for the k-means problem with penalties

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