This is a typed up copy of my lecture notes from the seminar at Linköping, 2010-08-25. This is not a perfect copy of what was said at the seminar, rather a starting point from which the talk grew.
In my workgroup at Stanford, we focus on topological data analysis — trying to use topological tools to understand, classify and predict data.
Topology gets appropriate for qualitative rather than quantitative properties; since it deals with closeness and not distance; also makes such approaches appropriate where distances exist, but are ill-motivated.
These approaches have already been used successfully, for analyzing
- physiological properties in Diabetes patients
- neural firing patterns in the visual cortex of Macaques
- dense regions in of 3×3 pixel patches from natural (b/w) images
- screening for CO2 adsorbative materials