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Mauro Maggioni : Random walks on data sets in high dimensions, and a new hot system of coordinates

I will motivate the need to analyze data sets in high dimensions, their geometrical properties and the properties of functions on them with several examples. I will focus on techniques based on random walks on data sets, and introduce a new nonlinear system of coordinates based on heat kernels, similar in spirit to the GPS system, for parametrizing data sets. If time allows, I will also discuss simple but surprisingly successful applications of the heat kernel to fit functions on data, that performs at the state-of-art or better as a classifier on a variety of benchmark data sets.

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