题名

聚类空间的代数结构探讨

并列篇名

Studying on the Algebra Structure of Clustering Spaces

DOI

10.6338/JDA.200606_1(3).0007

作者

朱强生(Qiang-Sheng Zhu)；田英(Ying Tian)；何华灿(Hua-Can He)

关键词

聚类空间 ； 分割 ； 加细 ； 格空间 ； 聚类分析 ； clustering space ； partition ； refinement ； lattice space ； clustering analysis

期刊名称

Journal of Data Analysis

卷期/出版年月

1卷3期（2006 / 06 / 01）

页次

105 - 112

内容语文

簡體中文
中文摘要

引入聚类空间上的一种二元关系，证明了它和空间中的元素构成了一个偏序集合，并由此探讨了该空间代数结构。由于聚类空间中的任意两个元素构成的集合都有最小上界和最大的下界，这样得出该代数结构是一种格结构。在该空间中我们定义了一个距离函数，这样可以量度两个分割之间的距离。自然地我们引入了该格空间的两个二元元算并和交。
英文摘要

By defining one binary relation on the clustering space, we prove that set composed by all the partitions of the pending data is a partial set. For subsets formed by arbitrary two partitions, there exist supremum and infimum in the space. So the clustering space is a kind of lattices. Then we give a distance function to measure the difference of two partitions. At last, two binary functions are naturally introduced in the clustering lattice space.
主题分类 基礎與應用科學 > 資訊科學
基礎與應用科學 > 統計
社會科學 > 管理學
参考文献
  1. P. Berkhin: Survey of Clustering Data Mining Techniques, Accrue software, [http://www.accrue.com/products/rp_cluster_review.pdf](2002).
  2. Cai, D.,He, X.,Han, J.(2005).Document Clustering Using Locality Preserving Indexing.IEEE Trans. Knowl. Data Eng.,17(2),1624-1637.
  3. Ding, C.,He, X.,Simon, H. D.(2005).On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering.Proc. SIAM Int'l Conf. Data Mining (SDM'05)
  4. Han, J.,Kamber, M.(2001).Data Mining: Concepts and Techniques.San Diego, CA:Academic.
  5. Jain, A. K.,Topchy, A.,Law, M.,Buhmann, J.(2004).Landscape of Clustering Algorithms.Proc. Intl. Conf on Pattern Recognition, ICPR'04,Cambridge, UK:
  6. Jain, A.,Dubes, R.(1981).Algorithms for Clustering Data.Prentice-Hall.
  7. Kleinberg, J.(2002).An Impossibility Theorem for Clustering.Advances in Neural Information Processing Systems (NIPS),15
  8. Lee, D. D.,Seung, H. S.(2001).Algorithm for Non-negative Matrix Factorization.Adv. in Neural Inform. Proc. Systems,13
  9. Lee, D. D.,Seung, H. S.(1999).Learning the Parts of Objects with Nonnegative Matrix Factorization.Nature,401,788.
  10. Puzicha, J.,Hofmann, T.,Buhmann, J. M.(2000).A theory of proximity based clustering: structure detection by optimization.Pattern Recognition,33(4),617-634.
  11. Theodoridis, S.,Koutroumbas, K.(2003).Pattern Recognition.London:Academic Press Inc. Ltd..
  12. Topchy, A.,Jain, A. K.,Punch, W.(2005).Clustering Ensembles: Models of Consensus and Weak Partitions.IEEE Transactions on Pattern Analysis and Machine Intelligence
print cancel