AI RESEARCH
Complex Diffusion Maps with $\omega$-Parameterized Kernels Revealing Inherent Harmonic Representations
arXiv CS.LG
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ArXi:2605.01691v1 Announce Type: new In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by the local Gaussian kernel relevant to the heat equation and the nonlocal Schr\"odinger kernel relevant to the Schr\"odinger equation, we propose a unified family of $\omega$-parameterized complex-valued kernels for the trade-off between local and nonlocal connections.