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Ordinal Distance Metric Learning with MDS for Image Ranking

Author

Listed:
  • Panpan Yu

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China)

  • Qingna Li

    (School of Mathematics and Statistics/Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing 100081, P. R. China)

Abstract

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as LTL, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

Suggested Citation

  • Panpan Yu & Qingna Li, 2018. "Ordinal Distance Metric Learning with MDS for Image Ranking," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-19, February.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:01:n:s0217595918500070
    DOI: 10.1142/S0217595918500070
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    References listed on IDEAS

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    5. Warren Torgerson, 1952. "Multidimensional scaling: I. Theory and method," Psychometrika, Springer;The Psychometric Society, vol. 17(4), pages 401-419, December.
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    Cited by:

    1. Fengzhen Zhai & Qingna Li, 2020. "A Euclidean distance matrix model for protein molecular conformation," Journal of Global Optimization, Springer, vol. 76(4), pages 709-728, April.

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