Speaker: Jisu Kim

Abstract: Traditionally, network data is embedded to Euclidean space, such as multidimensional scaling. However, embedding network data into Euclidean space is inappropriate if the degree distribution is heterogeneous. Considering the volume of a ball with increasing radius, then the volume grows polynomially in Euclidean space, while the volume grows exponentially in tree network data, and hence embedding tree network data into Euclidean space distort the distance structure in the data. Embedding network data in hyperbolic space has been vastly tried in visualizing internet network, where the degree of a network is believed to follow a power-law distribution. In this talk, we will review basic concepts in hyperbolic geometry, and see how network data can be embedded into hyperbolic space, or how to model network data using hyperbolic space.