on graphs and in 3DFlawnson TongBlockedUnblockFollowFollowingApr 18The vast majority of machine learning — and therefore deep learning — is performed on Euclidean data.

This includes datatypes in the 1-dimensional and 2-dimensional domain.

But we don’t exist in a 1D or 2D world.

All that we can perceive exists in 3D.

It’s about time artificial intelligence gets to our level.

Euclidean data is what we’ve all seen being used in machine learning.

We perceive it in numbers, images, text, etc:Euclidean DataIn contrast, Non-Euclidean data is closer to reality, as it captures far more information than 1D or 2D ever could:Non-Euclidean DataBuilding on this datatype, Geometric Deep Learning (GDL) is the niche field of deep learning that aims to cater neural networks to learn from non-euclidean data.

This includes data from tasks and industries like:Social media networksTraffic and transportationDelivery and distributionEnergy grid managementGenetic sequence mapsProtein Interaction networksNeural maps and imaging3D image and object processingThese are collected in the form of manifolds, point-clouds, and the main focus of this series: graphs.

Graphs allow us to captivate individual features, while also providing information regarding structure and relationships.

A Dynamic graphThere are various types of graphs, each with a set of rules, properties, and possible actions.

Graph theory is the study of graphs and what we can learn from them.

This will be covered in the next part of this series.

For a concrete example of how Graph Learning can greatly improve existing machine learning tasks we can take a look at the computational sciences.

One of the bottlenecks in computational chemistry, biology, and physics is the representation concepts, entities, and interactions.

The nature of science is empirical and is therefore the result of many external factors and relationships.

Here are some examples of where this is most obvious:Protein interactions networksNeural networksAtoms and moleculesFeynman diagramsOur current methods of representing these concepts computationally can be considered “lossy”, as in we lose alot of valuable information.

For example, using a SMILES string to represent a molecule has it’s benefits of being easy to compute, but at the expense of losing out on structural properties that are inherent to the molecule it aims to represent.

But by treating atoms as nodes, and bonds as edges, we can save structural information that can be used downstream in prediction or classification.

As an example of how Geometric Deep Learning lets us learn from datatypes never used before, consider a person posing for a camera:People pose for a 2D image capture (Courtesy of the MoNet team)This image is 2D, although in our minds, we are aware that it represents a 3D person.

Our current algorithms, namely CNNs, are pretty good at predicting labels like the person posing and/or the kinds of poses given only a 2D image.

The difficulty arises when poses become extreme and the angle is no longer fixed.

Often times there may be clothing or objects in an image that obstruct the view of an algorithm, making it difficult to predict the pose.

Now imagine a 3D model of this same person making poses:The CNN could be run on the object itself rather than an image of the object.

(Courtesy of the MoNet team)Unfortunately, Medium doesn’t support 3D images until 2027, but we can use our imagination.

Instead of learning from a 2D representation, which restricts us to a single perspective angle, imagine if we could run a CNN directly on the object itself.

Analogously to traditional CNNs, the filter would pass through every “pixel” represented as a node in a point-cloud (basically a graph that wraps around the 3D object).

Every corner and crevice would be considered.

In short, the comparison to be made is:Predicting who someone is given a picture of them versus predicting who someone is given a 3D model of them.

And as our 3D modelling, design, and printing technology improves, one could imagine how this would yield far more accurate and precise results.

Into the differencesDimensions in the traditional senseThe notion of dimensionality is already commonly used in data science and machine learning, where the number of “dimensions” correlates to the number of features/attributes per example/datapoint in a dataset.

The Hughes phenomenon (Courtesy of Visiondummy)While at first, the performance of machine learning algorithms spikes, after a certain number of features (dimensions), the performance levels off.

This is known as the curse of dimensionality.

Geometric Deep Learning doesn’t solve this problem.

Rather, algorithms like graph convolutions reduces the performance penalties incurred when using datatypes that have alot of features since instead of storing relational data independently as another feature.

With graph convolutions, all the edge features in a node’s neighborhood is aggregated together.

More on this later in the series.

What we talk about when we talk about dimensionalityYou can throw out your understanding of dimensionality in the Euclidean sense.

Methods like PCA are different in non-euclidean terms.

All dimension-dependant operations which are performed in deep learning is relative to the Euclidean domain.

But we are working in the non-euclidean domain, so we won’t be needing our previous understanding.

