Sparse kernel recursive least squares using L1 regularization and a fixed-point sub-iteration

A new kernel adaptive filtering (KAF) algorithm, namely the sparse kernel recursive least squares (SKRLS), is derived by adding a ℓ₁-norm penalty on the center coefficients to the least squares (LS) cost (i.e. the sum of the squared errors). In each iteration, the center coefficients are updated by a fixed-point sub-iteration. Compared with the original KRLS algorithm, the proposed algorithm can produce a much sparser network, in which many coefficients are negligibly small. A much more compact structure can thus be achieved by pruning these negligible centers. Simulation results show that the SKRLS performs very well, yielding a very sparse network while preserving a desirable performance.