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Few-shot learning with hierarchical pooling induction network

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Abstract

Learning to recognize new concepts from few-shot examples is a long-standing challenge in modern computer vision. Metric based few-shot learning is a prevalent way towards this goal where new query instances are classified to the support classes by comparing the query instance with each class prototype. To this end, a representative and discriminative class prototype should necessarily be induced from several support example features. In this work, we propose a simple but effective hierarchical pooling induction method to learn such generalized class-level representations, by concatenating the max pooling and mean pooling operations. The proposed induction method could form a representative prototype for given few-shot samples, enhancing both the discrimination of the intermediate features and the final classification performance. The benchmark miniImageNet dataset and some other practical Remote Sensing Image Scene Classification (RESISC) datasets are employed for generalization investigation and it shows that the proposed induction module could improve the performance of state-of-the-art method and outperforms other alternative induction methods. Qualitative visualization and quantitative analysis are also provided to demonstrate the effectiveness and robustness of the proposed method.

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Authors and Affiliations

  1. National University of Defense Technology, Changsha, China

    Chongyu Pan, Jian Huang, Jianxing Gong & Jianguo Hao

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  1. Chongyu Pan
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  2. Jian Huang
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  3. Jianxing Gong
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  4. Jianguo Hao
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Correspondence to Jian Huang.

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Appendix A:: Normal weighted induction

Appendix A:: Normal weighted induction

Definition:

For a set of discrete samples (x1, x2,⋯, xn), we first get the mean and variance of the samples, denoted as μ and σ, and then define a normal distribution f \(\sim \) N(μ, σ). The weight for each xi is defined as its probability density wi = f (xi) and their normalization values are

$$ {\bar {w_{i}}} = \frac{{{w_{i}}}}{{\sum\limits_{i} {{w_{i}}} }} $$
(4)

Finally, we define the normal weighted induction as:

$$ {p^{Norm}} = \sum\limits_{i} {{\bar {w_{i}}}{x_{i}}} $$
(5)

For a multi-dimensional vector or tensor, we perform the bitwise operations over each dimension, resulting in a vector or tensor of the same dimension.

To qualitatively demonstrate the normal weighted induction, we present the visualization results compared with the unbiased average pooling. Figure 7 shows the 2D samples as well as their induction prototypes, where the red stars indicate the samples and the two induction prototypes are indicated by the cross and circle, respectively.

Fig. 7
figure 7

Visualization of the normal weighted induction. Examples (Indicated by the red stars) are sampled from a normal distribution N((40, 60), (5, 8)), together with 3 apart outliers. The normal weighted induction prototype is closer to the real sampling center than the mean value under some disturbances

Full size image

We can see that although the unbiased estimation it is, the mean value deviates far from the real sampling center (40, 60), due to the disturbance of some singular points. However, with the normal weighted induction, the prototype gets closer to the sampling center, alleviating the influence of the outliers. Conclusions could be made that the normal weighted induction will be more helpful in the cases that there are some obvious outliers.

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Pan, C., Huang, J., Gong, J. et al. Few-shot learning with hierarchical pooling induction network. Multimed Tools Appl 81, 32937–32952 (2022). https://doi.org/10.1007/s11042-022-11999-w

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