Algebraic topology for understanding data
Adwaith Vijayakumar (~adwaith) |
Every data which we encounter in nature has an underlying shape and extracting this shape provides us with meaningful information about the topology of data.
In many practical applications involving classification and quantification, an idea regarding the underlying topology of the manifold from which the data points are sampled is necessary. Computational algebraic topology involves combining group theory , topology and linear algebra for extracting the topology underlying behind a noisy samples from the underlying manifold. A lot of packages has recently been developed in the area of computational topology. The talk presents a brief introduction to basics of computational topology and portrays how the existing python tools available for computational topology can be utilized for various applications.
- A gentle introduction to topology and algebra (10 min)
- How to associate algebraic structures to topological spaces (5 min)
- Analysing sampled version of topological spaces using a boundary homomorphism (5 min)
- Computing betti numbers using python (5 min)
A brief idea about metric topology and linear algebra.
The link to the slide is provided below https://drive.google.com/file/d/1bvUvuqO-k4nJxQTXAfFFHY5_zXo6ERzo/view?usp=sharing
Adwaith Vijayakumar is a Direct PhD student at IIT Bombay. He works in the area of Singular value decomposition and Computational topology.