# Mathematics Colloquia and Seminars

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### Data Analysis through Polyhedral Theory

**Student-Run Applied & Math Seminar**

Speaker: | Steffan Borgwardt, UC Davis |

Location: | 2112 MSB |

Start time: | Wed, Jan 28 2015, 6:10PM |

With geometric modeling techniques, one can represent the feasible solutions of problems in operations research as objects in high-dimensional space. The properties of these objects reveal information about the underlying problems and lead to algorithms. We model an application in the consolidation of farmland and private forests as a clustering problem where the clusters have to adhere to prescribed cluster sizes. In this approach, we connect least-squares assignments, cell complexes, and the studies of polyhedra. The devised methods lead to generalizations of the classical k-means algorithm and algorithms for soft-margin separation in general data analysis tasks. Further, we report on how these results were implemented in practice.