631 research outputs found
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
Adaptive Quadratic-Metric Parallel Subgradient Projection Algorithm and its Application to Acoustic Echo Cancellation
Publication in the conference proceedings of EUSIPCO, Florence, Italy, 200
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
Subsampling Algorithms for Semidefinite Programming
We derive a stochastic gradient algorithm for semidefinite optimization using
randomization techniques. The algorithm uses subsampling to reduce the
computational cost of each iteration and the subsampling ratio explicitly
controls granularity, i.e. the tradeoff between cost per iteration and total
number of iterations. Furthermore, the total computational cost is directly
proportional to the complexity (i.e. rank) of the solution. We study numerical
performance on some large-scale problems arising in statistical learning.Comment: Final version, to appear in Stochastic System
Robust Subspace Tracking Algorithms in Signal Processing: A Brief Survey
Principal component analysis (PCA) and subspace estimation (SE) are popular data analysis tools and used in a wide range of applications. The main interest in PCA/SE is for dimensionality reduction and low-rank approximation purposes. The emergence of big data streams have led to several essential issues for performing PCA/SE. Among them are (i) the size of such data streams increases over time, (ii) the underlying models may be time-dependent, and (iii) problem of dealing with the uncertainty and incompleteness in data. A robust variant of PCA/SE for such data streams, namely robust online PCA or robust subspace tracking (RST), has been introduced as a good alternative. The main goal of this paper is to provide a brief survey on recent RST algorithms in signal processing. Particularly, we begin this survey by introducing the basic ideas of the RST problem. Then, different aspects of RST are reviewed with respect to different kinds of non-Gaussian noises and sparse constraints. Our own contributions on this topic are also highlighted
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