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

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Other Title
  • BOOTSTRAPPING K-MEANS CLUSTERING

Abstract

Independent observations X1, X2, …, Xn are made on a distribution F on Rd. To devide these observations into k clusters, first choose a vector of optimal cluster centers bn=(bn1, bn2, …, bnk) to minimize Wn(a)=1/nΣni=1min1jk||Xi-aj||2 as a function of a=(a1, a2, …, ak), then assign each observation to its nearest cluster center. Each bnj 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 bn 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

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Details

  • CRID
    1390001204414227328
  • NII Article ID
    110001235576
  • DOI
    10.5183/jjscs1988.3.1
  • ISSN
    1881-1337
    0915-2350
  • MRID
    1108298
  • Text Lang
    en
  • Data Source
    • JaLC
    • CiNii Articles
    • Crossref

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