# Multi-Grained Similarity Preserving and Updating for Unsupervised Cross-Modal Hashing
## 4 Experiments
### Sensitivity to Hyperparameters  
This section, we conduct an analysis of the sensitivity of all hyperparameters used in the model: \(\alpha_{1},\eta_{1};\alpha_{2},\eta_{2};k;\lambda_{1},\lambda_{2},\lambda_{3}; \beta_{1},\beta_{2},\beta_{3}\). To explore the comprehensive impact of them, the accuracy of IZT and T2I task is used to visualize the trend of cross-modal hash performance. All these analysis are carried out in 16 bit hash code length on NUS-WIDE dataset. **Hyperparameter \(\alpha_{1},\eta_{1},\alpha_{2},\eta_{2}\)**. In semantic similarity matrix updating module, \(\alpha_{1},\eta_{1}\) are used to construct the refined similarity matrix \(\mathcal{S}^{r},\alpha_{2},\eta_{2}\) are used to execute the updating strategy to generate semantic similarity matrix \(\mathcal{S}\). We observe the performance change of MGSPU by varying \(\alpha_{1},\eta_{1}\) and \(\alpha_{2},\eta_{2}\). According to the experimental results in Figure 7, it is clearly that the retrieval accuracy is more susceptible to changes of \(\alpha_{1}\) when the value of \(\eta_{1}\) is small. We speculate that this phenomenon is caused by the noises that are injected in refined similarity matrix when the value of \(\eta_{1}\) is small. On the other hand, when we change the \(\alpha_{2}\) and \(\eta_{2}\), the fluctuations in model performance are relatively less severe, which still shows that our model performs a bit better if \(\eta_{2}\) is set to a large value (r.g., \(\eta_{2}=0.70\)). The reason behind this results is understandable: if a larger threshold \(\eta_{2}\) is taken, the discrimination of whether \(\mathcal{S}^{r}_{ij}\) and \(\mathcal{S}^{h}_{ij}\) are dissimilar will be more rigorous. Under this circumstance, the semantic similarity matrix updating will be executed more cautiously to preserve robust. **Hyperparameter \(k\)**. We recorded the performance change by varying the value of \(k\) on NUS-WIDE dataset to evaluate the effect by the the number of neighbors in \(k\)NN algorithm. As demonstrated in Figure 8, when \(k\in[40,80]\), the curve changes sharply, while the curve changes more modestly in the rest of the interval. We conjecture that when too many or too few neighbors we selected, noise will be introduced into the intra-modal similarity relationship representation, thereby affecting the latent similarity relationship learning within modality. Particularly, if \(k\) is set to 60, MGSPU achieves the highest mAP@50 score for both IZT and T2I task. It indicates that by selecting an appropriate number of neighbors, high-quality intra-modal similarity structure information can be aggregated by GCN to improve intra-modal similarity consistency preserving. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{3}{c}{**NUS-WIDE**} \\ \cline{2-9}  & \multicolumn{1}{c}{**IZT**} & \multicolumn{5}{c}{**T2I**} \\ \cline{2-9}  & \multicolumn{1}{c}{**16 bits**} & \multicolumn{1}{c}{**32 bits**} & \multicolumn{1}{c}{**64 bits**} & \multicolumn{1}{c}{**128 bits**} & \multicolumn{1}{c}{**16 bits**} & \multicolumn{1}{c}{**32 bits**} & \multicolumn{1}{c}{**64 bits**} & \multicolumn{1}{c}{**128 bits**} \\ \hline MGSPU-1 & 0.803 & 0.821 & 0.837 & 0.849 & 0.763 & 0.783 & 0.804 & 0.805 \\ MGSPU-2 & 0.796 & 0.809 & 0.819 & 0.821 & 0.746 & 0.775 & 0.777 & 0.776 \\ MGSPU-3 & 0.801 & 0.821 & 0.827 & 0.851 & 0.768 & **0.791** & 0.799 & 0.812 \\ MGSPU-4 & 0.794 & 0.826 & 0.843 & 0.847 & 0.773 & 0.786 & 0.798 & 0.797 \\
**Ours** & **0.811** & **0.826** & **0.844** & **0.858** & **0.780** & 0.786 & **0.806** & **0.813** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: mAP@50 score for ablation study on NUS-WIDE. **Hyperparameter \(\lambda_{1},\lambda_{2},\lambda_{3}\)**. As presented in Equation (20), \(\lambda_{1},\lambda_{2},\lambda_{3}\) are used to balance three components, i.e., \(\mathcal{L}_{re}\), \(\mathcal{L}_{mod}\) and \(\mathcal{L}_{sim}\) of hash code learning loss function.