BOOTSTRAPPING <i>K</i>-MEANS CLUSTERING

• Jhun Myoungshic

  Dept. of Statistics, Korea University

Bibliographic Information

Other Title

• BOOTSTRAPPING K-MEANS CLUSTERING

Abstract

Independent observations X₁, X₂, …, X_n are made on a distribution F on R^d. To devide these observations into k clusters, first choose a vector of optimal cluster centers b_n=(b_n1, b_n2, …, b_nk) to minimize W_n(a)=1/nΣni=1min₁≤j≤k||X_i-a_j||² as a function of a=(a₁, a₂, …, a_k), then assign each observation to its nearest cluster center. Each b_nj is the mean of observations in its cluster. Pollard (1982) obtained a central limit theorem for the means of the k-clusters. In this paper, it is shown that the bootstrap distribution of the centered b_n has the same limiting distribution; the argument rests on asymptotic behavior of empirical processes on Vapnik-Chervonenkis classes in triangular array setting. Advantages of the bootstrap methods are discussed and the performance of bootstrap confidence sets is compared with Pollard's confidence sets by Monte Carlo simulation. ²

Journal

• Journal of the Japanese Society of Computational Statistics

  Journal of the Japanese Society of Computational Statistics 3 (1), 1-14, 1990

  Japanese Society of Computational Statistics

Keywords

• <i>k</i>-means clustering
• bootstrap
• Vapnik-Chervonenkis class

Details

• CRID: 1390001204414227328
• NII Article ID: 110001235576
• NII Book ID: AA10823693
• DOI: 10.5183/jjscs1988.3.1
• ISSN: 18811337
• ISSN: 09152350
• MRID: 1108298
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed