## 4 Optimization for ISMLP
\begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**5\%Labeled Data**} & \multicolumn{4}{c}{**10\%Labeled Data**} & \multicolumn{4}{c}{**30\%Labeled Data**} \\ \cline{2-13}  & **R@1** & **R@2** & **R@4** & **R@8** & **R@1** & **R@2** & **R@4** & **R@8** & **R@1** & **R@2** & **R@4** & **R@8** \\ \hline EUCLID & 24.63 & 28.16 & 31.34 & 34.73 & 25.68 & 30.65 & 33.87 & 35.71 & 28.56 & 31.89 & 34.17 & 38.81 \\ LSeMML & 33.26 & 34.54 & 37.15 & 39.27 & 34.58 & 37.18 & 39.46 & 42.17 & 36.19 & 39.43 & 41.87 & 44.98 \\ SERAPH & 32.19 & 34.61 & 36.25 & 39.89 & 35.18 & 37.26 & 39.48 & 43.16 & 37.30 & 39.56 & 42.43 & 45.25 \\ S-RLMM & 34.37 & 36.81 & 37.18 & 39.96 & 36.58 & 38.78 & 40.41 & 44.34 & 38.48 & 41.68 & 44.15 & 47.28 \\ LRML & 32.82 & 35.33 & 36.83 & 37.41 & 33.72 & 35.41 & 37.19 & 39.71 & 38.18 & 41.29 & 43.21 & 45.87 \\ SLRML & 34.37 & 36.19 & 38.98 & 40.57 & 35.42 & 38.42 & 40.76 & 43.87 & 37.57 & 39.58 & 42.81 & 46.10 \\ APIT & 33.46 & 35.72 & 37.99 & 39.51 & 34.71 & 36.78 & 39.18 & 41.57 & 38.24 & 41.58 & 43.79 & 46.28 \\ CMM & 34.19 & 35.45 & 36.73 & 39.10 & 35.88 & 38.04 & 40.00 & 43.06 & 37.60 & 39.87 & 41.81 & 45.28 \\ APILR & 32.67 & 35.34 & 35.73 & 37.76 & 33.26 & 36.87 & 39.19 & 42.62 & 36.62 & 39.89 & 42.28 & 45.78 \\ LMNN & 31.30 & 33.53 & 35.84 & 36.92 & 32.19 & 34.48 & 36.49 & 38.84 & 34.39 & 36.62 & 40.19 & 44.17 \\ SSML-DR & **35.35** & **37.53** & **39.47** & **41.38** & 37.01 & 39.46 & 42.87 & 44.59 & 39.84 & 42.69 & 45.92 & 47.25 \\ ISMLP & 34.01 & 36.52 & 38.72 & 40.29 & **37.11** & **40.38** & **43.48** & **45.81** & **40.19** & **43.58** & **46.39** & **48.41** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The performance of the proposed ISMLP and compared methods on the Cars-196 dataset with varying labeling rates. The best performance under each index is marked in bold. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**5\%Labeled Data**} & \multicolumn{4}{c}{**10\%Labeled Data**} & \multicolumn{4}{c}{**30\%Labeled Data**} \\ \cline{2-13}  & **R@1** & **R@2** & **R@4** & **R@8** & **R@1** & **R@2** & **R@4** & **R@8** & **R@1** & **R@2** & **R@4** & **R@8** \\ \hline EUCLID & 25.75 & 29.82 & 32.73 & 34.82 & 26.85 & 32.57 & 34.12 & 36.45 & 29.68 & 32.22 & 36.90 & 39.29 \\ LSeMML & 32.84 & 34.54 & 36.90 & 38.73 & 34.53 & 36.72 & 38.13 & 40.65 & 35.90 & 37.81 & 39.72 & 42.20 \\ SERAPH & 33.11 & 35.61 & 37.81 & 39.98 & 35.02 & 36.87 & 38.42 & 41.97 & 37.83 & 39.24 & 42.69 & 44.73 \\ S-RLMM & 32.83 & 34.81 & 36.31 & 38.71 & 34.63 & 36.59 & 38.20 & 40.21 & 38.80 & 40.68 & 42.98 & 43.73 \\ LRML & 31.10 & 33.68 & 36.83 & 38.50 & 33.76 & 35.80 & 37.81 & 39.69 & 37.33 & 39.84 & 42.38 & 44.16 \\ SLRML & 33.63 & 34.19 & 37.24 & 39.42 & 35.82 & 37.67 & 39.29 & 42.19 & 37.90 & 39.19 & 40.57 & 42.78 \\ APIT & 32.52 & 34.57 & 37.99 & 38.68 & 34.68 & 36.85 & 39.09 & 36.98 & 37.81 & 40.83 & 42.68 & 44.73 \\ CMM & 32.13 & 34.11 & 36.73 & 38.10 & 34.82 & 37.40 & 37.49 & 39.80 & 37.86 & 40.13 & 41.68 & 42.68 \\ APILR & 31.16 & 33

### Sensitivity Analysis

In this section, we conduct an experiment on the Cars-196 dataset to analyze the sensitivity of the proposed ISMLP on different hyper-parameters. To simplify the experiment, we keep the other parameters fixed when analyzing the current one. Figure 4a depicts the R@1 accuracy of the proposed ISMLP with different \(\lambda\) when we set \(\mu=0.001\), \(p=50\), and \(m=c\), where c denotes the number of classes. One can observe that each curve has a turning point, and the fewer the amount of labeled data, the earlier the turning point appears. We gauge that this can be attributed to the utility of the entropy regularization; either an excessively large or a small \(\lambda\) will lead to a biased model. Figure 4b shows the sensitivity of ISMLP on \(\mu\). We can see that ISMLP is insensitive to the change of \(\mu\) to some extent.