25 research outputs found
Study of Set-Membership Kernel Adaptive Algorithms and Applications
Adaptive algorithms based on kernel structures have been a topic of
significant research over the past few years. The main advantage is that they
form a family of universal approximators, offering an elegant solution to
problems with nonlinearities. Nevertheless these methods deal with kernel
expansions, creating a growing structure also known as dictionary, whose size
depends on the number of new inputs. In this paper we derive the set-membership
kernel-based normalized least-mean square (SM-NKLMS) algorithm, which is
capable of limiting the size of the dictionary created in stationary
environments. We also derive as an extension the set-membership kernelized
affine projection (SM-KAP) algorithm. Finally several experiments are presented
to compare the proposed SM-NKLMS and SM-KAP algorithms to the existing methods.Comment: 4 figures, 6 page
Kernel Least Mean Square with Adaptive Kernel Size
Kernel adaptive filters (KAF) are a class of powerful nonlinear filters
developed in Reproducing Kernel Hilbert Space (RKHS). The Gaussian kernel is
usually the default kernel in KAF algorithms, but selecting the proper kernel
size (bandwidth) is still an open important issue especially for learning with
small sample sizes. In previous research, the kernel size was set manually or
estimated in advance by Silvermans rule based on the sample distribution. This
study aims to develop an online technique for optimizing the kernel size of the
kernel least mean square (KLMS) algorithm. A sequential optimization strategy
is proposed, and a new algorithm is developed, in which the filter weights and
the kernel size are both sequentially updated by stochastic gradient algorithms
that minimize the mean square error (MSE). Theoretical results on convergence
are also presented. The excellent performance of the new algorithm is confirmed
by simulations on static function estimation and short term chaotic time series
prediction.Comment: 25 pages, 9 figures, and 4 table
Speech Enhancement using Kernel and Normalized Kernel Affine Projection Algorithm
The goal of this paper is to investigate the speech signal enhancement using
Kernel Affine Projection Algorithm (KAPA) and Normalized KAPA. The removal of
background noise is very important in many applications like speech
recognition, telephone conversations, hearing aids, forensic, etc. Kernel
adaptive filters shown good performance for removal of noise. If the evaluation
of background noise is more slowly than the speech, i.e., noise signal is more
stationary than the speech, we can easily estimate the noise during the pauses
in speech. Otherwise it is more difficult to estimate the noise which results
in degradation of speech. In order to improve the quality and intelligibility
of speech, unlike time and frequency domains, we can process the signal in new
domain like Reproducing Kernel Hilbert Space (RKHS) for high dimensional to
yield more powerful nonlinear extensions. For experiments, we have used the
database of noisy speech corpus (NOIZEUS). From the results, we observed the
removal noise in RKHS has great performance in signal to noise ratio values in
comparison with conventional adaptive filters
Finite Dictionary Variants of the Diffusion KLMS Algorithm
The diffusion based distributed learning approaches have been found to be a
viable solution for learning over linearly separable datasets over a network.
However, approaches till date are suitable for linearly separable datasets and
need to be extended to scenarios in which we need to learn a non-linearity. In
such scenarios, the recently proposed diffusion kernel least mean squares
(KLMS) has been found to be performing better than diffusion least mean squares
(LMS). The drawback of diffusion KLMS is that it requires infinite storage for
observations (also called dictionary). This paper formulates the diffusion KLMS
in a fixed budget setting such that the storage requirement is curtailed while
maintaining appreciable performance in terms of convergence. Simulations have
been carried out to validate the two newly proposed algorithms named as
quantised diffusion KLMS (QDKLMS) and fixed budget diffusion KLMS (FBDKLMS)
against KLMS, which indicate that both the proposed algorithms deliver better
performance as compared to the KLMS while reducing the dictionary size storage
requirement
KLMAT: A Kernel Least Mean Absolute Third Algorithm
In this paper, a kernel least mean absolute third (KLMAT) algorithm is
developed for adaptive prediction. Combining the benefits of the kernel method
and the least mean absolute third (LMAT) algorithm, the proposed KLMAT
algorithm performs robustly against noise with different probability densities.
