Improving the Efficiency and Efficacy of the K-means Clustering Algorithm Through a New Convergence Condition

Pérez, O Joaquín; Pazos, Rodolfo; Cruz, R Laura; Reyes, Sebastián; Basave, T. Rosy; Fraire, Héctor

doi:10.1007/978-3-540-74484-9_58

Cited by 19 publications

(4 citation statements)

References 5 publications

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“…The centroids are replaced by an arithmetic partition average (stated another way, the histograms of all the time series assigned to a centroid are averaged), and the partition is built again using the new centroids. This process is repeated until a convergence criterion is met or a number of iterations is reached [ 44 ]. In this work, a fixed number of 10 iterations was used to keep the computational cost low and constant.…”

Section: Methodsmentioning

confidence: 99%

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Cuesta–Frau

Picó

Vargas

et al. 2019

Entropy

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Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear I R n mapping into I R , where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures.

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Section: Methodsmentioning

confidence: 99%

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Cuesta–Frau

Picó

Vargas

et al. 2019

Entropy

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show abstract

“…It gets action when there are two consecutive iterations and the square error of the last iteration exceeds that of the preceding iteration. It finds a solution at least as good as that of the standard K-means with a number of iterations smaller than or equal to that of standard Kmeans algorithm [12].…”

Section: F Early Stop K-meansmentioning

confidence: 99%

Enhancing K-Means Algorithm for Image Segmentation

Kalam¹,

Manikandan²

2011

2011 International Conference on Process Automation, Control and Computing

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K-means is a compute-intensive iterative algorithm. Its use in a complex scenario is cumbersome, specifically in data-intensive applications. In order to accelerate the K-means running time for data-intensive application, such as large sized image segmentation, we use a distributed multi-agent system accelerated by GPUs. In this K-means version, the input image data are divided into subsets of image data which can be performed independently on GPUs. In each GPU, we offloaded the data assignment and the K-centroids recalculation steps of the K-means algorithm for a massively parallel processing. We have implemented this K-means version on the Nvidia GPU with Compute Unified Device Architecture. The distributed multi-agent system was written with Java Agent Development framework.

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“…Some works have focused on finding the best value for the initial number of clusters k and the best way of choosing the initial centroids as described in [8], [9], [10], [11], [12], [13], [14], [15]. Other research works are focused on defining the best stopping criterion in order to avoid excessive iterations considering that K-Means converges at a local minimum [16]. Thus, in the following paragraphs, we focus on related works that propose improvements to minimize the number of calculations in the classification step of K-Means.…”

Section: Related Workmentioning

confidence: 99%

Improvement to the K-Means algorithm through a heuristics based on a bee honeycomb structure

Pérez

Mexicano

Santaolaya

et al. 2012

2012 Fourth World Congress on Nature and Biologically Inspired Computing (NaBIC)

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The object clustering problem, according to their similarity measures, can be formulated as a combinatorial optimization problem. The K-Means algorithm has been widely used for solving such problem; however, its computational cost is very high. In this work a new heuristics is proposed for reducing the computational complexity in the classification step of the algorithm based on a honeycomb structure, which the algorithm builds when clusters are visualized in a two-dimensional space. In particular it has been observed that an object can only change membership to neighboring clusters. The heuristics consists of performing distance calculations only with respect to centroids of neighboring clusters, which reduces the number of calculations. For assessing the performance of this heuristics, a set of experiments was carried out that involved 2 500, 10 000 and 40 000 objects uniformly distributed in a two-dimensional space, as well as real-world instances of 3 100 and 245 057 objects with 2 and 3 dimensions. The results were encouraging, since the calculation time was reduced 65% on average, with respect to the standard K-Means algorithm for the synthetic instance, and up to 62% on average for the real-world instances, while the quality was reduced on average by 0.05% and 2.5%, respectively.

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Improving the Efficiency and Efficacy of the K-means Clustering Algorithm Through a New Convergence Condition

Cited by 19 publications

References 5 publications

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Enhancing K-Means Algorithm for Image Segmentation

Improvement to the K-Means algorithm through a heuristics based on a bee honeycomb structure

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