Monday, July 7, 2014
Freie Universität Berlin
Institut für Informatik
Lecture - 14:15
Detecting hidden structures in (high-dimensional) data is a general and ubiquitous task. Examples include the assessment of insurance risks and the corresponding tariffing, issues of predictive maintenance, supply-chain diversification, medical treatment planning or business demand prediction. There is a wide range of analytical and statistical methods for data analysis and assessment. For instance, in auto insurance, parameter-based tariffing is employed that, in fact, leads to a box-classification of the parameter space followed by rather involved statistics.
In the talk we present a geometric clustering model that provides a shift towards a more involved and data-structure-based dissection of space that allows much simpler and more reliable subsequent statistics.
We prove that the model captures the intuition behind good clusterings and leads to efficient algorithms in practice: also, we report on results for some real-world tasks of the problems mentioned before.
Colloquium - 16:00
Maxwell (1982) defined the notion of "level" for Coxeter systems, and showed that the space-like weights of a level-2 Coxeter system correspond to an infinite ball packing. Inspired by studies of Hohlweg--Labbé--Ripoll (2014) on limit roots, Labbé and the speaker revisited Maxwell's work and reinterpreted the notion of level geometrically. This reinterpretation opens the possibility to extend the notion of level, while most of Maxwell's theorems remains valid. As a consequence, many more infinite ball packings can be generated from Coxeter systems. Notably, these Coxeter systems correspond to infinite-volume Coxeter polytopes, thus extend Vinberg's works. In this talk, we will review Maxwell's result, and see how the notion of "level" is extended. If time permits, I will also sketch the algorithm of enumerating level-2 Coxeter systems.