Multikernel least squares estimation

Abstract

The multikernel least squares (MKLS) algorithm for multivariate nonlinear estimation of vector-valued signals is introduced. This is achieved by finding optimal combinations of subkernels, in the least squares sense, which are specific for different regions of the input space. Sufficient conditions for the existence of Wiener solutions for both the monokernel and multikernel approaches are provided, and uniqueness of the multikernel structure is illuminated. The ability of the proposed MKLS to replicate non-homogeneous nonlinear multivariate mappings is illustrated both analytically and by comparison with its monokernel counterpart for the prediction of synthetic benchmark data and real-world body sensor multivariate data.

Quaternion Reproducing Kernel Hilbert Spaces: Existence and Uniqueness Conditions

“…The structure of the multikernel concept is intuitive and its ability to capture different types of nonlinear behaviour from the input data has been documented in [21], [22], [42], and [43]. Furthermore, the approach is flexible, since the number of subkernels does not depend on the dimension of the input or output data (L is not necessarily equal to n), but is only set as a design parameter based on the observed nonlinear features of the data and the available computational power.…”

“…An example of multikernel regression which employs an LMS update strategy to predict wind can be found in [21], where each subkernel within the multikernel approach accounts for different dynamical properties of the 3D wind. For additional insight into multikernel learning see [22], [42], [44].…”

“…Kernel algorithms operating in complex-valued feature spaces are mostly of a complex kernel least mean square type [16]- [18]. Furthermore, higherdimensional extensions of RKHS (in real vector-valued feature spaces [19], [20]) have also been developed and form the basis for both the multikernel least squares and multikernel least mean square [21], [22].…”

Convex combinations of kernel adaptive filters

“…The multikernel least-mean-square algorithm (MKLMS) was independently proposed in [17][18][19] and [20,21], with distinct functional frameworks and implementations. The former uses block 1-norm regularization This work was partially supported by the National Natural Science Foundation of China (61271415).…”