Alexander Gorban (Leicester)

Geometry of Data Sets

Plan
1. The problem
2. Approximation of multidimensional data by low-dimensional objects
2.1. Principal manifolds and elastic maps
2.2. Principal graphs and topological grammars
2.3. Three types of complexity: geometrical, topological and algorithmic
3. Self-simplification of essentially high-dimensional sets
4. Terra Incognita between low-dimensional sets and self-simplified high-dimensional ones.
5. Conclusion and open problems