Date
Tuesday, 15 Nov 2016 7:00 PM
Samir Chowdhury is a 4th year mathematics PhD student at Ohio State, specializing in network data analysis He will present a talk with the Columbus Graphistas meetup group titled: “Shape signatures via persistent homology of directed networks”
Description: When faced with the task of analyzing a complex network, a common approach is to extract certain signatures of the network, and then infer properties of the original network from the properties of these signatures. For example, if the network arises from high dimensional data, then one family of interesting signatures would comprise those from which we can infer the “shape” of the network, thus informing our decision on which tools to use in our analysis. In the restricted setting of networks that are also metric spaces, this idea has led to the development of a shape signature known as a persistence barcode, which captures the topology of the space across a range of resolutions and summarizes this information in a 2D representation. However, the standard persistent homology method cannot be applied directly in the setting of general networks (lack of symmetry being one of the obstructions).
In this talk, we will see recently-developed methods for associating persistence barcodes to general networks that are quantifiably robust to noise. This discussion will be motivated by an application to hippocampal networks, which arise from a model describing the neural circuitry that enables an animal to navigate through space.
