Blind source separation by weighted K-means clustering

Blind separation of sparse sources （BSSS） is discussed. The BSSS method based on the conventional K-means clustering is very fast and is also easy to implement. However, the accuracy of this method is generally not satisfactory. The contribution of the vector x（t） with different modules is theoretically proved to be unequal, and a weighted K-means clustering method is proposed on this grounds. The proposed algorithm is not only as fast as the conventional K-means clustering method, but can also achieve considerably accurate results, which is demonstrated by numerical experiments.

Source number estimation and separation algorithms of underdetermined blind separation

Recently,sparse component analysis (SCA) has become a hot spot in BSS re-search. Instead of independent component analysis (ICA),SCA can be used to solve underdetermined mixture efficiently. Two-step approach (TSA) is one of the typical methods to solve SCA based BSS problems. It estimates the mixing matrix before the separation of the sources. K-means clustering is often used to estimate the mixing matrix. It relies on the prior knowledge of the source number strongly. However,the estimation of the source number is an obstacle. In this paper,a fuzzy clustering method is proposed to estimate the source number and mixing matrix simultaneously. After that,the sources are recovered by the shortest path method (SPM). Simulations show the availability and robustness of the proposed method.

基于密度结构分析的改进FCM混合矩阵估计

欠定盲源分离问题中,针对传统FCM算法(fuzzy C-means,FCM)需要预先设定聚类数目和初始聚类中心,以及聚类结果易受噪点干扰的问题,提出一种基于密度结构分析的改进FCM聚类算法,并利用改进后的算法实现混合矩阵估计。这一改进算法首先用OPTICS(ordering points to identify the clustering structure,OPTICS)算法对信号进行密度结构分析,得到能反映信号密度结构的可达距离序列,从中确定出初始聚类中心和聚类数目,实现对FCM初始参数优化;而后进一步将可达序列作为动态加权因子应用到FCM目标函数中,实现对目标函数的优化。仿真结果表明,本文提出的改进算法可以从初始参数和目标函数2方面实现对传统FCM算法的优化,提高聚类的稳定性和最终混合矩阵的鲁棒性。