# A Discriminative-Based Geometric Deep Learning Model for Cross Domain Recommender Systems
## 3 Proposed Method  
Many large companies offer diversified products or services to customers. For instance, Google provides customers with mobile applications, web searches, and news services, and books, electronics, and clothes can be bought from Amazon. Single-domain recommender systems only focus on one domain while ignoring user interests in other domains, which also exacerbates sparsity and cold-start problems [40; 41]. A cross-domain recommender system, which assists target domain recommendation with the knowledge learned from source domains, provides a desirable solution for these problems. One of the most widely studied topics in cross-domain recommendation is transfer learning, which aims to improve learning tasks in one domain by using knowledge transferred from other domains [41]. Deep learning is well suited to transfer learning as it learns high-level abstractions that disentangle the variations of different domains. Several existing works, as reviewed in [41], demonstrate the efficacy of deep learning in catching the generalizations and differences across different domains and generating better recommendations on cross-domain platforms. Therefore, this is a promising but largely underexplored area where more studies are expected, hence the need for this study. The proposed discriminative-based geometric deep learning (D-GDL) for cross-domain recommender systems, particularly in the non-Euclidean domain, is presented in this section. Most of the objects that are recommended in recent times are 3D. A 3D object means a three-dimensional shape that can be defined as a solid figure with properties of depth (length), width and height. For example, virtual shopping malls, which integrate the advantages of 3D virtual environments and traditional online websites, accommodate users in a life-like shopping environment [42]. In these environments, users can effectively interact with virtual products by viewing them from different angles, zooming in and out, touching the surface and even trying them on. The virtual product experiences enable users to form a direct, intuitive and concrete understanding of the quality and performance of products and make better informed purchase decisions [43]. Examples of 3D datasets are the Flixter, Netflix and CiteUlike datasets. Hence, the recommender system must be modeled in a way to efficiently support such objects. The main objective of the approach is to introduce a general framework for geometric DL on non-Euclidean domain for cross-domain recommender systems. In this approach, a local representation learning is introduced into the structure of deep learning techniques to effectively capture the local geometric and visual information from the structure of the recommended 3D objects, which serves as the basis for 3D and recommended searches. A kernel-based technique is also adopted and introduced into the structure of the DL technique to map the complex structure of recommended objects into high dimensional feature space to achieve an effective recognition result. The kernels serve as a weighing function in building a high dimensional feature space, which makes it more robust to geometric noise and results in a good computation outcome. The proposed method could achieve an optimal dictionary to further enhance the power of discriminability of recommended objects and enables the realization of geometric DL representation of the 3D non-linear features. The D-GDL extracts visual and geometric features from recommended objects using LCNN and LDCBN models for optimal and efficient recognition performance. These models are pre-trained by depth image generation and voxelization instead of using down-sampling techniques. This is achieved by passing the extracted features through an improved kernel density estimator. With the extraction of geometric features, recommended objects are transformed into voxel-like forms from mesh and are almost like the original recommended object, which reduces the need for down-sampling.