5 research outputs found
A Sparsity-Aware Adaptive Algorithm for Distributed Learning
In this paper, a sparsity-aware adaptive algorithm for distributed learning
in diffusion networks is developed. The algorithm follows the set-theoretic
estimation rationale. At each time instance and at each node of the network, a
closed convex set, known as property set, is constructed based on the received
measurements; this defines the region in which the solution is searched for. In
this paper, the property sets take the form of hyperslabs. The goal is to find
a point that belongs to the intersection of these hyperslabs. To this end,
sparsity encouraging variable metric projections onto the hyperslabs have been
adopted. Moreover, sparsity is also imposed by employing variable metric
projections onto weighted balls. A combine adapt cooperation strategy
is adopted. Under some mild assumptions, the scheme enjoys monotonicity,
asymptotic optimality and strong convergence to a point that lies in the
consensus subspace. Finally, numerical examples verify the validity of the
proposed scheme, compared to other algorithms, which have been developed in the
context of sparse adaptive learning
Robust Reduced-Rank Adaptive Processing Based on Parallel Subgradient Projection and Krylov Subspace Techniques
In this paper, we propose a novel reduced-rank adaptive filtering algorithm
by blending the idea of the Krylov subspace methods with the set-theoretic
adaptive filtering framework. Unlike the existing Krylov-subspace-based
reduced-rank methods, the proposed algorithm tracks the optimal point in the
sense of minimizing the \sinq{true} mean square error (MSE) in the Krylov
subspace, even when the estimated statistics become erroneous (e.g., due to
sudden changes of environments). Therefore, compared with those existing
methods, the proposed algorithm is more suited to adaptive filtering
applications. The algorithm is analyzed based on a modified version of the
adaptive projected subgradient method (APSM). Numerical examples demonstrate
that the proposed algorithm enjoys better tracking performance than the
existing methods for the interference suppression problem in code-division
multiple-access (CDMA) systems as well as for simple system identification
problems.Comment: 10 figures. In IEEE Transactions on Signal Processing, 201
Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks
We propose an adaptive scheme for distributed learning of nonlinear functions
by a network of nodes. The proposed algorithm consists of a local adaptation
stage utilizing multiple kernels with projections onto hyperslabs and a
diffusion stage to achieve consensus on the estimates over the whole network.
Multiple kernels are incorporated to enhance the approximation of functions
with several high and low frequency components common in practical scenarios.
We provide a thorough convergence analysis of the proposed scheme based on the
metric of the Cartesian product of multiple reproducing kernel Hilbert spaces.
To this end, we introduce a modified consensus matrix considering this specific
metric and prove its equivalence to the ordinary consensus matrix. Besides, the
use of hyperslabs enables a significant reduction of the computational demand
with only a minor loss in the performance. Numerical evaluations with synthetic
and real data are conducted showing the efficacy of the proposed algorithm
compared to the state of the art schemes.Comment: Double-column 15 pages, 10 figures, submitted to IEEE Trans. Signal
Processin
Adaptive parallel quadratic-metric projection algorithms
This paper indicates that an appropriate design of metric leads to significant improvements in the adaptive projected subgradient method (APSM), which unifies a wide range of projection-based algorithms [including normalized least mean square (NLMS) and affine projection algorithm (APA)]. The key is to incorporate a priori (or a posteriori) information on characteristics of an estimandum, a system to be estimated, into the metric design. We propose a family of efficient adaptive filtering algorithms based on a parallel use of quadratic-metric projection, which assigns every point to the nearest point in a closed convex set in a quadratic-metric sense. We present two versions: (1) constant-metric and (2) variable-metric, i.e., the metric function employed is (1) constant and (2) variable among iterations. As a constant-metric version, adaptive parallel quadratic-metric projection (APQP) and adaptive parallel min-max quadratic-metric projection (APMQP) algorithms are naturally derived by APSM, being endowed with desirable properties such as convergence to a point optimal in asymptotic sense. As a variable-metric version, adaptive parallel variable-metric projection (APVP) algorithm is derived by a generalized APSM, enjoying an extended monotone property at each iteration. By employing a simple quadratic-metric, the computational complexity of the proposed algorithms is kept linear with respect to the filter length. Numerical examples demonstrate the remarkable advantages of the proposed algorithms in an application to acoustic echo cancellation. © 2007 IEEE