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Pointed Subspace Approach to Incomplete Data

Author

Listed:
  • Lukasz Struski

    (Jagiellonian University)

  • Marek Śmieja

    (Jagiellonian University)

  • Jacek Tabor

    (Jagiellonian University)

Abstract

Incomplete data are often represented as vectors with filled missing attributes joined with flag vectors indicating missing components. In this paper, we generalize this approach and represent incomplete data as pointed affine subspaces. This allows to perform various affine transformations of data, such as whitening or dimensionality reduction. Moreover, this representation preserves the information, which coordinates were missing. To use our representation in practical classification tasks, we embed such generalized missing data into a vector space and define the scalar product of embedding space. Our representation is easy to implement, and can be used together with typical kernel methods. Performed experiments show that the application of SVM classifier on the proposed subspace approach obtains highly accurate results.

Suggested Citation

  • Lukasz Struski & Marek Śmieja & Jacek Tabor, 2020. "Pointed Subspace Approach to Incomplete Data," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 42-57, April.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:1:d:10.1007_s00357-019-9304-3
    DOI: 10.1007/s00357-019-9304-3
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    References listed on IDEAS

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    1. Antonio D’Ambrosio & Massimo Aria & Roberta Siciliano, 2012. "Accurate Tree-based Missing Data Imputation and Data Fusion within the Statistical Learning Paradigm," Journal of Classification, Springer;The Classification Society, vol. 29(2), pages 227-258, July.
    2. van Buuren, Stef & Groothuis-Oudshoorn, Karin, 2011. "mice: Multivariate Imputation by Chained Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i03).
    3. Claudio Conversano & Roberta Siciliano, 2009. "Incremental Tree-Based Missing Data Imputation with Lexicographic Ordering," Journal of Classification, Springer;The Classification Society, vol. 26(3), pages 361-379, December.
    4. Isabella Sulis & Mariano Porcu, 2017. "Handling Missing Data in Item Response Theory. Assessing the Accuracy of a Multiple Imputation Procedure Based on Latent Class Analysis," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 327-359, July.
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