基于仿射投影-非线性主分量分析的盲源分离

仿射投影算法(APA)重复利用数据,可提高算法的收敛速度。针对现有盲源分离收敛速度慢的问题,以盲源分离的非线性主分量分析(PCA)为基础,结合仿射投影算法,提出了盲源分离的非线性APA-PCA准则,并设计出盲源分离的APA-Kalman,APA-RLS,APA-LMS新算法。在这些新算法中,预白化后的观测向量数据被重复利用,向量式数据转变成矩阵式数据,从而加快了盲源分离的收敛速度。仿真结果表明,非线性APA-PCA准则是有效的。     

改进FOA算法在语音信号盲分离中的应用

简要介绍了果蝇优化算法的基本理论,针对FastICA等算法的稳定性和收敛性不够,而粒子群优化的盲分离运算速度慢的问题,将改进的果蝇优化算法应用到盲源分离研究中,提出了一种基于改进的果蝇优化的盲源分离算法。算法以信号的规范四阶累积量为代价函数,以改进果蝇算法对代价函数求极值,逐一确定分离向量,完成对线性瞬时混合语音信号的分离。仿真结果表明,算法能够有效实现对各混合语音信号的有序盲分离,且分离顺序能够确保按照源信号的规范四阶累积量绝对值的降序进行,分离精度也有一定的提高。     

ICA,kernel methods and nonnegativity: New paradigms for dynamical component analysis of fMRI data

In the last decades, functional magnetic resonance imaging (fMRI) has been introduced into clinical practice. As a consequence of this advanced noninvasive medical imaging technique, the analysis and visualization of medical image time-series data poses a new challenge to both research and medical application. But often, the model data for a regression or generalized linear model-based analysis are not available. Hence exploratory data-driven techniques, i.e. blind source separation (BSS) methods are very popular in functional nuclear magnetic resonance imaging (fMRI) data analysis since they are neither based on explicit signal models nor on a priori knowledge of the underlying physiological process. The independent component analysis (ICA) represents a main BSS method which searches for stochastically independent signals from the multivariate observations. In this paper, we introduce a new kernel-based nonlinear ICA method and compare it to standard BSS techniques. This kernel nonlinear ICA (kICA) overcomes the restrictions of linearity of the mixing process usually encountered with ICA. Dimension reduction is an important preprocessing step for this nonlinear technique and is performed in a novel way: a genetic algorithm is designed which determines the optimal number of basis vectors for a reduced-order feature space representation as an optimization problem of the condition number of the resulting basis. For the fMRI data, a comparative quantitative evaluation is performed between kICA with different kernels, nonnegative matrix factorization (NMF) and other BSS algorithms. The comparative results are evaluated by task-related activation maps, associated time courses and ROC study. The comparison is performed on fMRI data from experiments with 10 subjects. The external stimulus was a visual pattern presentation in a block design. The most important obtained results in this paper represent that kICA and sparse NMF (sNMF) are able to identify signal components with high correlation to the fMRI stimulus, and kICA with a Gaussian kernel is comparable to standard ICA algorithms and even more, it yields spatially focused results.     

基于广义相关系数的后非线性盲信号分离算法

基于互信息最小化的独立性测度对各分离信号间的非线性相关度度量没有归一化的问题,提出一种基于广义相关系数的肓信号分离(BSS)算法.首先选取后非线性混叠模型(PNL)分析基于广义相关系数的独立性测度;然后采用Gram-Charlier扩展形式估计输出参数并获取评价几率函数,结合最陡下降法求得分离矩阵和参数化可逆非线性映射的算法迭代公式.仿真结果表明,采用所提出的算法能够定量分析各分离信号间的非线性相关程度,有效分离后非线性混叠信号.     

A new concept for separability problems in blind source separation

The goal of blind source separation (BSS) lies in recovering the original independent sources of a mixed random vector without knowing the mixing structure. A key ingredient for performing BSS successfully is to know the indeterminacies of the problem-that is, to know how the separating model relates to the original mixing model (separability). For linear BSS, Comon (1994) showed using the Darmois-Skitovitch theorem that the linear mixing matrix can be found except for permutation and scaling. In this work, a much simpler, direct proof for linear separability is given. The idea is based on the fact that a random vector is independent if and only if the Hessian of its logarithmic density (resp. characteristic function) is diagonal everywhere. This property is then exploited to propose a new algorithm for performing BSS. Furthermore, first ideas of how to generalize separability results based on Hessian diagonalization to more complicated nonlinear models are studied in the setting of postnonlinear BSS.     

一种新的联合块对角化卷积盲分离时域算法

提出一种基于高阶累积量联合块对角化的时域算法求解卷积混合盲信号分离问题。引入白化处理,将混叠矩阵转变成酉矩阵,混合信号转变为互不相关的,进而计算出其对应的一系列高阶累积量矩阵,通过最小化代价函数来实现高阶累积量矩阵联合块对角化的目的,在时域中解决超定卷积盲分离问题。实验表明,相比于经典的自然梯度算法,所提方法的分离精度更高,且运算速度也更快。     

盲信号分离技术研究与算法综述

盲信号分离技术是从接收信号中恢复未知源信号的有效方法,已经成为神经网络和信号处理等领域新的研究热点。首先介绍盲信号分离的发展状况,然后在介绍了盲信号分离的线性瞬时模型、线性卷积模型和非线性模型的基础上,对相应模型求解算法的基本原理、特点进行了阐述,接着还对与盲信号分离紧密相关的盲信号抽取技术进行了综述,最后指出盲信号分离技术的研究方向和广阔的应用前景。     

Joint frequency, 2-D DOA,and polarization estimation using parallel factor analysis

This paper proposes a new algorithm for joint frequency, two-dimensional (2-D) directions-of-arrival (DOA), and polarization estimation using parallel factor (PARAFAC) analysis model and cumulant. The proposed algorithm designs a new array configuration, and extends the PARAFAC analysis model from the common data-domain and subspace-domain to the cumulant one, and forms three-way arrays by using the three cumulant matrices obtained from the properly chosen dipole outputs, and analyzes the uniqueness of low-...     

