- Author: Memming
- Publisher:
- Published date: 2008-07-28
- Expiration date: 2008-07-31
Wednesday, July 30th, at 10:00am in Room NEB 409
The title of my dissertation is "Adaptive filtering in reproducing kernel Hilbert spaces".
The theory of linear adaptive filters has reached maturity, unlike
the field of nonlinear adaptive filters. Although nonlinear adaptive
filters are very useful in nonlinear and nonstationary signal
processing, complexity and non-convexity issues limit existing
algorithms like Volterra series, time-lagged feedforward networks
and Bayesian filtering in an online scenario. Kernel methods are
also nonlinear methods and their solid mathematical foundation and
experimental successes are making them very popular in recent years,
but most of the algorithms use block adaptation and are
computationally very expensive using a large Gram matrix of
dimensionality given by the number of data points; therefore
computationally efficient online algorithms are very much needed for
their useful flexibility in design.
This work develops systematically for the first time a class of
on-line learning algorithms in reproducing kernel Hilbert spaces
(RKHS). The reproducing kernel Hilbert space provides an elegant
means of obtaining nonlinear extensions of linear algorithms
expressed in terms of inner products by using the so-called kernel
trick. We shall present kernel extensions for three well-known
adaptive filtering methods, namely the least-mean-square, the
affine-projection-algorithms and the recursive-least-squares, study
their properties and validate them in real applications.
We shall focus on revealing the unique structures of the linear
adaptive filters and demonstrate how the nonlinear extensions are
derived. We will emphasize the fact that these algorithms
are universal approximators, use convex optimization (no local
minima) and display moderate complexity. Simulations of time series
prediction, nonlinear channel equalization, nonlinear fading channel
tracking, and noise cancelation will be included to illustrate the
applicability and correctness of our theory.
A unifying view of active data selection for kernel
adaptive filters will be introduced and analyzed to address their
growing structure.
