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MIA Talks

Topological data analysis: What can persistent homology see?

October 12, 2016
Dept. of Mathematics, Warren Center for Network and Data Sciences, University of Pennsylvania

The usual framework for TDA takes as its starting point that a data set is sampled (noisily) from a manifold embedded in a high dimensional space, and provides a reconstruction of topological features of that manifold. However, the underlying algebraic topology can be applied to data in a much broader sense, carries much richer information about the system than just the barcodes, and can be fine-tuned so it sees only features of the data we want it to see. I will discuss this framework broadly, with focus on few of these alternative viewpoints, including applications to neuroscience and matrix factorization.