A0221
Title: Spectral embeddings of correlation networks
Authors: Keith Levin - University of Wisconsin (United States) [presenting]
Abstract: In many applications, weighted networks are constructed based on time series data. Most typically, a time series is associated with each vertex, and edge weights are given by the correlations between time series. The result is a network with a dependency structure among the edges that violates the assumptions of most common network models. Nonetheless, it is common to apply network embedding methods to networks built from correlations. It is shown that this violation of assumptions is not critical. A setup in which a collection of time series signals are observed subject to noise is considered, and a network is constructed based on correlations between the noisy series. It is proven that, under suitable conditions, applying the adjacency spectral embedding to the network of correlations recovers a population embedding of the true time series. Additionally, it is shown that the resulting embedding encodes (up to orthogonal rotation) the Fourier coefficients of the true time series. This appears to be folklore among the signal processing community in the context of principle component analysis, but it is, to the best of knowledge, new to the networks' literature.
