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Sparse principal components by semi-partition clustering

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  • Doyo Enki
  • Nickolay Trendafilov

Abstract

A cluster-based method for constructing sparse principal components is proposed. The method initially forms clusters of variables, using a new clustering approach called the semi-partition, in two steps. First, the variables are ordered sequentially according to a criterion involving the correlations between variables. Then, the ordered variables are split into two parts based on their generalized variance. The first group of variables becomes an output cluster, while the second one—input for another run of the sequential process. After the optimal clusters have been formed, sparse components are constructed from the singular value decomposition of the data matrices of each cluster. The method is applied to simple data sets with smaller number of variables (p) than observations (n), as well as large gene expression data sets with p ≫ n. The resulting cluster-based sparse principal components are very promising as evaluated by objective criteria. The method is also compared with other existing approaches and is found to perform well. Copyright Springer-Verlag 2012

Suggested Citation

  • Doyo Enki & Nickolay Trendafilov, 2012. "Sparse principal components by semi-partition clustering," Computational Statistics, Springer, vol. 27(4), pages 605-626, December.
    • Handle: RePEc:spr:compst:v:27:y:2012:i:4:p:605-626
    DOI: 10.1007/s00180-011-0280-2
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    References listed on IDEAS

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    3. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
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    1. Kohei Adachi & Nickolay T. Trendafilov, 2016. "Sparse principal component analysis subject to prespecified cardinality of loadings," Computational Statistics, Springer, vol. 31(4), pages 1403-1427, December.
    2. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.

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