Multikernel Least Mean Square Algorithm

Abstract

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.

Kernel methods for short-term spatio-temporal wind prediction

“…While other kernels could be chosen, the Gaussian kernel has a physical interpretation as a measure of similarity, which is fitting here, and has out performed other candidate kernels (triangular and polynomial) in other similar work [9], [13]. The choice, or construction, of kernels is very much an open problem and the subject of ongoing research.…”

“…A sophisticated multi-kernel LMS algorithm is developed [13] which includes this feature, as well as the ability to combine multiple kernel functions. The drawback, of course, is the need to determine the parameters for each of these mechanisms.…”

“…Several linear methods have been 'kernelised' including the popular least means squares (LMS) [8] and recursive least squares (RLS) [9] algorithms, plus extensions, [10]- [13] for example. Reported applications to forecasting include high frequency wind prediction [13], [14] and load forecasting [15], among others.…”

“…Reported applications to forecasting include high frequency wind prediction [13], [14] and load forecasting [15], among others.…”

Quantized mixture kernel least mean square

“…Some of the multi-kernel adaptive filtering methods include multi-kernel least mean square (MKLMS) [1], multi-kernel normalized least mean square (MKNLMS) [2] and mixture kernel least mean square (MxKLMS) [3] algorithm. In addition to tackling this issue of kernel selection, the use of multiple kernels with KAF have shown fast convergence compared to the mono-kernel methods along with an ability to perform better in nonstationary environment.…”