A Multiresolution Signal Approximation Algorithm Based on Support Vector Machine
Zhou Yatong£¬Zhang Taiyi£¬Chen Zhigang
£¨School of Electronics and Information Engineering£¬Xi'an¡¡Jiaotong¡¡University£¬Xi'an
710049£¬China£©
Abstract£ºTo further improve the approximation performance of multiresolution signal
approximation £¨MSA£© algorithm£¬ a new MSA algorithm based on support vector machine
£¨SVM£©£¬ named SVMª²MSA is proposed£® Under the premise that the scale subspaces are
reproducing kernel Hilbert spaces£¬ the proposed algorithm firstly integrates the
approximation criterion of SVM into MSA£¬ and then an unconstrained programming is
derived£® Following that£¬ the unconstrained programming is reformulated as a
constrained programming by introducing some slack variables£® Finally£¬ for solving the
constrained programming the Lagrangian multiplier method is utilized to obtain the
approximation coefficients and expressions£® Theoretical analysis illustrates that
SVM-MSA not only preserves the MSA¡¯s characteristics of hierarchical approximation£¬
but also has good approximation accuracy and smoothness that SVM holds£® Experiments show
that in approximating sinc signal the SVM-MSA has better approximation accuracy and
smoothness than MSA£® Furthermore£¬ in the noise environment SVM-MSA has stronger
robustness than MSA if input signalª²noiseª²ratio is larger than about 2 dB£®
Keywords£ºmultiresolution£» support vector machine£» approximation£» reproducing
kernel Hilbertspace