We have developed various analysis approaches based on topology. Our early work explored using topological descriptors for shape analysis ( [mischaikow02]
[niethammer06]
). We have also explored using topology to characterize cell arrangements in the context of breast cancer ( [singh14]
) and as general shape descriptors ( [hofer17b]
). Another focus has been how to combine persistence diagrams with machine learning, in a kernel setting ( [kwitt15]
) as well as using deep learning ( [hofer17a]
[hofer19b]
). As persistence diagrams require the definition of a filtration we have explored learning the corresponding filter function as well ( [hofer20b]
). Most recently we have explored how to use topology to obtain distributions which are beneficial for small-sample learning ( [hofer20a]
).