# 2024: Graphs and Applications

The 24th edition of the Geilo Winter School will take place in Geilo, Norway from Sunday January 21 to Friday January 26, 2024. The topic of the school will be graphs and applications.

## Program

Benjamin Ricaud

The course is a guided tour inside the world of graphs and data over graphs. We will go through some of the theory and practive to discover the key concepts behind graph data mining and graph machine learning. We will see the central role played by the Graph Laplacian matrix and get a sharper view on the connection between the graph structure and the data. The lectures will be a mix of theory and practice. For the practice we will use jupyter notebooks, Python and the networkx module. Some graph visualizations may be done with the open-source software Gephi.

1. Graph: spectral graph theory

As a first step, we will explore the properties of the Laplacian matrix of a graph, its eigenvalues and eigenvectors. We will see some connection with Physics and with two powerful Data Science methods: Laplacian eigenmaps and spectral clustering. The aim is to understand better the information embedded in a graph and how to make use of it. This will prepare us for the next step.

2. Graphs and data: graph signal processing and graph Fourier transform

Graph signal processing starts when you add values to the nodes of a graph and combine the values with the graph structure. This can be generalized to vector of features associated to each node, which is at the heart of graph machine learning and graph neural networks. We will see what is the Graph Fourier transformation, the important differences with the standard setting and its relationship with graph machine learning.

3. Graphs, data and evolution: variation in data and variation in the graph

In this lecture we will cover some dynamical processes over graphs. We will start with standard ones such as PageRank and label propagation, where information is diffused over the graph. These methods are tightly connected to the topics of the first two lectures. We will then see how to deal with evolving data and evolving graphs. this will be connected to some of the recent advances in graph machine learning.

Raghavendra Selvan

All three lectures will consist of an in-plenum session (~45m) and an exercise session (~45min). We will heavily rely on Pytorch Geometric, and participants are encouraged to set-up a python environment that has Pytorch Geometric installed.

1. Introduction to Graph ML

Machine Learning (ML) can be viewed as learning from data.  But learning from graphs requires specialized adaptations of existing notions within Euclidean deep learning (DL). This lecture will cover basics of DL, graph representations for ML, and bridging classical ML with Graph ML.

2. Supervised and Unsupervised Graph Learning

In this lecture, different classes of graph learning in the presence and absence of labeled data will be presented. We will examine some of the fundamental classes of graph neural networks and get a peek into the exciting applications that GNNs are driving forward.

3. Going forward with Graph ML

Graph ML has profound connections with geometry, and even the recent class of transformer-models. In this lecture, we will present a unified view of ML using GNNs and discuss some of the challenges and caveats when using Graph ML.

Mridul Seth

During the 3 lectures we will cover the basics of graph theory and learn how to use python and NetworkX to model and analyze our data as a graph.

1. Graph Theory and NetworkX API

• A quick introduction to graph theory and thinking with graphs.
• Modeling data as graphs in python using the NetworkX API.

2. Classic graph algorithms

• Which node is the most important one? Centrality measures in graphs.
• Where should I jump next? Paths in graphs.
• Who should I be friends with? Structures inside graphs.

3. Graph viz and Dispatching with NetworkX

• Hairballs and visualization of graphs.
• Speeding up NetworkX code with dispatching to CuGraph (GPU) and GraphBLAS(CPU).

## Schedule

All lectures will take place at Dr. Holms Hotel in Geilo, Norway. Participants will receive more information by email. Exact times will also appear in the following schedule once the program is completely finalized.

Booking a train/checking the train schedule is done through Vy. The hotel is a walkable distance from the train station in Geilo.

You can subscribe to the above calendar by using this link.

## Lecturers

### Benjamin Ricaud

Benjamin Ricaud is associate professor at the Arctic University of Norway, Tromsø. He is a member of the machine learning group at UiT. His research topics are related to machine learning, graphs and graph machine learning. Prior to arriving in Norway two years ago, he was a researcher at EPFL, Switzerland, where he contributed to developing graph signal processing and graph machine learning.

### Raghavendra Selvan

Raghavendra Selvan (Raghav) is currently an Assistant Professor at Machine Learning (ML) Section, Dept. of Computer Science, University of Copenhagen. He is also affiliated with Department of Neuroscience and the Data Science Laboratory. His current research interests are broadly pertaining Resource Efficient ML, Medical Image Analysis with ML, and Graph Neural Networks. Of late, another overarching theme of his research interests lie at the intersection of sustainability and ML where he is interested in investigating sustainability with ML, and also the sustainability of ML.

### Mridul Seth

Mridul Seth is a core developer of NetworkX and currently working on the project funded through a grant (EOSS) from Chan Zuckerberg Initiative. He is also collaborating with folks from the Scientific Python project and Anaconda to help develop and maintain the broader Scientific Open Source ecosystem. To share his love of Python and Network Science, he has presented workshops at multiple conferences like PyCon, (Euro)SciPy, PyData London and many more!

## Costs and registration

There is no registration fee for the winter school, but participants must cover their own travel costs and hotel costs at Dr. Holms. Signups are now closed - if you'd still like to attend get in touch with us at .

## Room allocation

The winter school has a limited number of rooms at Dr. Holms which will be reserved on a first come first serve basis. We have in previous years exceeded our room allocation, so please register as early as possible!

## Posters

We welcome all posters to be presented, and will make space in the program for a poster session in which participants can present their work to colleagues and others. The aim of the session is to make new contacts and share your research, and it is an informal event. You need to indicate in your registration if you want to present a poster during the poster session. Please limit your poster to A0 in portrait orientation.

## Organizing Committee

The organizing committee for the Geilo Winter School consists of

• Torkel Andreas Haufmann, Research Manager (Department of Mathematics and Cybernetics, SINTEF).
• Øystein Klemetsdal, Research Scientist (Department of Mathematics and Cybernetics, SINTEF).
• Filippo Remonato, Research Scientist (Department of Mathematics and Cybernetics, SINTEF).

To get in touch with the committee, send an email .