# Learning with Asymmetric Kernels: Least Squares and Feature Interpretation

arXiv: https://arxiv.org/abs/2202.01397 · HTML: https://mlsanity.com/paper/2202.01397/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 67 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond](https://mlsanity.com/paper/2004.11154/) (2020)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [On Reproducing Kernel Banach Spaces: Generic Definitions and Unified Framework of Constructions](https://mlsanity.com/paper/1901.01002/) (2019)
- [Node Representation Learning for Directed Graphs](https://mlsanity.com/paper/1810.09176/) (2018)
- [Asymmetric kernel in Gaussian Processes for learning target variance](https://mlsanity.com/paper/1803.06952/) (2018)

## Built on by (most cited first, 11 of 11)

- [A Kernel-Based View of Language Model Fine-Tuning](https://mlsanity.com/paper/2210.05643/) (2022)
- [Scalable Neural Network Kernels](https://mlsanity.com/paper/2310.13225/) (2023)
- [Random Fourier Features for Asymmetric Kernels](https://mlsanity.com/paper/2209.08461/) (2022)
- [Nonlinear SVD with Asymmetric Kernels: feature learning and asymmetric Nystr"om method](https://mlsanity.com/paper/2306.07040/) (2023)
- [Learning in Feature Spaces via Coupled Covariances: Asymmetric Kernel SVD and Nystr"om method](https://mlsanity.com/paper/2406.08748/) (2024)
- [HeNCler: Node Clustering in Heterophilous Graphs via Learned Asymmetric Similarity](https://mlsanity.com/paper/2405.17050/) (2024)
- [Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning](https://mlsanity.com/paper/2406.01435/) (2024)
- [Enhancing Kernel Flexibility via Learning Asymmetric Locally-Adaptive Kernels](https://mlsanity.com/paper/2310.05236/) (2023)
- [Revisiting Forest Proximities via Sparse Leaf-Incidence Kernels](https://mlsanity.com/paper/2601.02735/) (2026)
- [A Kernelizable Primal-Dual Formulation of the Multilinear Singular Value Decomposition](https://mlsanity.com/paper/2410.10504/) (2024)
- [Sparse and robust geometric twin support vector machine via asymmetric RoBoSS loss function](https://mlsanity.com/paper/2608.11567/) (2026)

## Abstract (arXiv)

Asymmetric kernels naturally exist in real life, e.g., for conditional probability and directed graphs. However, most of the existing kernel-based learning methods require kernels to be symmetric, which prevents the use of asymmetric kernels. This paper addresses the asymmetric kernel-based learning in the framework of the least squares support vector machine named AsK-LS, resulting in the first classification method that can utilize asymmetric kernels directly. We will show that AsK-LS can learn with asymmetric features, namely source and target features, while the kernel trick remains applicable, i.e., the source and target features exist but are not necessarily known. Besides, the computational burden of AsK-LS is as cheap as dealing with symmetric kernels. Experimental results on the Corel database, directed graphs, and the UCI database will show that in the case asymmetric information is crucial, the proposed AsK-LS can learn with asymmetric kernels and performs much better than the existing kernel methods that have to do symmetrization to accommodate asymmetric kernels.