# Wheel Hub Defects Image Recognition Base on Zero-Shot Learning
## 5 Experiment and Analysis
### Experiment Analysis  
(1) Analysis of structure matching components  
The effect of structure matching was analyzed by changing \(\rho\in\{10^{-3},\ 10^{-2},\ 10^{-1},\ 10^{0},\ 10^{1},\ 10^{2}\}\), and the change in accuracy was recorded. We conducted experiments using the WHD-9, the results of which are recorded in Figure 6.  
It can be seen from Figure 6 that based on the WHD-9, the conventional unseen class accuracy (Figure 6a) and the generalized seen class accuracy (Figure 6b) are better than or similar to the baseline model DEM, while, the accuracy of the generalized unseen class (Figure 6c) is higher than that of DEM, and the harmonic mean (Figure 6d) is significantly better than that of DEM. It can be seen from Figure 6d that when \(\rho=\ 10^{1}\), the effect of the harmonic mean is the best. Compared with baseline DEM, we verified that the DEM+R strategy contributes to hubness reduction. Hubness is measured by a bias of 1 nearest neighbor histogram (N1) [50]. A smaller skewness of the N1 histogram means less hubness prediction, and we used test samples of unseen classes in the generalized setting, as shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & **aPY** & & & & **WHD-9** & \\ \hline Methods & TU & GS & GU & H & TU & GS & GU & H \\ DAP[150] & 33.6 & 79.6 & 6.3 & 11.7 & 40.0 & 57.7 & 2.7 & 5.2 \\ IAP[140] & 36.9 & 67.3 & 7.5 & 13.5 & 31.7 & 65.1 & 1.9 & 3.7 \\ ConSE[141] & 28.7 & **92.7** & 0.0 & 0.0 & 37.2 & **83.2** & 2.1 & 4.1 \\ SYNC[142] & 24.3 & 68.1 & 9.1 & 16.1 & 45.6 & 67.8 & 9.3 & 16.4 \\ DeViSE[143] & **40.6** & 78.0 & 6.7 & 12.3 & 51.3 & 58.0 & 15.7 & 24.7 \\ DEM[102] & 36.4 & 76.9 & 13.2 & 22.5 & 48.7 & 63.4 & 20.4 & 30.9 \\ DEM+R(Our) & 31.2 & 72.3 & 17.1 & 27.6 & 50.0 & 59.7 & 23.4 & 33.6 \\ DEM+RA(Our) & 37.7 & 74.0 & 32.2 & 44.8 & 54.9 & 55.1 & 47.2 & 50.8 \\ DEM+RAC(Our) & 37.8 & 65.4 & **35.9** & **46.4** & **55.1** & 54.6 & **48.6** & **51.4** \\ \hline \hline \end{tabular} Note: _GS = acc\({}_{s}\), GU = acc\({}_{u}\), H is obtained through Equation (10)._  
\end{table} 
Table 3: Experiment results based on aPY and WHD-9. In Table 4, WHD-9 and aPY datasets are used for experiments of DEM and DEM+R. Let \(\rho=~{}0.1\), the average value of multiple experiments is recorded in the Table, as can be seen from Table 4, the hubness of the N1 histogram generated by the DEM+R method on both data sets is smaller. This means that the use of an additional structural matching strategy will reduce hubness, therefore it can alleviate the trouble of dimension disaster. Domain adaptive component analysis  
As can be seen from Table 3, compared with DEM+R, the unseen class accuracy of DEM+RA increased by 88% (aPY), 101% (WHD-9), harmonic mean increased by 62.3% (aPY), 51.2% (WHD-9). Figure 7 shows the effect of domain adaptation by using t-SNE [51] on WHD-9. As shown in Figure 7a, the unseen class semantic embedding (purple) is very near to the seen class feature (blue). However, through the domain adaptation step, as shown in Figure 6b, the unseen class semantics are transformed, which is obviously close to the center of the feature family (red) of the unseen class. Analysis of Calibration Mechanism  
In Table 3, compared with the DEM+RA model, the \"GU\" performance of the DEM+RA model was improved by 11.4%(aPY), 2.9% (WHD-9), and \"H\" performance increased by 3.6% (aPY), 1.2% (WHD-9), the reason may be that domain adaptive steps have already transferred the semantic embedding of unseen classes and accordingly shrunk the bias on seen classes and made further calibration not obvious. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method/Dataset** & **WHD-9** & **aPY** \\ \hline DEM & 1.69 & 1.83 \\ DEM+R & 1.15 & 1.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hubness reduction using structure matching strategy.