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Kernel adaptive filters, a class of adaptive nonlinear time-series models,are known by their ability to learn expressive autoregressive patterns fromsequential data. However, for trivial monotonic signals, they struggle toperform accurate predictions and at the same time keep computational complexitywithin desired boundaries. This is because new observations are incorporated tothe dictionary when they are far from what the algorithm has seen in the past.We propose a novel approach to kernel adaptive filtering that compares newobservations against dictionary samples in terms of their unit-norm(normalised) versions, meaning that new observations that look like previoussamples but have a different magnitude are not added to the dictionary. Weachieve this by proposing the unit-norm Gaussian kernel and define asparsification criterion for this novel kernel. This new methodology isvalidated on two real-world datasets against standard KAF in terms of thenormalised mean square error and the dictionary size.

Improving Sparsity in Kernel Adaptive Filters Using a Unit-Norm Dictionary