K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality

Selim, Shokri Z.; Ismail, Mohamed A.

doi:10.1109/tpami.1984.4767478

Cited by 980 publications

(380 citation statements)

References 10 publications

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“…objective (20). The H-means algorithm is sufficiently flexible and it may be adjusted to use such criteria as well (on applicability of H-means see [9,32] and references therein).…”

Section: Heuristics For Construction Of Given Number Of Hubsmentioning

confidence: 99%

Trading Hubs Construction for Electricity Markets

Borisovsky

Eremeev

Grinkevich³

et al. 2009

Optimization in the Energy Industry

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In this chapter, we consider a problem of constructing trading hubs in the structure of the electricity wholesale markets. The nodes of a trading hub are used to calculate a reference price that can be employed by the market participants for different types of hedging. The need for such a reference price is due to considerable variability of energy prices at different nodes of the electricity grid at different periods of time. The hubs construction is viewed as a mathematical programming problem here. We discuss its connections with clustering problems, consider the heuristic algorithms of solution and indicate some complexity issues. The performance of algorithms is illustrated on the real-life data.

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“…objective (20). The H-means algorithm is sufficiently flexible and it may be adjusted to use such criteria as well (on applicability of H-means see [9,32] and references therein).…”

Section: Heuristics For Construction Of Given Number Of Hubsmentioning

confidence: 99%

Trading Hubs Construction for Electricity Markets

Borisovsky

Eremeev

Grinkevich³

et al. 2009

Optimization in the Energy Industry

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“…The most popular class of clustering algorithms is K-means algorithm [3] which is a centre based, simple and fast algorithm but has the insufficiencies that it highly depends on the initial states and is easily trapped in local minima from the starting position of the search and global solutions of large problems cannot find with reasonable amount of computation effort [4]. In order to overcome local optima problem, the researchers from diverse fields are applying hierarchical clustering, partition-based clustering, density-based clustering, and artificial intelligence based clustering methods, such as: statistics [5], graph theory [6], expectation-maximization algorithms [7], artificial neural networks [8], evolutionary algorithms [9], swarm intelligence algorithms [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Artificial Bee Colony Algorithm is More Effective on Small Size Datasets as Compared to Large Size Datasets in Data Clustering

Danish¹,

Hassan²,

Badshah³

2018

IJCA

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Data clustering is a widespread data compression, vector quantization, data analysis and data mining technique. The principle objective of data clustering is to make clusters (or groups) such that data having high degree of similarity is gathered in the same cluster while data having high degree of dissimilarity is gathered in the different clusters and plays a key role for users to organize, summarize, and steer the data adequately. In this work Artificial Bee Colony (ABC) algorithm is applied to different size datasets. Results clearly show that ABC when applied on small size datasets were more effective than those of large size datasets in terms of intra-cluster distance, computation cycles and time required to complete those cycles.

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“…Agglomerative hierarchical clustering [1]- [10] imposes a hierarchical decomposition on a dataset through the iterative fusion of points and clusters and a final clustering is determined according to some pre-determined cut-off criterion. Partitional algorithms, including k-means [5], [7], [8], [11]- [16] and fuzzy c-means (FCM) [17]- [22], follow an iterative optimisation strategy for partitioning a database into a pre-determined number of clusters. The process is initialised by defining seed points or an initial partition and the successive swapping of data points determines a locally optimal partition.…”

Section: Introductionmentioning

confidence: 99%

Autonomous clustering using rough set theory

Bean

Kambhampati

2008

Int. J. Autom. Comput.

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-This paper proposes a clustering technique that minimises the need for subjective human intervention and is based on elements of rough set theory. The proposed algorithm is unified in its approach to clustering and makes use of both local and global data properties to obtain clustering solutions. It handles single-type and mixed attribute data sets with ease and results from three data sets of single and mixed attribute types are used to illustrate the technique and establish its efficiency.

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K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality

Cited by 980 publications

References 10 publications

Trading Hubs Construction for Electricity Markets

Trading Hubs Construction for Electricity Markets

Artificial Bee Colony Algorithm is More Effective on Small Size Datasets as Compared to Large Size Datasets in Data Clustering

Autonomous clustering using rough set theory

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