# A Discriminative-Based Geometric Deep Learning Model for Cross Domain Recommender Systems
## 2 Review of Related Works  
### The Conception of Geometric Deep Learning  
Many current studies in various scientific fields concern data belonging to the non-Euclidean domain rather than the Euclidean domain [11]. Examples of these include, but are not limited to, multimedia technology, social networks in computational sciences, functional networks, regulatory networks, sensor networks and meshed surfaces in computer graphics. The structure of geometric data is known to be very complex and non-linear in nature; hence, many scientific researchers are focusing on this area. For instance, deep learning is one the techniques being exploited and is an important tool in realizing solutions for RSs [11; 12]. However, most of the existing approaches have been implemented in the Euclidean domain, with a few of them paying attention to data belonging to the non-Euclidean domain. As a result, there is a need for a representation solution to effectively explore data repositories of non-Euclidean data. This led to a generalized learning algorithm referred to as geometric deep learning (GDL) for the non-Euclidean domains, such as manifolds and graphs.  
The aim of the following sections concerning GDL (an umbrella term used to describe emerging technology aiming to structure or generalize techniques in the non-Euclidean domain) is to discuss some of the conceptions of the technique and also to present some available solutions, challenges. Additionally, research directions and how the proposed approach will be utilized in addressing challenges will be discussed. DL is the process of hierarchically learning complex concepts from simple ones in a multi-layer fashion. Examples of such learning approaches include, but are not limited to, neural networks (NN), artificial NN, feedforward NN and Convolution Neural Network (CNN), which have the ability to train large sets of data and have resulted in significant breakthroughs in multimedia applications, computer vision, and speech recognition.  
In a broader sense, GDL issues can be categorized into two groups. In the first group, we intend to associate characteristics with the structure of the data, and in the second group, we analyze the functions based on which a given non-Euclidean domain is defined [11]. The two groups are interrelated in the sense that because particular information is transmitted and understanding the properties of functions defined on a domain is essential. The same can also be said about the properties forced on the function by the structure of the domain. As an example of the first group of problems, an assumption could be made that a group of data points are given, where low-dimensional constructions are entrenched into a high-dimensional Euclidean space. If that is the case, then recuperating that low-dimensional construction from the high dimensional space is mostly termed as nonlinear dimensionality reduction or manifold learning [12]. This is an instance of un-supervised learning, and most such methods consist of two phases. The first phase begins with the structuring of a representation solution based on the local affinity of the data point, and in the second phase, the data points are entrenched into a low-dimensional feature space with the aim of preserving originality.  
Some examples of studies examining manifold learning include, but are not limited to, the ones discussed in [13; 14; 15] that attempt to preserve global geometric information such as the geodesic coverage of the graph. Other studies examine decomposing the graphs into minute sub-graphs referred to as graph-lets or motifs, rather than embedding the vertices [16; 17; 18; 19]. Graphs or manifolds are well-known and utilized for constructing representation solutions for social network analysis [20; 21], natural language processing [22; 23; 24] and many other applications by capturing local geometric information.