Towards multiparameter persistent homology descriptors for machine learning
The developpement of data science and data acquisition technologies in the industry in the last decade led to the emergence of enormous datasets. In the context of Machine Learning, this induces several challenges both on the theorical side, as well as on the practical side. On one hand, the so-called curse of dimensionality prevents the construction of usual statistics directly from such datasets, and on the other hand, the size of these datasets constraints the complexity of algorithms that we can use. Topological Data Analysis (TDA) aims at proposing solutions to these issues for geometrical datasets, by computing concise and interpretable geometric features that can be used afterwards along with various machine learning techniques, such as classification, statistical regularization, clustering, visualization. Surprisingly, several general machine learning problems and data sets, ranging from time series to medical images, can be framed as geometrical questions. This wide range of applications has highlighted the usefulness of TDA tools, which attracted a lot of attention over the last years. In this talk, I will introduce the main descriptor of TDA, Persistent Homology, as well as its generalization called Multiparameter Persistent Homology.
