54 research outputs found
Improving Sparsity in Kernel Adaptive Filters Using a Unit-Norm Dictionary
Kernel adaptive filters, a class of adaptive nonlinear time-series models,
are known by their ability to learn expressive autoregressive patterns from
sequential data. However, for trivial monotonic signals, they struggle to
perform accurate predictions and at the same time keep computational complexity
within desired boundaries. This is because new observations are incorporated to
the 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 new
observations against dictionary samples in terms of their unit-norm
(normalised) versions, meaning that new observations that look like previous
samples but have a different magnitude are not added to the dictionary. We
achieve this by proposing the unit-norm Gaussian kernel and define a
sparsification criterion for this novel kernel. This new methodology is
validated on two real-world datasets against standard KAF in terms of the
normalised mean square error and the dictionary size.Comment: Accepted at the IEEE Digital Signal Processing conference 201
A stochastic behavior analysis of stochastic restricted-gradient descent algorithm in reproducing kernel Hilbert spaces
This paper presents a stochastic behavior analysis of a kernel-based
stochastic restricted-gradient descent method. The restricted gradient gives a
steepest ascent direction within the so-called dictionary subspace. The
analysis provides the transient and steady state performance in the mean
squared error criterion. It also includes stability conditions in the mean and
mean-square sense. The present study is based on the analysis of the kernel
normalized least mean square (KNLMS) algorithm initially proposed by Chen et
al. Simulation results validate the analysis
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