# Multi-Modal 3D Shape Clustering with Dual Contrastive Learning
## 1 Introduction  
With the development of 3D scanning and modeling technology, 3D shapes have been widely employed in various applications of computer vision and multimedia fields, such as 3D printing, model retrieval, augmented reality, etc. [1, 2, 3]. How to effectively analyze large numbers of 3D shapes has become a research hot spot. In recent years, owing to the advanced development of deep learning, a series of deep 3D shape classification methods [4, 5, 6] have obtained satisfactory results. However, the success of deep neural networks critically relies on large-scale human-annotated data [7, 8, 9], which requires a laborious data annotation procedure. Under these circumstances, clustering has received increasing attention due to its powerful ability to divide massive amounts of unlabeled data [10, 11]. Exploring effective 3D shape clustering methods has become a promising approach to overcome the above obstacle. In practical application scenarios, 3D shapes are generally represented by different modalities due to the diversity of acquisition devices. As two popular 3D modalities, point clouds and multiple views are produced by 3D scanners and RGB cameras respectively, which have the advantages of flexible acquisition and low costs [12]. Specifically, point clouds describe 3D shapes with a series of disordered points, and the positional arrangement of those points preserves the spatial geometry of the 3D shapes [13]. Different from point clouds, multiple views are formed by a series of 2D images corresponding to different camera angles [14, 15]. They contain rich visual information of 3D shapes, such as texture and color [16]. Since point clouds and multiple views describe 3D shapes from different perspectives, effectively exploiting the multi-modal properties is conducive to capturing more discriminative descriptions of 3D shapes and better revealing compact 3D shape clustering partitions. Recently, contrastive learning has shown great success in unsupervised representation learning [17]. The core idea of contrastive learning is to maximize the representation similarities of positives while minimizing those of negatives, thus capturing more effective representations of data. Driven by this, some unsupervised 3D shape representation learning methods [18; 19] successfully extract better cross-modal 3D shape representations by performing contrastive learning among different 3D modalities. However, since the above methods lack clustering-oriented learning objectives, the performance is usually limited when directly applying traditional clustering algorithms to the learned representations. In order to learn cross-modal representations that are suitable for clustering, several previous works [20; 21] have integrated contrastive learning into multi-modal clustering for text and image data. By maximizing the similarities among the representations or the clustering assignments of different modalities in a contrastive learning manner, these methods have achieved encouraging results. Nonetheless, no existing work has focused on the multi-modal 3D shape clustering task. For the point clouds and multiple views of 3D shapes, in addition to the inter-modal correlations, different views within the multi-view modality also describe different local appearances of 3D shapes from particular angles. Therefore, how to jointly explore the inter-view correlations within the multi-view modality and the inter-modal correlations between the point cloud and multi-view modalities during the learning procedure of contrastive clustering remains a challenging issue for the multi-modal 3D shape clustering task. To address the above issue, this paper proposes a dual contrastive learning network (DCL-Net) for multi-modal 3D shape clustering. The key motivation behind our design involved two aspects. Firstly, as for a 3D shape, different views within multi-view modality contain diverse appearances from different perspectives.