# Grouping Bilinear Pooling for Fine-Grained Image Classification
## 4 Experiment
### Comparing with Other Compact Bilinear Pooling  
In this section, GBP is compared with other compact bilinear pooling methods [15; 17; 19; 32] in detail. Assuming that the categories to be classified are \(N\), and bilinear pooling is carried out on the feature layers with the size of \(c\times h\times w\), where \(c\) is the feature channels, the height and width of feature layers are \(h\) and \(w\) (VGG-16: \(h=w=28\), \(c=512\); ResNet-50: \(h=w=14\), \(c=2048\)). For a more intuitive comparison, taking the experiment on CUB as an example, the input size of the images is \(448\times 448\). The configurations \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**The Groups** & **2** & **4** & **8** & **16** & **32** & **64** & **128** & **256** & **512** & **1024** \\ \hline
**CUB (\%)** & 83.79 & 84.19 & 85.13 & 85.28 & 85.23 & 85.11 & 85.07 & 85.21 & 85.32 & **85.54** \\
**Model size (MB)** & 987.81 & 497.81 & 297.81 & 197.81 & 147.81 & 122.81 & 110.31 & 104.06 & 100.94 & 99.37 \\ \hline
**Stanford Cars (\%)** & 92.11 & 92.34 & 92.35 & 92.29 & 92.33 & 92.49 & 92.61 & 92.75 & 92.74 & **92.86** \\
**Model size (MB)** & 971.81 & 489.81 & 293.81 & 195.81 & 146.81 & 122.31 & 110.06 & 103.94 & 100.87 & 99.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The performances of Inter-GBP based on ResNet-50 on CUB dataset and Stanford Cars dataset. Figure 4: (**a**) The classification accuracy of Intra-GBP and Inter-GBP based on VGG-16 on Stanford Cars dataset; (**b**) The corresponding model size with different \(g\) (including backbone CNN); (**c**) The amount of calculation for pooling and classification. Figure 3: (**a**) The classification accuracy of Intra-GBP and Inter-GBP based on VGG-16 on CUB dataset; (**b**) The corresponding model size with different \(g\)(including backbone CNN); (**c**) The amount of calculation for pooling and classification. of the comparative experiment are as follows: \(g\) = 128 (VGG-16), \(g\) = 1024 (ResNet-50), \(m\) = 100, \(r\) = 8, \(d\) = 8192, N = 200. The detailed comparisons of different compact bilinear pooling methods are shown in Table 3. The comparison contents include the dimensions of representation, computational complexity of pooling and classifying, and the number of parameters. Under the same configurations, the classification accuracy of different compact bilinear pooling methods based on VGG-16 is shown in Table 4.  
As can be seen from Table 3, among all bilinear pooling methods, GBP has the lowest representation dimension. When VGG-16 is used as a backbone, the representation dimension of Inter-GBP is only 0.4% of FBP, the pooling computation is reduced by four orders of magnitude, and the parameters needed to learn are reduced by 99.6%. When ResNet-50 is used as a backbone, the representation dimension of FBP will up to 4.19 million and the parameters needed to learn will reach 3200 MB, while Inter-GBP are 2048 and 1.6 MB respectively. It can be seen intuitively that GBP has a huge advantage in the compression of representation. Table 4 shows that the performance of GBP is not weaker than or even better than other compact bilinear pooling methods when using the same backbone. The Inter-GBP based on VGG-16 reaches the best accuracy of 92.49% on the Stanford Cars dataset. As an earlier compact bilinear pooling method [17], CBP improves bilinear pooling to some extent and inspires a series of subsequent approaches. iFBP [32] proposes the matrix square-root normalization to improve the performance of the bilinear model, and achieves the best performance on the CUB dataset, but it still requires a lot of computing and storage space. LRBP [19] obtains statistics without performing bilinear pooling, instead using the Frobenius norm as the classification score, which reduces the computation to a certain extent and has advantages in reducing parameters, but it requires the learning of additional projection parameters.