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Improvement of the Fast Clustering Algorithm Improved by K-Means in the Big Data

Abstract

Clustering as a fundamental unsupervised learning is considered an important method of data analysis, and K-means is demonstrably the most popular clustering algorithm. In this paper, we consider clustering on feature space to solve the low efficiency caused in the Big Data clustering by K-means. Different from the traditional methods, the algorithm guaranteed the consistency of the clustering accuracy before and after descending dimension, accelerated K-means when the clustering centeres and distance functions satisfy certain conditions, completely matched in the preprocessing step and clustering step, and improved the efficiency and accuracy. Experimental results have demonstrated the effectiveness of the proposed algorithm.

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A Mathematical Model to describe the herd behaviour considering group defense

Abstract

A model for predator-prey interactions with herd behaviour is proposed. Novelty includes a smooth transition from individual behaviour (low number of prey) to herd behaviour (large number of prey). The model is analysed using standard stability and bifurcations techniques. We prove that the system undergoes a Hopf bifurcation as we vary the parameter that represents the efficiency of predators (dependent on the predation rate, for instance), giving rise to sustained oscillations in the system. The proposed model appears to possess more realistic features than the previous approaches while being also relatively easier to analyse and understand.

Open access
Chapter 1. Stability of Hybrid Systems on Time Scale
Chapter 2 Stability of Hybrid Systems with Aftereffect
Chapter 3. Stability of Hybrid Systems in a Metric Space
Chapter 4. Hybrid Systems with Impacts
Chapter 5. Material Point Over Moving Limiters
Chapter 6. Difference Equations and Inequalities
Contents
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Frontmatter
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