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Barcodes - or How to Discover Shapes in Complex Data

David Meintrup, PhD, Professor of Mathematics, Statistics and Operations Research, Ingolstadt University of Applied Sciences, Germany

Data complexity, for example due to volume, dimensionality, noise or nonlinear relations, can lead to failure of traditional data exploration techniques. Topological data analysis (TDA) is a modern and rapidly expanding field, where methods from algebraic topology, originally an abstract branch of pure mathematics, are applied to data sets to discover shapes hidden in complex data. Although the mathematical methods are advanced, the results of the computations can easily be summarized in graphs, for example in so-called barcodes. In this talk, I will introduce the basic ideas behind TDA, and use JMP to demonstrate how to generate barcodes of real-world data sets. I do not assume any familiarity with mathematics or topology. We will benefit from two key features of JMP: First, the integration of R allows us via JSL to perform the required computations for the barcodes with a recently published R package; second, the graphical and interactive nature of JMP is perfectly suited to display the barcodes and to continue the data exploration.

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