Gram-Schmidt-Based Sparsification for Kernel Dictionary

Kernel methods have been used to solve nonlinear problems in signal processing and machine learning. To avoid a too large growth of the dictionary, different sparsification techniques have emerged in the literature. In this letter, we propose a Gram-Schmidt-based sparsification technique for kernel dictionaries. It projects the mapped vectors by the kernel into a finite-dimensional subspace spanned by an orthonormal basis and can be used with any Mercer kernel. In particular, we apply it to a least-mean-square-type (LMS) algorithm. Simulation results show that the proposed algorithm presents a lower computational cost when compared to kernel LMS implemented with other sparsification techniques, while maintaining the performance.