# A Discriminative-Based Geometric Deep Learning Model for Cross Domain Recommender Systems
## 1 Introduction
(2022) utilizes Latent Dirichlet Allocation (LDA) and ontology methods to extract additional information from user reviews to create an ontological profile for each user by mapping genres to user profiles using a dictionary. In the work of [PERSON] et al. (2022), domain-shared and domain-specific features are extracted to enable knowledge transfer between multiple heterogeneous source and target domains. To ensure positive transfer, the domain-shared subspaces from multiple domains are maximally matched by a multiclass domain discriminator in an adversarial learning process. The recommendation in the target domain is completed by a matrix factorization module with aligned latent features from both the user and the item side. Moreover, the matrix factorization-based techniques suffer lower accuracy performances when the data is extremely sparse. Additionally, without significant modification to their models, they cannot be applied directly to non-Euclidean data feature extraction. The traditional deep neural network was not originally designed to capture new data trends (non-Euclidean), such as graphs, manifolds, and 3D ([PERSON] et al., 2021). Hence, they cannot correctly represent the local information of these complex data. Furthermore, most traditional deep networks are based on convolutions that do not include a generalization operator, making them linearly incompatible with the representation of non-Euclidean data ([PERSON] et al., 2022). On the other hand, geometric deep learning (GDL) is an emerging field of research that employs deep learning on non-Euclidean data. GDL has seen several successes in classification [3], drug discovery [4], biochemistry [5]; however, it has not been exploited in the area of recommender systems (either single-domain or cross-domain). However, these techniques could not fully exploit the local information existing in the complex and nonlinear structure of items/users concerning the magnitude of items and users as indicated in the following works [6; 7; 8; 9; 10]. Therefore, in this paper, considering the intrinsic and extrinsic feature capabilities of recommender systems from the manifolds domain, we propose a novel geometric deep-learning approach for cross-domain RSs based on different modalities to address the item/user cold-start and sparsity problems. The proposed method combines the advantages of geometric DL techniques, considering geometric information and complex visual information of cross recommender models using varied viewing angles. In summary, the geometrically based modalities and the visual features are learned using geometric deep local convolutional neural networks with a local fusing technique based on the restricted Boltzmann machine (LRBM) and a kernel-based density estimator for the selection of relevant recommender systems. The proposed approach uses an adopted local sensitivity based deep convolutional belief network (LDCBN) and a local-sensitivity convolutional neural network (LCNN) to learn or extract geometric information and visual-based information for cross domain recommender systems. A more discriminative result is obtained by fusing the geometric and the visual information using LRBM. Figure 1 depicts the framework of the proposed model. Contributions: The prime contributions made by this work are as follows:  
1. We modelled and implemented a novel cross-domain recommendation network capable of learning from complex data representations effectively by incorporating a space local sensitivity mechanism into a geometric deep learning algorithm to resolve the problem of sparsity. 2. We introduce a local sensitive adaptor to enforce discriminability by capturing fully the essential local geometric information, which maybe hidden in the structure of recommender systems, for efficient and effective recognition results. Figure 1: The Framework of the proposed model. We performed a comprehensive experiment on the proposed model to ascertain its performance on multiple datasets in the sparse and dense settings.