Geometric Deep Learning: A Brief Study

Working with 2D data is a passé!

Machine learning generally relies on user-defined heuristics to obtain features, thus encoding the structural details of a graph. While 2D is outdated, researchers have started focusing on how they can leverage 3D data to build AI models.

Of late, there has been quite an interest in geometric deep learning across the industry.

What is geometric deep learning?

Geometric deep learning uses complex data defined on graphs and manifolds to learn the signals. In Michael M. Bronstein’s paper, he mentioned how he was able to determine the application of deep learning (DL) in areas like 3D object correspondence, 3D object classification, and graph analytics.

His paper also mentions how research in multiple scientific fields such as brain imaging, network sensors, and physics calls for speculation about non-Euclidean data. Not to mention DL is applicable in multiple areas like natural language processing (NLP), computer vision, and audio analysis that actually needs 2D data or Euclidean data. Now to ease the work of 3D data, researchers have started exploring geometric deep learning. It is an umbrella term used for emerging technologies that further facilitates the study of deep neural models to a non- Euclidean domain like manifolds and graphs. No wonder why researchers are motivated to use this method to address complex problems in computer graphics and computational biology. For instance, the study of protein function and 3D facial recognition.

In such cases, we can try to propose the usage of a deep graph neural network to address even a semi-supervised multi-label classification problem (protein prediction). While for 3D facial recognition, we can use a deep residual B-Spline graph convolution network to have end-to-end training without the need to use hand-crafted feature descriptions.

Can we surpass deep learning methods?

Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), and LSTM are deep learning algorithms that have helped curb problems related to computer vision, language transition, image generation, and speech recognition. And to be precise, these algorithms work well on 2D data and Euclidean. As a result, researchers think that by using 3D data, we can easily boost the accuracy of the findings.

However, there are certain challenges that need to be first addressed. The usage of traditional deep neural networks does not allow parsing data. And since these networks are all based on convolutions, they can only work on Euclidean data.

Now if we’re looking to work in areas such as physics, biology, recommender system, and network science we might need to use non-Euclidean data like manifolds and graphs. Thus, they cannot be stuffed inside two dimensional-spaces.

Here’s a simple example,

A mesh in the computer graphic and graphic specialization is non-Euclidean data, and non-Euclidean data has the capability to represent more complex data as compared to 1D and 2D.
And since the world is inclined toward manifesting 3D, researchers believe that this model has the capability to achieve human-level efficiencies.

Non-Euclidean data, what is it?

One of the perfect examples of a non-Euclidean datatype is a graph. These graphs are composed of nodes that are interconnected with edges and are used to model almost everything and anything.
Let’s hypothetically quote an example,

Consider social networks as a graph and each user as a node, and the way they react with other users are the edges. And the researchers that are modeling the sensors and the computer network are graphs, wherein each signal or any type of communicating signifies vertices in a graph.

Another example of non-Euclidean data is manifolds. These include a large number of geometric surfaces like twists or curves or even diverse 3D shapes. In short, manifolds are just multi-dimensional spaces composed of many points. Now the data used here can come from multiple sources such as numerical values or images.

Applications of geometric deep learning

• 3D modeling
• Molecular modeling

Besides molecular and 3D modeling, geometric deep learning can also help address problems related to physics, biology, and computational chemistry.

During COVID-19, researchers made use of Knowledge Graph Convolutional Network (KGCN) in Relation prediction (a task that helps identify a named relation between two named semantic entities).

Geometric deep learning can also be applicable in drug discovery, wherein these molecules can be represented to be graphs and atoms to be the nodes and bonds as edges.
Conclusion

Geometric deep learning helps address fundamental problems that underlie computational biology and 3D computer vision communities. This model develops methods for protein function prediction to make the most of functional annotation obtained from time-consuming protein function characterization experiments.

As a result, the geometric DL methods are capable of providing solutions to mesh or graph-structured data to perform multiple tasks such as 3D shape recognition and multi-label or multi-class semi-supervised node classification.
Such methods can instigate more people to take full advantage of geometric deep learning to resolve problems in multiple fields underlying manifolds and graphs.