IDEAS home Printed from https://ideas.repec.org/a/spr/jclass/v37y2020i1d10.1007_s00357-019-9304-3.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00357-019-9304-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00357-019-9304-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Burim Ramosaj & Markus Pauly, 2019. "Predicting missing values: a comparative study on non-parametric approaches for imputation," Computational Statistics, Springer, vol. 34(4), pages 1741-1764, December.
    2. Sandip Sinharay, 2022. "Reporting Proficiency Levels for Examinees With Incomplete Data," Journal of Educational and Behavioral Statistics, , vol. 47(3), pages 263-296, June.
    3. Noémi Kreif & Richard Grieve & Iván Díaz & David Harrison, 2015. "Evaluation of the Effect of a Continuous Treatment: A Machine Learning Approach with an Application to Treatment for Traumatic Brain Injury," Health Economics, John Wiley & Sons, Ltd., vol. 24(9), pages 1213-1228, September.
    4. Abhilash Bandam & Eedris Busari & Chloi Syranidou & Jochen Linssen & Detlef Stolten, 2022. "Classification of Building Types in Germany: A Data-Driven Modeling Approach," Data, MDPI, vol. 7(4), pages 1-23, April.
    5. Boonstra Philip S. & Little Roderick J.A. & West Brady T. & Andridge Rebecca R. & Alvarado-Leiton Fernanda, 2021. "A Simulation Study of Diagnostics for Selection Bias," Journal of Official Statistics, Sciendo, vol. 37(3), pages 751-769, September.
    6. Ivan Miguel Pires & Faisal Hussain & Nuno M. Garcia & Eftim Zdravevski, 2020. "Improving Human Activity Monitoring by Imputation of Missing Sensory Data: Experimental Study," Future Internet, MDPI, vol. 12(9), pages 1-18, September.
    7. Christopher J Greenwood & George J Youssef & Primrose Letcher & Jacqui A Macdonald & Lauryn J Hagg & Ann Sanson & Jenn Mcintosh & Delyse M Hutchinson & John W Toumbourou & Matthew Fuller-Tyszkiewicz &, 2020. "A comparison of penalised regression methods for informing the selection of predictive markers," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-14, November.
    8. Liangyuan Hu & Lihua Li, 2022. "Using Tree-Based Machine Learning for Health Studies: Literature Review and Case Series," IJERPH, MDPI, vol. 19(23), pages 1-13, December.
    9. Norah Alyabs & Sy Han Chiou, 2022. "The Missing Indicator Approach for Accelerated Failure Time Model with Covariates Subject to Limits of Detection," Stats, MDPI, vol. 5(2), pages 1-13, May.
    10. Feldkircher, Martin, 2014. "The determinants of vulnerability to the global financial crisis 2008 to 2009: Credit growth and other sources of risk," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 19-49.
    11. Ida Kubiszewski & Kenneth Mulder & Diane Jarvis & Robert Costanza, 2022. "Toward better measurement of sustainable development and wellbeing: A small number of SDG indicators reliably predict life satisfaction," Sustainable Development, John Wiley & Sons, Ltd., vol. 30(1), pages 139-148, February.
    12. Georges Steffgen & Philipp E. Sischka & Martha Fernandez de Henestrosa, 2020. "The Quality of Work Index and the Quality of Employment Index: A Multidimensional Approach of Job Quality and Its Links to Well-Being at Work," IJERPH, MDPI, vol. 17(21), pages 1-31, October.
    13. Christopher Kath & Florian Ziel, 2018. "The value of forecasts: Quantifying the economic gains of accurate quarter-hourly electricity price forecasts," Papers 1811.08604, arXiv.org.
    14. Esef Hakan Toytok & Sungur Gürel, 2019. "Does Project Children’s University Increase Academic Self-Efficacy in 6th Graders? A Weak Experimental Design," Sustainability, MDPI, vol. 11(3), pages 1-12, February.
    15. J M van Niekerk & M C Vos & A Stein & L M A Braakman-Jansen & A F Voor in ‘t holt & J E W C van Gemert-Pijnen, 2020. "Risk factors for surgical site infections using a data-driven approach," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-14, October.
    16. Joost R. Ginkel, 2020. "Standardized Regression Coefficients and Newly Proposed Estimators for $${R}^{{2}}$$R2 in Multiply Imputed Data," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 185-205, March.
    17. Lara Jehi & Xinge Ji & Alex Milinovich & Serpil Erzurum & Amy Merlino & Steve Gordon & James B Young & Michael W Kattan, 2020. "Development and validation of a model for individualized prediction of hospitalization risk in 4,536 patients with COVID-19," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-15, August.
    18. Matthew Carli & Mary H. Ward & Catherine Metayer & David C. Wheeler, 2022. "Imputation of Below Detection Limit Missing Data in Chemical Mixture Analysis with Bayesian Group Index Regression," IJERPH, MDPI, vol. 19(3), pages 1-17, January.
    19. Gerko Vink & Laurence E. Frank & Jeroen Pannekoek & Stef Buuren, 2014. "Predictive mean matching imputation of semicontinuous variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(1), pages 61-90, February.
    20. Tsai, Tsung-Han, 2016. "A Bayesian Approach to Dynamic Panel Models with Endogenous Rarely Changing Variables," Political Science Research and Methods, Cambridge University Press, vol. 4(3), pages 595-620, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jclass:v:37:y:2020:i:1:d:10.1007_s00357-019-9304-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.