Serdecznie zapraszamy na nasze spotkanie w poniedziałek 9 grudnia 2019, odbędzie się ono o 18.oo w sali 106 ETI PG.
Prelegentem będzie Patryk Wyżgowski.
Temat prelekcji to: Topologiczna analiza danych – Homologia persystentna
Parę słów od Prelegenta (ang.):
The presentation is an introduction to Topological Data Analysis covering both theoretical background and applications both from the past and the time near presentation (some 2019 publications discussed on the session).
The agenda comes as follows:
- Topology as a branch of mathematics treating generalizations of shapes and their continuous deformations.
- Representations of topological spaces and simplicial complexes (graph generalizations) as great mathematical tool for computational topology.
- Simplicial complex from point cloud data – Nerve theorem as a bridge between continuous and combinatorial space description.
- Betti numbers (ranks of Homology groups) as invariant simplicial complex and equivalent topological (under homotopy equivalence)
- Peristent homology fixing the problem of covering radius choice.
- Barcodes and persistence diagrams for persitent homology visualisation.
- Some human-in-a-loop applications (exploratory data analysis)
- Some advanced applications (machine learning tasks, new kind of features – multi-scale topological features, time series analysis – – classification and quasi-atractor identification)
- *Klein Bottle in natural image patches space (2-dimensional surface in 8 dimensional space that parametrizes patches space)