As explained by this awesome StackExchange A.

I stream post, Non-Euclidean geometry can be summed up with the phrase:“the shortest path between 2 points isn’t necessarily a straight line”.

Other strange rules include:Interior angles of triangles always add up to more than 180 degreesParallel lines can meet, either infinitely or neverQuadrilateral shapes can have curved lines as sidesIn the non-euclidean domain, these are facts.

To understand how something that seems so absurd could still hold true, here’s Carl Sagan explaining how higher dimensions are perceived by beings of lower dimensions.

TL;DW some things can only exist in thought and be expressed as math.

There isn’t a need to fully understand non-euclidean geometry, merely acknowledging that the rules are a bit different is enough to understand how Geometric Deep Learning works.

The standard vs the newMachine learning has centered around Deep learning, which itself is centered by a handful of commonly used algorithms.

Each algorithm roughly specializes in a specific datatype.

Just as RNNs were built for time-dependent data and CNNs for image-type data, Graph neural networks (GNNs) are a type of Geometric Deep Learning algorithm built for graphs and networks.

As said by Graham Ganssle, Head of Data Science at Expero:Graph convolutional networks are the best thing since sliced bread because they allow algos to analyze information in its native form rather than requiring an arbitrary representation of that same information in lower dimensional space which destroys the relationship between the data samples thus negating your conclusions.

— Graham Ganssle (in a Tweet)Graph convolutional networks, or GCNs is to a Graph neural networks what CNNs are to Vanialla neural networks.

The implication of this new method makes a big difference; we are no longer forced to leave behind important information in a dataset.

Information like structure, relationships, and connections, which are integral to some of the most important data-giving tasks and industries like transportation, social media, and protein networks.

In short, the field of Geometric Deep Learning has 3 main contributions:We can make use of non-euclidean dataWe can maximize on the information from the data we collectWe can use this data to teach machine learning algorithmsIn a paper where it was demonstrated that graph learning algorithms can be generalized and made modular for a various applications and augmentations, it was said that:We argue for making generalization a top priority for AI, and advocate for embracing integrative approaches which draw on ideas from human cognition, traditional computer science, standard engineering practice, and modern deep learning.

— DeepMind, Google Brain, MIT, and the University of EdinburghIn other words, we have have much to expect from Geometric Deep Learning.

In EssenceThe notion of relationships, connections, and shared properties is a concept that is naturally occurring in humans and nature.

Understanding and learning from these connections is something we take for granted.

Geometric Deep Learning is significant because it allows us to take advantage of data with inherent relationships, connections, and shared properties.

Key TakeawaysThe Euclidean domain and non-euclidean domain have different rules that are followed; data in each domain specializes in certain formats (image, text vs graphs, manifolds) and convey differing amounts of informationGeometric Deep Learning is the class of Deep Learning that can operate on the non-euclidean domain with the goal of teaching models how to perform predictions and classifications on relational datatypesThe difference between traditional Deep Learning and Geometric Deep Learning can be illustrated by imagining the accuracy between scanning an image of a person versus scanning the surface of the person themselves.

In traditional Deep Learning, dimensionality is directly correlated with the number of features in the data whereas in Geometric Deep Learning, it refers to the type of the data itself, not the number of features it has.

One of the reasons I set out to write about Geometric Deep Learning because there is hardly any entry level resources, tutorial, or guides for this relatively new niche.

With that ultimate goal in mind, I am writing a series of articles all on Graph Learning.

Throughout, we will cover the nitty gritty of the various methods and algorithms in Graph Learning.

All articles can be accessed here:Graph Learning — Part 0: Graph Theory and Deep Learning prerequisitesGraph Learning — Part 1: A survey of the architectures and modelsGraph Learning — Part 2: Building a basic Graph Convolutional NetworkGraph Learning — Part 3: Building a dataset from scratch and training a GCNGraph Learning — Part 4: Applications of Geometric Deep LearningGraph Learning — Part 5: Problems and Future workGraph Learning — Part 6: Tools, Resources, Research, and DatasetsNeed to see more content like this?Follow me on LinkedIn, Facebook, Instagram, and of course, Medium for more content.

All my content is on my website and all my projects are on GitHubI’m always looking to meet new people, collaborate, or learn something new so feel free to reach out to flawnsontong1@gmail.

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