A comparative study of kernel adaptive filtering algorithms

Kernel adaptive filtering is a growing field of signal processing that is concerned with nonlinear adaptive filtering. When implemented naïvely, the time and memory complexities of these algorithms grow at least linearly with the amount of data processed. A large number of practical solutions have been proposed throughout the last decade, based on sparsification or pruning mechanisms. Nevertheless, there is a lack of understanding of their relative merits, which often depend on the data they operate on. We propose to study the quality of the solution as a function of either the time or the memory complexity. We empirically test six different kernel adaptive filtering algorithms on three different benchmark data sets. We make our code available through an open source toolbox that includes additional algorithms and allows to measure the complexities explicitly in number of floating point operations and bytes needed, respectively.