# Efficient KLMS and KRLS Algorithms: A Random Fourier Feature Perspective

arXiv: https://arxiv.org/abs/1606.03685 · HTML: https://mlsanity.com/paper/1606.03685/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2016.

## Built on by (most cited first, 2 of 2)

- [Resource-Aware Asynchronous Online Federated Learning for Nonlinear Regression](https://mlsanity.com/paper/2111.13931/) (2021)
- [Asynchronous Online Federated Learning with Reduced Communication Requirements](https://mlsanity.com/paper/2303.15226/) (2023)

## Abstract (arXiv)

We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space, using random features of the kernel's Fourier transform. The advantage is that, the inner product of the mapped data approximates the kernel function. The resulting "linear" algorithm does not require any form of sparsification, since, in contrast to all existing algorithms, the solution's size remains fixed and does not increase with the iteration steps. As a result, the obtained algorithms are computationally significantly more efficient compared to previously derived variants, while, at the same time, they converge at similar speeds and to similar error floors.