Geometry of Data

Abstract: Collecting and more importantly analysing (big) sets of data is one of the greatest challenges of our society. One possible tool is geometrical data analysis, i.e., appropriately embed the data points on a geometrical object, for example using polynomials. Many problems in science can be described by polynomial equations. The solution set of the corresponding polynomial system is referred to as an algebraic geometrical model for the problem. We will see how geometrical modeling is used in fields like Kinematics and Biochemistry. Sampling, i.e., appropriately choosing data points on the model, is a powerful technique in the study of geometrical models. The key challenge is to estimate the right density of the data points in order to recover the shape of the model. An exciting and surprising aspect of the story is that classical geometrical tools (from early 1900) have shown to be effective and essential for data analysis.

Mathematics

Audience: general audience

VCU Mathematics and Applied Mathematics Colloquium Series

Series comments: A series of public lectures in Mathematics and Applied Mathematics from Virginia Commonwealth University.

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