a
Corresponding author: author@e-mail.org
A Nonlinear Blind Source Separation Method Based On Radial
Basis Function and Quantum Genetic Algorithm
Pidong Wang
1,2
, Ruoyun Tang
1,3
, Di Zhao
1
, Hongyi Li
1,3,*
, and Jiaxin Chen
4
1
LMIB, School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
2
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
3
School of Software Engineering, Beihang University, Beijing 100191, China
4
School of Computer Science and Engineering, Beihang University, Beijing 100191, China
*Corresponding author (E-mail:Hongyili_buaa@163.com)
Abstract. Blind source separation is a hot topic in signal processing. Most existing works focus on dealing
with linear combined signals, while in practice we always encounter with nonlinear mixed signals. To
address the problem of nonlinear source separation, in this paper we propose a novel algorithm using radial
basis function neutral network, optimized by multi-universe parallel quantum genetic algorithm.
Experiments show the efficiency of the proposed method.
Keywords. EMI signal, Non-linear blind source separation, Radial basis function, Quantum genetic
algorithm
1 Introduction
In practice, the nonlinear mixed signals are widespread
in blind source separation(BSS), which traditional
methods based on linear mixture assumption like ICA
are unable to deal with. According to [1,10-12],
supposing that x, y are two independent random
variables, and f, g are two nonlinear functions, then f(x)
and g(y) are independent, too. This fact means that the
nonlinear function of source signals could possibly be
recovered with the independence assumption of source
signals. [2] discusses the existence and uniqueness of
solutions to nonlinear ICA and concludes that the
solution exists but more assumptions should be added to
confirm the uniqueness of solution.
Recently, a method utilizing the radial basis function
neutral network (RBFNN) and chaotic self-adaptive
particle swarm optimization was introduced in [3].
RBFNN does not deed to determine the mixture model.
Theoretically, it is unsupervised and can approximate an
arbitrary function [4- 5]. However, RBFNN always
converges to a local minimum by adopting general
optimization method, such as the gradient descent
algorithm. Optimization algorithm searching for global
minimum such as Genetic Algorithm [9-12] also doesn’t
perform well due to large amounts of control parameters,
complex calculation and being sensitive to initial values.
Quantum genetic algorithm (QGA) combine the features
of quantum probability amplitude, superposition,
polymorphism and group optimization, which could
effectively improve the efficiency. Moreover, the multi-
universe parallel quantum genetic algorithm (MPQGA)
[6] integrates the concept of subgroup with QGA. We
utilize the RBFNN to process signals, and employ
fourth-order joint cumulants as independent criterion for
separation to optimize parameters.
The rest of this article is as follows: in the second
section presents the preliminaries. In section 3, we
describe our proposed method in great detail. Then, in
section 4, experiments results on synthetic data are
provided to demonstrate the performance of the
proposed method. Finally, we draw conclusions in the
last section.
2 Preliminaries
In this section, we will briefly introduce the nonlinear
mixed model, radial basis function neural network, and
the multi-universe parallel quantum genetic algorithm.
2.1 Nonlinear mixed model
Nonlinear mixing model for nonlinear BSS could be
expressed as x(t)=f(s(t)), where s(t) means the source
signal, x(t) is the mixed signal, and
)(f is a unknown
nonlinear function.
Supposing
)(f is reversible, and its inverse function
exists, denoted by
),(
T
g , where
T
is the undetermined
parameter. Thus, we obtain the following
)(),))(((),)(()( tstsfgtxgty
T
T
(1)
DOI: 10.1051/
01014 (2016)
,
1014matecconf/2016MATEC Web of Conferences
61
610
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the
Creative
Commons
Attribution
License 4.0 (http://creativecommons.org/licenses/by/4.0/).
2016
APOP
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