# Kernel Least Mean Square with Adaptive Kernel Size

arXiv: https://arxiv.org/abs/1401.5899 · HTML: https://mlsanity.com/paper/1401.5899/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2014.

## Built on by (most cited first, 4 of 4)

- [Can Transformers Learn Optimal Filtering for Unknown Systems?](https://mlsanity.com/paper/2308.08536/) (2023)
- [Structure Parameter Optimized Kernel Based Online Prediction with a Generalized Optimization Strategy for Nonstationary Time Series](https://mlsanity.com/paper/2108.08180/) (2021)
- [StreaMRAK a Streaming Multi-Resolution Adaptive Kernel Algorithm](https://mlsanity.com/paper/2108.10411/) (2021)
- [Conjugate Gradient Adaptive Learning with Tukey's Biweight M-Estimate](https://mlsanity.com/paper/2203.10205/) (2022)

## Abstract (arXiv)

Kernel adaptive filters (KAF) are a class of powerful nonlinear filters developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is usually the default kernel in KAF algorithms, but selecting the proper kernel size (bandwidth) is still an open important issue especially for learning with small sample sizes. In previous research, the kernel size was set manually or estimated in advance by Silvermans rule based on the sample distribution. This study aims to develop an online technique for optimizing the kernel size of the kernel least mean square (KLMS) algorithm. A sequential optimization strategy is proposed, and a new algorithm is developed, in which the filter weights and the kernel size are both sequentially updated by stochastic gradient algorithms that minimize the mean square error (MSE). Theoretical results on convergence are also presented. The excellent performance of the new algorithm is confirmed by simulations on static function estimation and short term chaotic time series prediction.