# Deep Class-Guided Hashing for Multi-Label Cross-Modal Retrieval
## 3 Methodology
### Optimization
The mAP@H \(\leq\) 2 results for different hash

\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Task**} & \multirow{2}{*}{**Methods**} & \multicolumn{3}{c}{**MIRFLICKR-25K**} & \multicolumn{3}{c}{**NUS-WIDE**} & \multicolumn{3}{c}{**MS COCO**} \\ \cline{3-11}  & & **16 bits** & **32 bits** & **64 bits** & **16 bits** & **32 bits** & **64 bits** & **16 bits** & **32 bits** & **64 bits** \\ \hline \multirow{9}{*}{Img2 Txt} & DCMH (CVPR’17) & 0.7687 & 0.7736 & 0.7797 & 0.5379 & 0.5513 & 0.5617 & 0.5399 & 0.5444 & 0.5627 \\  & SSAH (CVPR’18) & 0.8079 & 0.8129 & 0.8220 & 0.6032 & 0.6058 & 0.6095 & 0.5411 & 0.4855 & 0.5395 \\  & CMHH (ECCV’18) & 0.6932 & 0.6979 & 0.6984 & 0.5439 & 0.5546 & 0.5520 & 0.5145 & 0.4509 & 0.5209 \\  & AGAH (ICMR’19) & 0.7248 & 0.7217 & 0.7195 & 0.3945 & 0.4107 & 0.4258 & 0.5501 & 0.5515 & 0.5518 \\  & DAPH (ICMR’20) & 0.8098 & 0.8162 & 0.8193 & 0.6350 & 0.6568 & 0.6546 & 0.5952 & 0.6118 & 0.6237 \\  & SCAHN (JNeUCOM’20) & 0.7955 & 0.8248 & 0.8297 & 0.6463 & 0.6616 & 0.6645 & 0.6376 & 0.6475 & 0.6519 \\  & MESDCH (JNeUCOM’22) & 0.7258 & 0.7438 & 0.7421 & 0.5638 & 0.5801 & 0.5875 & 0.5759 & 0.5670 & 0.5636 \\  & DCMHT (MM’22) & 0.8201 & 0.8253 & 0.8222 & 0.6596 & 0.6706 & 0.6863 & 0.6309 & 0.6216 & 0.6553 \\  & MIAN (TKDE’22) & 0.8262 & 0.8444 & 0.8501 & 0.6431 & 0.6548 & 0.6625 & 0.5952 & 0.5987 & 0.6121 \\  & DAPH (SIGIR’23) & 0.7939 & 0.8071 & 0.8168 & 0.6642 & 0.6835 & 0.6925 & 0.6344 & 0.7030 & 0.7300 \\  & DSPH (ICSVT’23) & 0.8129 & 0.8435 & 0.8541 & 0.6830 & 0.6934 & 0.7087 & 0.6985 & 0.7466 & 0.7635 \\  & DNNH (TOMM’24) & 0.8108 & 0.8269 & 0.6898 & 0.6891 & 0.6939 & 0.6438 & 0.6910 & 0.7294 \\  & DAPH (TKDE’24) & 0.8299 & 0.8437 & 0.8531 & 0.6678 & 0.6799 & 0.6901 & **0.7284** & 0.7415 & 0.7475 \\  & SCH (AAAI’24) & **0.8363** & **0.8507** & 0.8602 & 0.6436 & 0.6677 & 0.6823 & 0.5792 & 0.6642 & 0.7217 \\  & DCGH (Present study) & 0.8245 & 0.8482 & **0.8633** & **0.6869** & **0.7038** & **0.7214** & 0.7120 & **0.7492** & **0.7737** \\ \hline \multirow{9}{*}{Txt2 Img} & DCMH (CVPR’17) & 0.7857 & 0.7998 & 0.8029 & 0.5747 & 0.5810 & 0.5853 & 0.5271 & 0.5424 & 0.5450 \\  & SSAH (CVPR’18) & 0.8089 & 0.8127 & 0.8017 & 0.6011 & 0.6058 & 0.6167 & 0.4901 & 0.4798 & 0.5053 \\  & CMHH (ECCV’18) & 0.7181 & 0.7104 & 0.7294 & 0.4956 & 0.4831 & 0.4820 & 0.4910 & 0.4930 & 0.4889 \\  & AGAH (ICMR’19) & 0.7082 & 0.7182 & 0.7344 & 0.4344 & 0.3980 & 0.4382 & 0.5012 & 0.5146 & 0.5191 \\  & DADH (ICMR’20) & 0.8019 & 0.8101 & 0.8137 & 0.6111 & 0.6182 & 0.6218 & 0.5649 & 0.5790 & 0.5870 \\  & SCAHN (JNeUCOM’20) & 0.7826 & 0.8066 & 0.8064 & 0.6587 & 0.6626 & 0.6648 & 0.6377 & 0.6512 & 0.6493 \\  & MESDCH (J.NeUCOM’22) & 0.7385 & 0.7387 & 0.7437 & 0.5562 & 0.5720 & 0.5803 & 0.5044 & 0.5083 & 0.5085 \\  & DCMHT (MM’22) & 0.7983 & 0.8048 & 0.8031 & 0.6761 & 0.6837 & 0.6943 & 0.6241 & 0.6212 & 0.6486 \\  & MIAN (TKDE’22) & 0.8139 & 0.8180 & 0.8216 & 0.6733 & 0.6922 & 0.6936 & 0.5947 & 0.6000 & 0.6067 \\  & DAPH (SIGIR’23) & 0.7949 & 0.8134 & 0.8212 & 0.6611 & 0.6813 & 0.7016 & 0.6307 & 0.6870 & 0.7180 \\  & DSPH (ICSVT’23) & 0.8000 & 0.8216 & 0.8294 & 0.6997 & 0.7116 & 0.7326 & 0.7002 & 0.7483 & 0.7696 \\  & DNNH (TOMM’24) & 0.8015 & 0.8176 & 0.8166 & 0.6871 & 0.6994 & 0.7182 & 0.6468 & 0.7012 &



Figure 5: Results of Precision-Recall curves on NUS-WIDE. (**a**) PR@16 bits. (**b**) PR@16 bits. (**c**) PR@32 bits. (**d**) PR@32 bits. Figure 6: Results of Precision-Recall curves on MS COCO. (**a**) PR@16 bits. (**b**) PR@16 bits. (**c**) PR@32 bits. ### Ablation Studies

To validate the effectiveness of the DCGH method, we implemented three variations to calculate the mAP values for the tasks of the image retrieval of text and the text retrieval

Figure 8: The mAP@H \(\leq\) 2 results for different code lengths on the MIRFLICKR-25K, NUS-WIDE, and MS COCO datasets. Figure 7: Results of TopN-precision curves on the MIRFLICKR-25K, NUS-WIDE, and MS COCO datasets for 32 bits. of images. In detail, (1) DCGH-_P-V_: uses only proxy loss, \(\mathcal{L}_{proxy}\), to train the model.