# Multi-Modal 3D Shape Clustering with Dual Contrastive Learning
## 4 Experimental Results
### Comparison Results  
To demonstrate the performance of the proposed DCL-Net, several existing multi-modal clustering methods were adopted for comparison, including DMSC [40], EAMC [43], and CoMVC [21]. Note that the selected methods were not designed for the multi-modal 3D shape clustering task, thus it was incapable of directly comparing them with the proposed method. To this end, they were extended as DMSC*, EAMC*, and CoMVC* to adapt to the multi-modal 3D shape clustering task. Specifically, the feature extractor corresponding to the input point cloud was replaced with PointNet [51], which was consistent with the proposed DCL-Net. Then, the point cloud and an arbitrarily selected view of each 3D shape were fed into the corresponding feature extractors of different modalities to obtain the final clustering results. Additionally, to ensure the reliability of the experimental results, all of the experiments were repeated ten times with random initializations to reduce the effects of randomness and the mean results of the repeated experiments are reported in this paper.  
The quantitative comparison results on the ModelNet10 and ModelNet40 datasets are shown in Table 1. As shown in the table, the proposed DCL-Net achieved a better clustering performance than the comparison methods on both the ModelNet10 and ModelNet40 datasets, which effectively proved the superiority of the proposed method. In particular, the DCL-Net significantly outperformed CoMVC* and EAMC* by large margins. Even compared to the advanced method DMSC*, the proposed method also achieved the performance improvements of 2.94%, 9.27%, 2.20%, and 1.68% for the ACC, NMI, ARI, and F-score metrics on the ModelNet10 and the performance improvements of 6.04%,3.99%, 5.25%, and 4.66% for the ACC, NMI, ARI, and F-score metrics on the ModelNet40. This was mainly because the comparison methods were proposed for general multi-modal clustering and directly transferring them into the 3D shape clustering task failed to leverage the characteristics of 3D shapes, thus resulting in unsatisfactory clustering performances. In contrast, the proposed method took full advantage of the inter-view correlations within the multi-view modality, as well as the inter-modal correlations between the point cloud and the multi-view modalities, and developed a dual contrastive learning network. By jointly exploring the cross-view and cross-modal consistent representations and clustering assignments, the proposed method was more suitable for the multi-modal 3D shape clustering task. Additionally, it is worth mentioning that the clustering accuracy of the comparison methods dropped by more than 20% when the benchmark dataset was changed from ModelNet10 to ModelNet40. The main reason for this was that ModelNet40 held more classes and more imbalanced data distributions than ModelNet10, making it challenging for the multi-modal clustering task. Nevertheless, the proposed method obtained the values of 61.20%, 72.46%, 57.61%, and 60.22% for the ACC, NMI, ARI, and F-score metrics on the ModelNet40 dataset respectively, which further proved the robustness of our method.  
To further evaluate the superiority of the proposed DCL-Net over the comparison methods, t-SNE [56] visualizations of the 3D shape features utilized for clustering in the different methods were provided on the ModelNet10 dataset. The visualization results are shown in Figure 2, in which the different colors indicate different classes. As shown in Figure 2, the features extracted by the comparison methods were quite dispersed and the boundaries between the different classes were inconspicuous. By contrast, the proposed DCL-Net provided more clear and compact clustering partitions, which further demonstrated the effectiveness of the proposed method.