Multiscale network analysis through tail-greedy bottom-up approximation, with applications in neuroscience

We propose the TGUH (Tail-Greedy Unbalanced Haar) transform for networks, which results in an orthonormal, adaptive decomposition of the network adjacency matrix into Haar-wavelet like components. The `tail-greediness' of the algorithm - indicating multiple greedy steps are taken in a single pass through the data - enables both fast computation and consistent estimation of network signals. We focus on development of our multiscale network decomposition and a corresponding method for network signal denoising. Moreover, we establish consistency of our resulting denoising methodology, present numerical simulations illustrating compression, and illustrate through application to signals on diffusion tensor imaging (DTI) networks.