Multikernel Least Mean Square Algorithm

• Published in: IEEE transaction on neural networks and learning systems Vol. 25; no. 2; pp. 265 - 277
• Main Authors: Tobar, Felipe A., Sun-Yuan Kung, Mandic, Danilo P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2014; Institute of Electrical and Electronics Engineers
• Subjects: Adaptive sparsification; Algorithm design and analysis; Applied sciences; Approximation algorithms; Computer science; control theory; systems; Data processing. List processing. Character string processing; Earth, ocean, space; Estimation; Exact sciences and technology; External geophysics; Hilbert space; Kernel; kernel methods; least mean square (LMS); Least squares approximations; Memory organisation. Data processing; Meteorology; multiple kernels; Software; Training; vector RKHS; wind prediction; Winds and their effects; Dictionaries; Dynamic characteristic; Adaptive algorithm; least mean square (LMS); Non stationary condition; vector RKHS; Adaptive estimation; multiple kernels; Adaptive method; Kernel method; Time varying system; Multidimensional analysis; wind prediction; Least squares method; Adaptive sparsification; Inertial navigation; kernel methods; Sparse representation; Hilbert space; Non linear effect; Meteorology
• ISSN: 2162-237X; 2162-2388; 2162-2388
• DOI: 10.1109/TNNLS.2013.2272594

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.