Blind source separation using higher order statistics in kernel space

Abstract

Purpose

Higher order statistics (HOS)-based blind source separation (BSS) technique has been applied to separate data to obtain a better performance than second order statistics-based method. The cost function constructed from the HOS-based separation criterion is a complicated nonlinear function that is difficult to optimize. The purpose of this paper is to effectively solve this nonlinear optimization problem to obtain an estimation of the source signals with a higher accuracy than classic BSS methods.

Design/methodology/approach

In this paper, a new technique based on HOS in kernel space is proposed. The proposed approach first maps the mixture data into a high-dimensional kernel space through a nonlinear mapping and then constructs a cost function based on a higher order separation criterion in the kernel space. The cost function is constructed by using the kernel function which is defined as inner products between the images of all pairs of data in the kernel space. The estimations of the source signals is obtained through the minimizing the cost function.

Findings

The results of a number of experiments on generic synthetic and real data show that HOS separation criterion in kernel space exhibits good performance for different kinds of distributions. The proposed method provided higher signal-to-interference ratio and less sensitive to the source distribution compared to FastICA and JADE algorithms.

Originality/value

The proposed method combines the advantage of kernel method and the HOS properties to achieve a better performance than using a single one. It does not require to compute the coordinates of the data in the kernel space explicitly, but computes the kernel function which is simple to optimize. The use of nonlinear function space allows the algorithm more accurate and more robust to different kinds of distributions.

Citation

Liu, N., Li, J., Liu, Q., Su, H. and Wu, W. (2016), "Blind source separation using higher order statistics in kernel space", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 35 No. 1, pp. 289-304. https://doi.org/10.1108/COMPEL-04-2015-0172