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Sparse distance metric learning

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  • Tze Choy
  • Nicolai Meinshausen

Abstract

Nearest neighbour classification requires a good distance metric. Previous approaches try to learn a quadratic distance metric learning so that observations of different classes are well separated. For high-dimensional problems, where many uninformative variables are present, it is attractive to select a sparse distance metric, both to increase predictive accuracy but also to aid interpretation of the result. We investigate the $$\ell 1$$ ℓ 1 -regularized metric learning problem, making a connection with the Lasso algorithm in the linear least squared settings. We show that the fitted transformation matrix is close to the desired transformation matrix in $$\ell 1$$ ℓ 1 -norm by assuming a version of the compatibility condition. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Tze Choy & Nicolai Meinshausen, 2014. "Sparse distance metric learning," Computational Statistics, Springer, vol. 29(3), pages 515-528, June.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:3:p:515-528
    DOI: 10.1007/s00180-013-0437-2
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    References listed on IDEAS

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    1. Simon Hix & Abdul Noury & Gérard Roland, 2006. "Dimensions of Politics in the European Parliament," American Journal of Political Science, John Wiley & Sons, vol. 50(2), pages 494-520, April.
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    Cited by:

    1. Nickolay Trendafilov & Martin Kleinsteuber & Hui Zou, 2014. "Sparse matrices in data analysis," Computational Statistics, Springer, vol. 29(3), pages 403-405, June.

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