Facebook and Instagram, like many other social networking services, utilise network analysis to determine who to suggest as a potential friend or follower. This method of analysis takes into account various factors, such as mutual friends or interests, to suggest relevant connections to users. Many of us are already familiar with this type of recommendation system, as it has quickly become commonplace in the modern age.

Comparing and contrasting network analysis and geometric deep learning is the focus of this essay.

## The meaning of a network has eluded me.

A set of things or people may have their most salient traits represented symbolically by a network. In mathematics, it goes by the name “graph.”

As a project manager, you are responsible for ensuring the efficient operation of four machines with the help of two workers. This involves planning out their shifts and assigning them to the right machinery, as well as monitoring the progress of the work to make sure it is carried out correctly. This is a task that requires a significant amount of effort on your part, although the use of networks can be used as an effective time-saving tool. To illustrate this further, let’s take a look at an example.

Here, the connections between the various nodes (shown by circles) and the objects (represented by vertices) can be represented by arrows, which are often referred to as “edges.” By utilising this visual representation of the data, we can more effectively analyse the items in question and streamline our efforts.

A social network analysis of Instagram users, for instance, might utilise people as nodes and their connections (such as friendships) as edges.

## Why is network analysis important?

Network analysis can be a powerful tool for exploring biological systems, social networks, and complex systems in the banking, aviation, and supply chain industries. The procedure for utilising network analysis typically involves collecting data and constructing a network model, followed by analysing the model to identify insights. Once the model has been analysed, the results can be used to optimise the network and facilitate efficient decision-making.

- Social network research is useful for identifying the group’s key influencer.
- It can track how much fuel an airline uses or how far a flight has travelled using its network.
- It may aid in the identification of the kind, value, timing, and geographical location of financial transactions in a network environment.
- It may determine the load capacity, year of manufacturing, maintenance cost, etc., in supply chain networks.

## How do you define geometric deep learning?

In 2017, Bronstein et al. introduced the concept of Geometric Deep Learning in their work titled “Geometric Deep Learning: Going beyond Euclidean Data.” This concept is defined as an “umbrella word encompassing new approaches that seek to extend organised deep neural models to non-Euclidean domains, such as graphs and manifolds.” It serves as an important development in the field of deep learning, opening up new possibilities for the application of deep learning in non-Euclidean domains.

Theoretically, deep geometric learning has the potential to provide a unified mathematical basis for a wide range of neural network designs, including convolutional neural networks (CNNs), recurrent neural networks (RNNs), and transformers. Furthermore, it could enable us to gain specific physics-based knowledge that can be encoded into any architecture.

Geometric Deep Learning (GDL) is an emerging subfield of Machine Learning (ML) that enables researchers to analyse and comprehend complex data structures, such as networks and 3D point clouds. Thanks to the recent advancements in computing power, ML techniques such as Convolutional Neural Networks (CNNs), Long Short-Term Memories (LSTMs), and Generative Adversarial Networks (GANs) have achieved incredibly accurate results on a broad spectrum of tasks.

### Spaces that are Euclidean and those that are not

A Euclidean space is a real vector space that is equipped with an inner product, as defined by the online encyclopaedia Wikipedia. In other words, it is a space that is defined by a set of n-dimensional functions ranging from one-dimensional up to n plus one-dimensional.

In contrast to the non-Euclidean view, which looks to the curvature of a surface, the Euclidean view seeks a flat one. Graphs, networks, manifolds and any other related structures are all examples of non-Euclidean spaces. Content which can be represented by text, sound, or visuals are all examples of Euclidean spaces.

The use of traditional methods that are applicable only to Euclidean data is still commonplace in Machine Learning applications. However, Manifolds are merely one of several possible three-dimensional representations of data. High-dimensional spaces provide a useful analogy to describe this concept, wherein similar forms are grouped together into a single point within a new space. This means that any shape composed of multiple points can be represented by a single point in this space.

The application of deep neural networks to data that is not in Euclidean form necessitates the use of alternative methods that take into account the restrictions that this type of information imposes. Several of these methods include utilising graph-based neural networks, recurrent neural networks, and convolutional neural networks. Through the utilisation of these alternative methods, deep neural networks can be successfully applied to non-Euclidean data.

- There is no agreed-upon method of determining location.
- Deficiency of a definite vector-space structure
- There was no variation in the shift.

## When did geometric deep learning become necessary?

As the complexity of learning increases with the number of dimensions, the amount of data can become overwhelming. To illustrate this, consider a solid ball in three dimensions expanding to an infinite number of dimensions. This will cause the ball’s volume to spread outward from its centre, creating a hollow sphere. Conversely, if the ball is sent to a dimension below our own, the sphere is restored. This illustrates the fact that data in higher dimensions is less dense, making it more difficult to draw meaningful conclusions from it.

Due to the absence of data, it is not possible to identify a solution that is comparable to the other dataset. Nevertheless, many tasks or functions that need to be estimated possess latent regularities that can be explored using geometric principles in lower dimensions, which is a process that can be facilitated by Geometric Deep Learning.

It is difficult for regular deep neural networks to comprehend or learn from graph-structured data. This is because the majority of contemporary neural networks are based on convolutions, which are designed to work best on datasets that follow the principles of Euclidean geometry. Non-Euclidean datasets include, but are not limited to, those involving graphs, manifolds, and other structures that do not share a standard shift-invariant coordinate system.

In order to combat the challenges posed by non-Euclidean environments and expand the capabilities of deep neural networks, researchers have been exploring a new field known as geometric deep learning. This form of deep learning seeks to address the issues that arise in non-Euclidean environments and explore ways to make deep neural networks more versatile and applicable to a variety of settings.

## Distinctions between Geometric Deep Learning and Network Analysis

## Analysing networks

- Avoids deep learning methods in favour of memorising network architecture.
- Provides a more effective method of handling abstract ideas like connections and interactions.
- The application of graph theory can be applied to the study of any type of network, including social networks, medical networks, and supply chains. Social networks are probably the most widely known application of graphs in data science.
- Metrics such as centrality, modularity, and assortativity can be utilised to analyse the structure of networks and gain insights into their properties. Through the application of such metrics, it is possible to obtain a greater understanding of the characteristics of networks.

## The Power of Geometric Deep Learning

- Makes use of deep learning methods on non-Euclidean data sets.
- Geared more at feeding graph or network-structured datasets as input to deep learning issues like regression.
- Graph representation and brain architecture are two of the most investigated topics.

The future of deep learning is inextricably linked to the transition from two-dimensional data to three-dimensional volumetric data. By leveraging the power of machine learning and deep learning, artificial intelligence can be made to approach the level of efficiency achieved by the human brain. Geometric deep learning is making significant progress as a result of the increased availability of non-Euclidean data. For example, technology can now match billions of atoms in order to identify potential novel treatments for current ailments. This could potentially be a life-saving development for chronic disorders which are currently difficult to treat.