To further enhance the convergence rate of the KLMAT algorithm, a variable
step-size version (VSS-KLMAT algorithm) is proposed based on a Lorentzian
function. Moreover, the stability and convergence property of the proposed
algorithms are analyzed. Simulation results in the context of time series
prediction demonstrate that the effectiveness of proposed algorithms.Comment: submitted to the journal in March, 17th, 201
Random Euler Complex-Valued Nonlinear Filters
Over the last decade, both the neural network and kernel adaptive filter have
successfully been used for nonlinear signal processing. However, they suffer
from high computational cost caused by their complex/growing network
structures. In this paper, we propose two random Euler filters for
complex-valued nonlinear filtering problem, i.e., linear random Euler
complex-valued filter (LRECF) and its widely-linear version (WLRECF), which
possess a simple and fixed network structure. The transient and steady-state
performances are studied in a non-stationary environment. The analytical
minimum mean square error (MSE) and optimum step-size are derived. Finally,
numerical simulations on complex-valued nonlinear system identification and
nonlinear channel equalization are presented to show the effectiveness of the
proposed methods
Generalized Gaussian Kernel Adaptive Filtering
The present paper proposes generalized Gaussian kernel adaptive filtering,
where the kernel parameters are adaptive and data-driven. The Gaussian kernel
is parametrized by a center vector and a symmetric positive definite (SPD)
precision matrix, which is regarded as a generalization of the scalar width
parameter. These parameters are adaptively updated on the basis of a proposed
least-square-type rule to minimize the estimation error. The main contribution
of this paper is to establish update rules for precision matrices on the SPD
manifold in order to keep their symmetric positive-definiteness. Different from
conventional kernel adaptive filters, the proposed regressor is a superposition
of Gaussian kernels with all different parameters, which makes such regressor
more flexible. The kernel adaptive filtering algorithm is established together
with a l1-regularized least squares to avoid overfitting and the increase of
dimensionality of the dictionary. Experimental results confirm the validity of
the proposed method
Online dictionary learning for kernel LMS. Analysis and forward-backward splitting algorithm
Adaptive filtering algorithms operating in reproducing kernel Hilbert spaces
have demonstrated superiority over their linear counterpart for nonlinear
system identification. Unfortunately, an undesirable characteristic of these
methods is that the order of the filters grows linearly with the number of
input data. This dramatically increases the computational burden and memory
requirement. A variety of strategies based on dictionary learning have been
proposed to overcome this severe drawback. Few, if any, of these works analyze
the problem of updating the dictionary in a time-varying environment. In this
paper, we present an analytical study of the convergence behavior of the
Gaussian least-mean-square algorithm in the case where the statistics of the
dictionary elements only partially match the statistics of the input data. This
allows us to emphasize the need for updating the dictionary in an online way,
by discarding the obsolete elements and adding appropriate ones. We introduce a
kernel least-mean-square algorithm with L1-norm regularization to automatically
perform this task. The stability in the mean of this method is analyzed, and
its performance is tested with experiments
Adaptive Learning in Cartesian Product of Reproducing Kernel Hilbert Spaces
We propose a novel adaptive learning algorithm based on iterative orthogonal
projections in the Cartesian product of multiple reproducing kernel Hilbert
spaces (RKHSs). The task is estimating/tracking nonlinear functions which are
supposed to contain multiple components such as (i) linear and nonlinear
components, (ii) high- and low- frequency components etc. In this case, the use
of multiple RKHSs permits a compact representation of multicomponent functions.
The proposed algorithm is where two different methods of the author meet:
multikernel adaptive filtering and the algorithm of hyperplane projection along
affine subspace (HYPASS). In a certain particular case, the sum space of the
RKHSs is isomorphic to the product space and hence the proposed algorithm can
also be regarded as an iterative projection method in the sum space. The
efficacy of the proposed algorithm is shown by numerical examples
Study of Set-Membership Adaptive Kernel Algorithms
In the last decade, a considerable research effort has been devoted to
developing adaptive algorithms based on kernel functions. One of the main
features of these algorithms is that they form a family of universal
approximation techniques, solving problems with nonlinearities elegantly. In
this paper, we present data-selective adaptive kernel normalized least-mean
square (KNLMS) algorithms that can increase their learning rate and reduce
their computational complexity. In fact, these methods deal with kernel
expansions, creating a growing structure also known as the dictionary, whose
size depends on the number of observations and their innovation. The algorithms
described herein use an adaptive step-size to accelerate the learning and can
offer an excellent tradeoff between convergence speed and steady state, which
allows them to solve nonlinear filtering and estimation problems with a large
number of parameters without requiring a large computational cost. The
data-selective update scheme also limits the number of operations performed and
the size of the dictionary created by the kernel expansion, saving
computational resources and dealing with one of the major problems of kernel
adaptive algorithms. A statistical analysis is carried out along with a
computational complexity analysis of the proposed algorithms. Simulations show
that the proposed KNLMS algorithms outperform existing algorithms in examples
of nonlinear system identification and prediction of a time series originating
from a nonlinear difference equation.Comment: 34 pages, 10 figure