# SCCS Kolloquium

The SCCS Colloquium is a forum giving students, guests, and members of the chair the opportunity to present their research insights, results, and challenges. Do you need ideas for your thesis topic? Do you want to meet your potential supervisor? Do you want to discuss your research with a diverse group of researchers, rehearse your conference talk, or simply cheer for your colleagues? Then this is the right place for you (and you are also welcome to bring your friends along).

# Veselina Vazova: Scalable Manifold Learning through Landmark Diffusion

Manifold learning by spectral embedding is a technique that can be used for non-linear dimensionality reduction. By extracting the spectral properties of high-dimensional data, the intrinsic manifold where the data is located on can be fitted into a lower dimension.
A newly proposed algorithm in the field of spectral embedding that has the goal of providing a scalable and robust approach to dimensionality reduction is Roseland.
The algorithm takes two sets: the data set and the landmark set and returns an embedding of the data set in a desired lower dimension q'. To achieve this, the data is first fitted: a landmark-set affinity matrix is computed that represents the affinities between the points in the data set and the points in the landmark set. After normalization of the resulting matrix, the singular value decomposition of the normalized matrix is computed. Using the singular vectors and the singular values, the Roseland embedding for a given diffusion time t is finally computed.
In its core, the algorithm is similar to the Diffusion Maps (DM) algorithm, whereas the main differences lie in the affinity matrix and the decomposition. In Diffusion Maps, the affinities between the data points themselves are calculated, without first "detouring" through a landmark set. Instead of the singular value decomposition, the eigendecomposition is performed. Since the affinity matrix of the DM is larger than the Roseland landmark-set affinity matrix, Roseland fits the data set faster than DM.
In this thesis, we implement the Roseland algorithm in the datafold package. We aim to show that Roseland can be used in the same context of dimensionality reduction as Diffusion Maps. We consider different approaches to constructing the landmark set when it is not given, and we compare the results. Finally, we evaluate the efficiency of the novel algorithm by comparing it to the performance of Diffusion Maps.

Bachelor's thesis submission talk (Informatics). Veselina is advised by Dr. Felix Dietrich.

You don't want to miss a talk? Subscribe to our mailing list and our Colloquium calendar .

## Contribute a talk

To register and schedule a talk, you should fill the form Colloquium Registration at least two weeks before the earliest preferred date. Keep in mind that we only have limited slots, so please plan your presentation early. In special cases, contact colloquium@mailsccs.in.tum.de.

You can try the platform beforehand using Try BigBlueButton, or by starting your own room at the RBG BBB. For troubleshooting, you could also try the WebRTC Troubleshooter.

## When should I present?

We invite students doing their Bachelor's or Master's thesis, as well as IDP, Guided Research, or similar projects at SCCS to give one 20min presentation to discuss their results and potential future work. The time for this is typically after submitting your final text. Check also with your study program regarding any requirements for a final presentation of your project work.

New: In regular times, we will now have slots for presenting early stage projects (talk time 2-10min). This is an optional opportunity for getting additional feedback early and there is no strict timeline.

Apart from students, we also welcome doctoral candidates and guests to present their projects.

## What should I expect during the Colloquium?

During the colloquium, things usually go as follows:

• 10min before the colloquium starts, the speakers setup their equipment with the help of the moderator. The moderator currently is Gerasimos Chourdakis. Make sure to be using an easily identifiable name in the online session's waiting room.
• The colloquium starts with an introduction to the agenda and the moderator asks the speaker's advisor/host to put the talk into context.
• Your talk starts. The scheduled time for your talk is normally 20min with additional 5-10min for discussion.
• The moderator keeps track of the time and will signal 2min before the end of time (e.g. by turning on their video).
• During the discussion session, the audience can ask questions, which are meant for clarification or for putting the talk into context. The audience can also ask questions in the chat.
• Congratulations! Your talk is over and it's now time to celebrate! Have you already tried the parabolic slides that bring you from the third floor to the Magistrale?

## How can I prepare a great talk?

Do you remember a talk that made you feel very happy for attending? Do you also remember a talk that confused you? What made these two experiences different?

Here are a few things to check if you want to improve your presentation:

• What is the main idea that you want people to remember after your presentation? Do you make it crystal-clear? How quickly are you arriving to it?
• Which aspects of your work can you cover in the given time frame, with a reasonable pace and good depth?
• What can you leave out (but maybe have as back-up slides) to not confuse or overwhelm the audience?
• How are you investing the crucial first two minutes of your presentation?
• How much content do you have on your slides? Is all of it important? Will the audience know which part of a slide to look at? Will somebody from the last row be able to read the content? Will somebody with limited experience in your field have time to understand what is going on?
• Are the figures clear? Are you explaining the axes or any other features clearly?

In any case, make sure to start preparing your talk early enough so that you can potentially discuss it, rehearse it, and improve it.

Here are a few good videos to find out more:

Did you know that the TUM English Writing Center can also help you with writing good slides?

## Work with us!

Do your thesis/student project in Informatics / Mathematics / Physics: Student Projects at the SCCS.