Diffusion Representation for Asymmetric Kernels via Magnetic Transform

Published: 21 Sept 2023, Last Modified: 26 Dec 2023NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: Asymmetric kernels, diffusion maps, magnetic transform, dimension reduction
Abstract: As a nonlinear dimension reduction technique, the diffusion map (DM) has been widely used. In DM, kernels play an important role for capturing the nonlinear relationship of data. However, only symmetric kernels can be used now, which prevents the use of DM in directed graphs, trophic networks, and other real-world scenarios where the intrinsic and extrinsic geometries in data are asymmetric. A promising technique is the magnetic transform which converts an asymmetric matrix to a Hermitian one. However, we are facing essential problems, including how diffusion distance could be preserved and how divergence could be avoided during diffusion process. Via theoretical proof, we successfully establish a diffusion representation framework with the magnetic transform, named MagDM. The effectiveness and robustness for dealing data endowed with asymmetric proximity are demonstrated on three synthetic datasets and two trophic networks.
Supplementary Material: pdf
Submission Number: 6885