![]() Owing to this sparsity, one cannot find something that is close to the other dataset. What this implies is that higher dimensional data is sparse and it becomes difficult to learn from sparse data. But, if the ball is brought into a lower dimension, the sphere will be refilled. For instance, if a solid ball is taken to infinite dimensions, the volume will shift from the center to the circumference and the ball will become hollow. These are:Ī problem with learning in higher dimensions is that as the dimensions increase, so does the volume. In order to apply deep neural networks on these types of datasets, it’s imperative to use other techniques by keeping the limits of non-Euclidean data in mind. ![]() Here, a shape composed of any point is represented by a single point in this new space, and similar shapes are close to each other. These can be explained as multi-dimensional spaces. There is also a wide range of 3D-shaped representations, one of which is manifolds. Many algorithms used in ML applications are old and only work on Euclidean data. A few examples of Euclidean space are text, audio, images, etc. Some examples of non-Euclidean space are graphs/networks, manifolds, and similar complex structures. ![]() Simply put, it involves the functional of 1D, 2D to n number of dimensions.Įuclidean looks for a flat surface whereas non-Euclidean looks for a curved surface. Euclidean and non-euclidean spacesĪccording to Wikipedia, “A Euclidean space is a finite-dimensional vector space over the reals R, with an inner product”. have helped achieve amazing accuracy on different types of problems. In recent years, algorithms like CNN, long short-term memory (LSTM), generative adversarial network (GAN), etc. can have a common mathematical framework, and ii) if we can have certain prior physical knowledge that can be embedded in any architecture.Ī new field of ML, geometric deep learning can learn from complex data like graphs and multi-dimensional points. Geometric deep learning posits i) whether we can give the world a base where different architectures like convolutional neural networks (CNNs), recurrent neural networks (RNNs), transformers, etc. It is defined as “an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains, such as graphs and manifolds”. Geometric deep learning was first introduced by Bronstein et al in their 2017 paper titled ‘Geometric Deep Learning: Going beyond Euclidean data’. In supply chain networks, it can ascertain the load capacity, year of manufacture, maintenance cost, etc.In banking networks, it can help recognize the type, amount, time, and location of transactions.In airlines' networks, it can identify the fuel usage or distance covered.In a social network, network analysis helps identify the most influential person in the group.It also helps in comprehending networks like those in banking, airlines, and supply chain. It helps in understanding the complex relationships in social networks or in analyzing the biological systems of organisms. Network analysis is beneficial for many applications. Image source : Why do we need network analysis? In this way, we can create a network to make work easier.įor example, if we study a social relationship between Instagram users, nodes will be the target users and edges will be the relationship, such as the friendships between users. They represent the objects we will analyze. Here, the arrows are known as ‘edges’ and represent the relationships between the objects and the circles, known as ‘vertices’ or ‘nodes’. One way to save time is with the help of networks. All this seems like a lot of effort and it is. You then need to check if the work assigned is being performed to par. What do you do? You try to figure out how to make the most out of the men by drafting a schedule detailing what time they will work and on which machines. Let’s understand this better with an example: say you’re a project manager and are asked to use four machines with the help of two men. It is also known as a graph in mathematics. What is a network?Ī network is a symbolic representation of the essential characteristics of a group of objects/people. This article will explore network analysis and geometric deep learning in detail and examine the differences between them. ![]() A common technology used for this is network analysis. How do social networking platforms like Facebook and Instagram generate friend or follower suggestions? What’s more, we tend to know many of these suggestions.
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