# Diffusion Representation for Asymmetric Kernels

arXiv: https://arxiv.org/abs/2401.12251 · HTML: https://mlsanity.com/paper/2401.12251/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 18 references that are in the map.
- First posted on arXiv 20 Jan 2024.

## Builds on (most cited first, 1 of 1)

- [Diffusion Representations](https://mlsanity.com/paper/1511.06208/) (2015)

## Built on by (most cited first, 3 of 3)

- [Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise](https://mlsanity.com/paper/2407.14882/) (2024)
- [KAN versus MLP on Irregular or Noisy Functions](https://mlsanity.com/paper/2408.07906/) (2024)
- [Complex Diffusion Maps with ω-Parameterized Kernels Revealing Inherent Harmonic Representations](https://mlsanity.com/paper/2605.01691/) (2026)

## Abstract (arXiv)

We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work we study data sets in which its geometry structure is induced by an asymmetric kernel. We use a priori coordinate system to represent this geometry and, thus, be able to improve the computational complexity of reducing the dimensionality of data sets. A coordinate system connected to the tensor product of Fourier basis is used to represent the underlying geometric structure obtained by the diffusion-map, thus reducing the dimensionality of the data set and making use of the speedup provided by the two-dimensional Fast Fourier Transform algorithm (2-D FFT). We compare our results with those obtained by other eigenvalue expansions, and verify the efficiency of the algorithms with synthetic data, as well as with real data from applications including climate change studies.