The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
The Kernel Recursive Least-Squares Algorithm
Abstract
We present a nonlinear version of the recursive least squares (RLS) algorithm. Our algorithm performs linear regression in a high-dimensional feature space induced by a Mercer kernel and can therefore be used to recursively construct minimum mean-squared-error solutions to nonlinear least-squares problems that are frequently encountered in signal processing applications. In order to regularize solutions and keep the complexity of the algorithm bounded, we use a sequential sparsification process that admits into the kernel representation a new input sample only if its feature space image cannot be sufficiently well approximated by combining the images of previously admitted samples. This sparsification procedure allows the algorithm to operate online, often in real time. We analyze the behavior of the algorithm, compare its scaling properties to those of support vector machines, and demonstrate its utility in solving two signal processing problems-time-series prediction and channel equalization.
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Cites
The Nature of Statistical Learning Theory
Vapnik, V. N. (1995) · doi:10.1007/978-1-4757-2440-0 · Cited by 39,138
A state-space approach to adaptive RLS filtering
Sayed, A. H., & Kailath, T. (1994) · IEEE Signal Processing Magazine · doi:10.1109/79.295229 · Cited by 449 · cited 1×
“Other directions include the utilization of specialized kernels tailored to specic problems, such as time series prediction; optimization of the kernel function by tuning its hyper-parameters; noise estimation (in the spirit of adaptive RLS); an exponentially weighted version of KRLS; and adaptive model order identica…”
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Cited by
Dlib-ml: A Machine Learning Toolkit
King, D. E. (2009) · doi:10.5555/1577069.1755843 · Cited by 2,777
Multivariate Online Anomaly Detection Using Kernel Recursive Least Squares
Ahmed, T., Coates, M., & Lakhina, A. (2007) · IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications · doi:10.1109/infcom.2007.79 · Cited by 148
Detection for 5G-NOMA: An Online Adaptive Machine Learning Approach
Awan, D. A., Cavalcante, R. L. G., Yukawa, M., & Stanczak, S. (2018) · 2018 IEEE International Conference on Communications (ICC) · doi:10.1109/icc.2018.8422449 · Cited by 37
Secure distributed estimation under Byzantine attack and manipulation attack
Wan, F., Ma, T., Hua, Y., Liao, B., & Qing, X. (2022) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2022.105384 · Cited by 19
Taylor-Informed Indirect Adaptive Predictive Control Using Jacobian-Frozen Affine Predictors
Nguyen, T. W. (2026) · arXiv · doi:10.48550/arxiv.2609.03348
“Polynomial, kernel, and other nonlinear observable representations can thus increase expressiveness while preserving parameter linearity [15]–[17].”
Metadata
- Authors
- Engel, Y., Mannor, S., & Meir, R.
- Venue
- IEEE Transactions on Signal Processing
- Published
- 2004-08
- Volume
- 52
- Issue
- 8
- Pages
- 2275-2285
- ISSN
- 1053-587X (ISSN-L)
- OpenAlex
- W2153290280
- Cited by
- 1,104
- References
- 2
- FWCI
- 21.96
- Type
- journal article
- Language
- en
- Open access
- closed
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