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An effective few-shot learning approach via location-dependent partial differential equation

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Abstract

Recently, learning-based partial differential equation (L-PDE) has achieved success in few-shot learning area, while its feature weighting mechanism and recognition stability require further improvement. To address these issues, we propose a novel model called “location-dependent PDE” (LD-PDE) based on Navier–Stokes equation and rotational invariants in this paper. To our best knowledge, LD-PDE is the first application of the Navier–Stokes equation to achieve image recognition as a high-level vision task. Specifically, we formulate the feature variation with respect to each time step as a linear combination of rotational invariants in LD-PDE. Meanwhile, we design location-dependent mechanism to adaptively weight each invariant in an attention-based approach, which provides hierarchical discrimination in the spatial domain. Once the ultimate feature is learned, we measure the model error with the cross-entropy loss and update the parameters by the coordinate descent algorithm. As a verification, experimental results on face recognition datasets show that LD-PDE method outperforms the state-of-the-art approaches with few training samples. Moreover, compared to L-PDE, LD-PDE achieves a much more stable recognition with low sensitivity to its hyper-parameters.

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Notes

  1. The model was downloaded from the website http://www.robots.ox.ac.uk/~vgg/software/vgg_face/.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 91648204 and 11701566).

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Authors and Affiliations

  1. National University of Defense Technology, Changsha, China

    Haotian Wang & Yuhua Tang

  2. College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China

    Zhenyu Zhao

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  1. Haotian Wang
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  2. Zhenyu Zhao
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  3. Yuhua Tang
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Correspondence to Zhenyu Zhao.

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Wang, H., Zhao, Z. & Tang, Y. An effective few-shot learning approach via location-dependent partial differential equation. Knowl Inf Syst 62, 1881–1901 (2020). https://doi.org/10.1007/s10115-019-01400-y

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