Dear all,

this is a reminder for Michael Schaub's talk with the title "How can algebraic topology help with data analysis?" taking place today (27.06) at 12:30 in the B-IT room 5053.2. Please find the details below

--- Abstract ---

Topology is concerned with studying properties of spaces that are preserved under continuous transformation. In particular, using notions from topology we can classify spaces according to certain global properties that are invariant under such transformations. While commonly considered a branch of pure mathematics, the use of topological ideas for data analysis has recently seen a surge of interest under the name "Topological Data Analysis".

Topological Data Analysis (TDA) is typically concerned with high-dimensional point cloud data. TDA aims to extract the "global shape" of this point cloud using computational tools, such as persistent homology, which aim to extract a global topological description of the point cloud. Stated differently, the whole dataset is treated as a single object, which we aim to characterize. This view contrasts somewhat with the standard perspective of unsupervised learning in which the objects of interest are the points (feature vectors of different objects) themselves, and we are interested in characterizing these objects relative to each other.

In this talk, we will provide a brief introduction to topological data analysis and its relation to unsupervised machine learning. We will showcase a few methods that aim to bridge the gap between these two seemingly different viewpoints, and discuss open directions and challenges in this context.

----------------

Part of the programme of the research training group UnRAVeL is a series of lectures on the topics of UnRAVeL’s research thrusts algorithms and complexity, verification, logic and languages, and their application scenarios. Each lecture is given by one of the researchers involved in UnRAVeL.

This years topic is "UnRAVeL - New Ideas!". In these lectures, UnRAVeL professors will discuss current research as well as highlight open problems and offer a perspective on potential future directions.

All interested doctoral researchers and master students are invited to attend the UnRAVeL lecture series 2024 and engage in discussions with researchers and doctoral students. We are looking forward to seeing you at the lectures. Kind regards, Jan-Christoph for the organisation committee