Multikernel least mean square algorithm

Felipe A. Tobar, Sun Yuan Kung, Danilo P. Mandic

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


The multikernel least-mean-square algorithm is introduced for adaptive estimation of vector-valued nonlinear and nonstationary signals. This is achieved by mapping the multivariate input data to a Hilbert space of time-varying vector-valued functions, whose inner products (kernels) are combined in an online fashion. The proposed algorithm is equipped with novel adaptive sparsification criteria ensuring a finite dictionary, and is computationally efficient and suitable for nonstationary environments. We also show the ability of the proposed vector-valued reproducing kernel Hilbert space to serve as a feature space for the class of multikernel least-squares algorithms. The benefits of adaptive multikernel (MK) estimation algorithms are illuminated in the nonlinear multivariate adaptive prediction setting. Simulations on nonlinear inertial body sensor signals and nonstationary real-world wind signals of low, medium, and high dynamic regimes support the approach.

Original languageEnglish (US)
Article number6568881
Pages (from-to)265-277
Number of pages13
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number2
StatePublished - Feb 2014

All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence
  • Computer Networks and Communications
  • Computer Science Applications


  • Adaptive sparsification
  • kernel methods
  • least mean square (LMS)
  • multiple kernels
  • vector RKHS
  • wind prediction


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