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Abstract
Distance metric learning has been successfully incorporated in many machine learning applications. The main challenge arises from the positive semidefiniteness constraint on the Mahalanobis matrix, which results in a high computational cost. In this paper, we develop a novel approach to reduce this computational burden. We first map each training example into a new space by an orthonormal transformation. Then, in the transformed space, we simply learn a diagonal matrix. This two-phase approach is thus much easier and less costly than learning a full Mahalanobis matrix in one phase as is commonly done.

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MLA
Nguyen Cong, Bac, et al. “Distance Metric Learning : A Two-Phase Approach.” Proceedings of the 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2017), ESANN, 2017, pp. 123–28.
APA
Nguyen Cong, B., Morell, C., & De Baets, B. (2017). Distance metric learning : a two-phase approach. Proceedings of the 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2017), 123–128. ESANN.
Chicago author-date
Nguyen Cong, Bac, Carlos Morell, and Bernard De Baets. 2017. “Distance Metric Learning : A Two-Phase Approach.” In Proceedings of the 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2017), 123–28. ESANN.
Chicago author-date (all authors)
Nguyen Cong, Bac, Carlos Morell, and Bernard De Baets. 2017. “Distance Metric Learning : A Two-Phase Approach.” In Proceedings of the 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2017), 123–128. ESANN.
Vancouver
1.
Nguyen Cong B, Morell C, De Baets B. Distance metric learning : a two-phase approach. In: Proceedings of the 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2017). ESANN; 2017. p. 123–8.
IEEE
[1]
B. Nguyen Cong, C. Morell, and B. De Baets, “Distance metric learning : a two-phase approach,” in Proceedings of the 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2017), Bruges, Belgium, 2017, pp. 123–128.
@inproceedings{8532218,
  abstract     = {{Distance metric learning has been successfully incorporated in many machine learning applications. The main challenge arises from the positive semidefiniteness constraint on the Mahalanobis matrix, which results in a high computational cost. In this paper, we develop a novel approach to reduce this computational burden. We first map each training example into a new space by an orthonormal transformation. Then, in the transformed space, we simply learn a diagonal matrix. This two-phase approach is thus much easier and less costly than learning a full Mahalanobis matrix in one phase as is commonly done.}},
  author       = {{Nguyen Cong, Bac and Morell, Carlos and De Baets, Bernard}},
  booktitle    = {{Proceedings of the 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2017)}},
  isbn         = {{9782875870391}},
  language     = {{eng}},
  location     = {{Bruges, Belgium}},
  pages        = {{123--128}},
  publisher    = {{ESANN}},
  title        = {{Distance metric learning : a two-phase approach}},
  url          = {{https://www.elen.ucl.ac.be/Proceedings/esann/esannpdf/es2017-8.pdf}},
  year         = {{2017}},
}