稀疏增量Delta-Bar-Delta算法：提升系统识别效率

117 浏览量更新于2024-08-26 收藏 159KB PDF 举报

"稀疏增量Delta-Bar-Delta用于系统识别" 本文主要探讨了一种针对系统识别的新型算法——稀疏增量Delta-Bar-Delta (Sparse Incremental Delta-Bar-Delta, SIDBD)。该算法结合了元学习（Metalearning）的思想与增量Delta-Bar-Delta (IDBD)算法的优势，并引入了稀疏性概念，以优化系统识别的性能。 IDBD算法是一种自适应滤波器，属于最小均方误差（Least Mean Square, LMS）家族，常用于在线学习和系统识别任务。其工作原理是通过迭代更新权重来最小化预测误差平方和，从而逼近目标系统。然而，原始的IDBD算法并未考虑到实际系统可能存在的稀疏结构。在SIDBD算法中，研究者们考虑了系统的稀疏特性，将l（0）范数惩罚项纳入标准IDBD的成本函数。l（0）范数代表非零元素的数量，其引入相当于在迭代过程中添加零吸引子。这一策略对于稀疏系统尤其有利，因为如果目标系统具有稀疏结构，那么在迭代过程中可以更快地驱动非重要权重变为零，从而加速收敛速度并减少计算复杂度。元学习是一种机器学习方法，它的目的是通过学习多个相关任务的经验来提升基础学习算法的性能。在SIDBD中，元学习被用来优化IDBD的学习过程，使其能更好地适应具有稀疏性的系统识别任务。通过仿真实验，文章对比了SIDBD算法与传统竞争算法在稀疏系统识别中的表现，结果显示SIDBD在性能上具有显著优势。这表明，SIDBD不仅能够更有效地识别稀疏系统，而且在处理含有大量冗余或不相关信息的复杂系统时，也能展现出更好的泛化能力和效率。关键词：自适应滤波器，增量Delta-Bar-Delta，最小均方误差，l（0）范数，元学习，稀疏，系统识别。总结起来，这篇文章提出了稀疏增量Delta-Bar-Delta算法，这是一种创新的系统识别方法，结合了元学习和稀疏优化技术，旨在提升对稀疏系统的学习效率和识别精度。通过在IDBD算法中引入l（0）范数惩罚，SIDBD能够在迭代过程中更好地捕捉系统的关键特征，从而加速学习过程并降低错误率。实验结果验证了该算法的有效性和优越性。

Sparse Incremental Delta-Bar-Delta for System Identification

Ying Liu

1,a

,Yan Ye

1,b

and Chunguang Li

1,c

Department of Information Science and Electronic Engineering,

ZhejiangUniversity,Hangzhou 310027, China

yingliu@zju.edu.cn,

414214205@qq.com,

cgli@zju.edu.cn

Keywords: Adaptive filter, incremental delta-bar-delta, least mean square, l

norm, metalearning,

sparse, system identification.

Abstract. Metalearning algorithm learns the base learning algorithm, targeted for improving the

performance of the learning system. The incremental delta-bar-delta (IDBD) algorithm is such a

metalearning algorithm. On the other hand, sparse algorithms are gaining popularity due to their

good performance and wide applications. In this paper, we propose a sparse IDBD algorithm by

taking the sparsity of the systems into account. The

norm penalty is contained in the cost function

of the standard IDBD, which is equivalent to adding a zero attractor in the iterations, thus can speed

up convergence if the system of interest is indeed sparse. Simulations demonstrate that the proposed

algorithm is superior to the competing algorithms in sparse system identification.

Introduction

Matelearning means learning of the base learning system, hence to improve the performance of

the base learning system. The delta-bar-delta (DBD) [1] is one of the most well-known

metalearning algorithms, which consists of a weight update and a learning rate update both based on

the delta rule. The incremental delta-bar-delta (IDBD) [2] is an extension of the DBD algorithm,

which is applicable to incremental tasks, that is, supervised learning tasks in which the examples are

processed one-by-one and then discarded. In the IDBD, both the update rules of weight and learning

rate are derived by gradient descent. The base learning algorithm in the IDBD is the well-known

least-mean square (LMS) algorithm. It was shown that the IDBD exhibits faster convergence rate

and lower mean square deviation (MSD) than the LMS.

Sparse systems, whose impulse responses contain only a few large coefficients interspersed

among many negligible ones, widely exists in nature [3]. It is also shown that utilizing the sparse

property of a system can improve the adaptive filtering performance and many algorithms have

been proposed [4,5].

Motivated by LASSO [6] and recent progress in compressive sensing, several sparse LMS

algorithm have been proposed [7-9]. Their basic idea is to introduce a penalty, e.g. the

norm

of the coefficient vector, into the cost function, which favors the sparsity of the system. Moreover, it

was shown in [8, 9] that the

-LMS is superior to the sparse algorithms based on

norm.

Therefore, only the case of

norm penalty is considered in this paper. Considering that the IDBD

is superior to the LMS, we propose a sparse IDBD algorithm by incorporating the

norm penalty

into the cost function of the standard IDBD algorithm and then use the gradient descent method to

attain the new algorithm, which is named as

-IDBD. Numerical simulations demonstrate that the

-IDBD has faster convergence rate, faster tracking rate and lower MSD than the

-LMS.

Sparse Incremental Delta-Bar-Delta Algorithm

In this paper, a sparse algorithm based on IDBD and

-LMS is proposed. In the following, we

denote theinput vector, the coefficient vector, the desired output, thesystemoutput and the

estimation errorby

( ) [ ( ), ( 1), , ( 1)]

n x n x n x n L= − − +x

…

0 1 1

( ) [ ( ), ( ), , ( )]

n w n w n w n

−

…

( )

d n

( ) ( ) ( )

y n n n

w x

,and

( ) ( ) ( )

e n d n y n

= −

, respectively, where

is time and

is thefilter length.

Applied Mechanics and Materials Vol. 665 (2014) pp 643-646 Submitted: 13.06.2014

doi:10.4028/www.scientific.net/AMM.665.643

下载后可阅读完整内容，剩余3页未读，立即下载

weixin_38557896

粉丝: 0
资源: 971

稀疏增量Delta-Bar-Delta算法：提升系统识别效率

自适应滤波器原理 第五版 英文版 Simon Haykin

改进的稀疏表示静止-视频人脸识别算法.pdf

稀疏矩阵--仿真程序Demo4.rarPROCEEDINGS OF THE IEEE.rar

cross_val_score的参数详解

用matlab编一个程序，查找一稀疏矩阵 A-1003 0:100 1:0900:2000中的非零 元素，要求打印出具体值及其所在的位置。

基于稀疏表示的人脸识别matlab

matlab稀疏算法实现人脸识别

基于稀疏表示有遮挡的人脸识别csdn

对稀疏矩阵进行创建和输出的操作

Pythonr稀疏表示人脸识别

最新资源

自适应滤波器原理第五版英文版 Simon Haykin

用matlab编一个程序，查找一稀疏矩阵 A-1003 0:100 1:0900:2000中的非零元素，要求打印出具体值及其所在的位置。