We will introduce elements of the theory of topological data analysis (TDA) and show the participants how to apply standard topological data pipelines, such as persistent homology and Mapper, to datasets of different origin (spatial data, word embeddings, brain networks). We will also show how TDA can be used for feature engineering or as a preprocessing step in standard machine learning pipelines, and how to assess the significance of the unearthed features. Finally, since TDA outputs can sometimes be of difficult interpretation, we will guide the participants through some common pitfalls in the interpretation and provide some examples of successful applications.
The workshop will consist of: an introductory section on TDA methods; hands-on exercises focused on implementing the required pipelines and performing the analysis; a session on validation methods and null models for TDA; a session on strengths and weaknesses of topological methods.
We will use Jupyter notebooks in Python for analysis and visualization.