# Spectral Analysis of Symmetric and Anti-Symmetric Pairwise Kernels

arXiv: https://arxiv.org/abs/1506.05950 · HTML: https://mlsanity.com/paper/1506.05950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2015.

## Built on by (most cited first, 1 of 1)

- [Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry](https://mlsanity.com/paper/2103.17233/) (2021)

## Abstract (arXiv)

We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or anti-symmetrizing pairwise kernel functions. Through spectral analysis, we show that these transformations reduce the kernel's effective dimension. Further, we provide an analysis of the approximation properties of the resulting kernels, and bound the regularization bias of the kernels in terms of the corresponding bias of the original kernel.