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Local k-proximal plane clustering

Abstract

k-Plane clustering (kPC) and k-proximal plane clustering (kPPC) cluster data points to the center plane, instead of clustering data points to cluster center in k-means. However, the cluster center plane constructed by kPC and kPPC is infinitely extending, which will affect the clustering performance. In this paper, we propose a local k-proximal plane clustering (LkPPC) by bringing k-means into kPPC which will force the data points to center around some prototypes and thus localize the representations of the cluster center plane. The contributions of our LkPPC are as follows: (1) LkPPC introduces localized representation of each cluster center plane to avoid the infinitely confusion. (2) Different from kPPC, our LkPPC constructs cluster center plane that makes the data points of the same cluster close to both the same center plane and the prototype, and meanwhile far away from the other clusters to some extent, which leads to solve eigenvalue problems. (3) Instead of randomly selecting the initial data points, a Laplace graph strategy is established to initialize the data points. (4) The experimental results on several artificial datasets and benchmark datasets show the effectiveness of our LkPPC.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Nos. 11201426, 11371365, and 10971223), the Zhejiang Provincial Natural Science Foundation of China (Nos. LQ12A01020, LQ13F030010, and LQ14G010004), the Ministry of Education, Humanities and Social Sciences Research Project of China (No. 13YJC910011), and the Scientific Research Fund of Zhejiang Provincial Education Department (No. Y201432746).

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Correspondence to Yan-Ru Guo.

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Yang, ZM., Guo, YR., Li, CN. et al. Local k-proximal plane clustering. Neural Comput & Applic 26, 199–211 (2015). https://doi.org/10.1007/s00521-014-1707-9

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Keywords

  • k-Plane clustering
  • k-Proximal plane clustering
  • k-Means
  • Eigenvalue problem
  • Laplace graph