Clustering by analytic functions

Malinen, Mikko; Fränti, Pasi

doi:10.1016/j.ins.2012.06.018

Cited by 12 publications

(6 citation statements)

References 19 publications

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“…Specifically, mean squared error (MSE) [67], as the fitness function of comparative clustering approaches, is introduced in the comparison experiments, which is determined by (12) in the following:…”

Section: Comparison With Other Exisitng Approachesmentioning

confidence: 99%

An Extended Membrane System with Monodirectional Tissue-like P Systems and Enhanced Particle Swarm Optimization for Data Clustering

Wang

Liu

et al. 2023

Applied Sciences

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In order to establish a highly efficient P system for resolving clustering problems and overcome the computation incompleteness and implementation difficulty of P systems, an attractive clustering membrane system, integrated with enhanced particle swarm optimization (PSO) based on environmental factors and crossover operators and a distributed parallel computing model of monodirectional tissue-like P systems (MTP), is constructed and proposed, which is simply named ECPSO-MTP. In the proposed ECPSO-MTP, two kinds of evolution rules for objects are defined and introduced to rewrite and modify the velocity of objects in different elementary membranes. The velocity updating model uses environmental factors based on partitioning information and randomly replaces global best to improve the clustering performance of ECPSO-MTP. The crossover operator for the position of objects is based on given objects and other objects with crossover probability and is accomplished through the hybridization of the global best of elementary membranes to reject randomness. The membrane structure of ECPSO-MTP is abstracted as a network structure, and the information exchange and resource sharing between different elementary membranes are accomplished by evolutional symport rules with promoters for objects of MTP, including forward and backward communication rules. The evolution and communication mechanisms in ECPSO-MTP are executed repeatedly through iteration. At last, comparison experiments, which are conducted on eight benchmark clustering datasets from artificial datasets and the UCI Machine Learning Repository and eight image segmentation datasets from BSDS500, demonstrate the effectiveness of the proposed ECPSO-MTP.

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Section: Comparison With Other Exisitng Approachesmentioning

confidence: 99%

An Extended Membrane System with Monodirectional Tissue-like P Systems and Enhanced Particle Swarm Optimization for Data Clustering

Wang

Liu

et al. 2023

Applied Sciences

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“…In K‐means methods, clusters are groups of data characterized by a small distance to the cluster center. An objective function, typically the sum of the distance to a set of putative cluster centers, is optimized until the best cluster center candidates are found. However, because a data point is always assigned to the nearest center, these approaches are not able to detect non‐spherical clusters …”

Section: Related Workmentioning

confidence: 99%

A grouping approach based on non‐uniform binary grid partitioning for crowd evacuation simulation

Liu

et al. 2018

Concurrency and Computation

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Summary Small social groups based on kinship or friendships are ubiquitous in human crowds. Therefore, the effect of social groups on crowd evacuations and that of crowd evacuations on social groups must be investigated. To simulate the group phenomenon when an emergency occurs, we propose an improved social force model that takes into account the social group relationship among the population, and based on our proposed model, a novel grouping algorithm predicated on non‐uniform binary grid partitioning is put forward. The approach initially maps the individuals into the plane space, and then it adopts top‐down binary grid partitioning iteratively until the divided grid contains only the individuals with relations; then, the values of the relation and density of the non‐empty grid cells are calculated, and the grids are sorted according to these values. After sorting, selecting, merging, and forming the core grids, the other grids are merged to the core grids. We have compared the algorithm with the hierarchical classification algorithm and the grid‐based algorithm. The results show that the accuracy, speed, and scalability are all advantages. We also establish a simulation platform to illustrate the proposed grouping algorithm and the improved social force model for crowd evacuation simulation.

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“…(see, e.g., Boyd and Vandenberghe, 2004;Malinen and Fränti, 2012), instead of solving the problem (5), we can solve the following optimization problem (Kogan, 2007;Teboulle, 2007):…”

Section: K Sabomentioning

confidence: 99%

“…Let us mention one possibility for the choice of the smoothing parameter > 0 (see also Malinen and Fränti, 2012). If we want a relative deviation…”

Section: -Clustering Algorithmmentioning

confidence: 99%

Center-based l1–clustering method

Sabo

2014

International Journal of Applied Mathematics and Computer Science

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In this paper, we consider the l1-clustering problem for a finite data-point set which should be partitioned into k disjoint nonempty subsets. In that case, the objective function does not have to be either convex or differentiable, and generally it may have many local or global minima. Therefore, it becomes a complex global optimization problem. A method of searching for a locally optimal solution is proposed in the paper, the convergence of the corresponding iterative process is proved and the corresponding algorithm is given. The method is illustrated by and compared with some other clustering methods, especially with the l2-clustering method, which is also known in the literature as a smooth k-means method, on a few typical situations, such as the presence of outliers among the data and the clustering of incomplete data. Numerical experiments show in this case that the proposed l1-clustering algorithm is faster and gives significantly better results than the l2-clustering algorithm.

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Clustering by analytic functions

Cited by 12 publications

References 19 publications

An Extended Membrane System with Monodirectional Tissue-like P Systems and Enhanced Particle Swarm Optimization for Data Clustering

An Extended Membrane System with Monodirectional Tissue-like P Systems and Enhanced Particle Swarm Optimization for Data Clustering

A grouping approach based on non‐uniform binary grid partitioning for crowd evacuation simulation

Center-based l1–clustering method

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