基于Givens矩阵和联合非线性不相关的盲源分离新算法

针对源信号统计独立的盲源分离(Blind Source Separation,BSS)问题,提出了一种基于Givens矩阵和联合非线性不相关的盲源分离新算法.由于分离信号独立性的度量是影响算法有效性的重要因素,因此首先提出了一种改进的度量独立性的方法,该方法以独立源信号的联合非线性不相关来度量独立性;其次,结合Givens矩阵可以对分离矩阵施加正交性约束且能减少要估计参数个数的性质,将盲源分离问题转化成无约束优化问题,并利用拟牛顿法中的BFGS算法求解该无约束优化问题,得到分离矩阵;最后,通过模拟混合信号和真实语音混合信号的分离实验验证了该算法的有效性.     

基于粒子群优化的工频干扰消除算法*

提出了一种基于粒子群优化的消除微弱信号采集过程中工频干扰的算法。通过人工构造观测信号,使系统模型符合盲源分离的数学模型要求。使用信号的四阶累积量作为信号独立性的判据,利用粒子群优化算法寻找使判据最大化的分离矩阵,进而消除被采集信号中的工频干扰。在粒子群优化算法的求解过程中,采用将对分离矩阵的直接辨识转换成对一系列Givens矩阵的辨识方法,从而减少了算法中对未知元素辨识的数量,避免反复白化过程,有效降低了算法的计算量,克服了粒子群优化过程中容易早熟收敛的问题。仿真结果表明,本算法在保护有用信号的前提下,能     

基于高阶累计统计量的微生物发酵过程监测

传统多向核独立成分分析(MKICA)方法的实质是把基于独立成分分析(ICA)中的白化处理主元分析(PCA)替换为核主元分析(KPCA)后利用二阶统计量进行过程监控,并未利用过程数据的阶段特性和高阶累积量信息,为了解决此问题,提出高阶累积量分析(HCA)与多向核熵独立成份分析(MKECA)相结合的多向高阶累计量的核熵独立成分分析方法(HCA-MKEICA).首先,采用核熵独立成份分析(KECA)对原始数据进行数据转换,解决数据的非线性;然后,在高维核熵空间利用HCA技术构建新的统计量用于过程监控;最后,将该方法应用于青霉素仿真平台和实际的工业过程并与MKICA方法进行对比,以验证所提出方法的有效性.     

嵌入式深度神经网络高光谱图像聚类

目的 高光谱图像的高维特性和非线性结构给聚类任务带来了"维数灾难"和线性不可分问题，以往的工作将特征提取过程与聚类过程互相剥离，难以同时优化。为了解决上述问题，提出了一种新的嵌入式深度神经网络模糊C均值聚类方法（EDFCC）。方法 EDFCC算法为了提取更加有效的深层特征，联合优化高光谱图像的特征提取和聚类过程，将模糊C均值聚类算法嵌入至深度自编码器网络中，可以保持两任务联合优化的优势，同时利用深度自编码器网络降维以及逼近任意非线性函数的能力，逐步将原始数据映射到潜在特征空间，提取数据的深层特征。所提方法采用模糊C均值聚类算法约束特征提取过程，学习适用于聚类的高光谱数据深层特征，动态调整聚类指示矩阵。结果 实验结果表明，EDFCC算法在Indian Pines和Pavia University两个高光谱数据集上的聚类精度分别达到了42.95%和60.59%，与当前流行的低秩子空间聚类算法（LRSC）相比分别提高了3%和4%，相比于基于自编码器的数据聚类算法（AEKM）分别提高了2%和3%。结论 EDFCC算法能够从高光谱图像的高维光谱信息中提取更加有效的深层特征，提升聚类精度，并且由于EDFCC算法不需要额外的训练过程，大大提升了聚类效率。     

具有非奇异约束的线性卷积混合信号盲分离联合对角化方法

联合对角化能够成功解决盲分离问题, 但在求解时会得到非期望的奇异解, 从而无法完全分离出源信号. 鉴于此, 提出一种用于线性卷积混合盲分离的联合对角化方法, 将卷积混合模型变换为瞬时模型, 并对变换后的模型应用联合对角化求取分离矩阵. 在求解过程中, 引入约束条件对解的范围进行限定, 避免了奇异解的出现. 仿真结果表明, 所提出的方法能够成功实现卷积混合信号盲分离.

     

Blind Source Separation Based on Cumulants With Time and Frequency Non-Properties

This paper presents new results on blind separation of instantaneously mixed independent sources based on high-order statistics together with their time and frequency non-properties (i.e., the non-stationarity and non-whiteness of sources). Separation criteria of mixtures are established on a set of cumulants at different time instants using the non-stationarity of sources and/or time-delayed cumulants using the non-whiteness of sources. It is shown that cumulants at different time instants and time-delayed cumulants can be used as criteria for blind source separation (BSS). Furthermore, it is proved that the cumulant-based separation criteria are directly related to the separability conditions. Batch-data and online learning rules are developed based on the joint diagonalization of symmetric fourth-order cumulant matrices, and the learning rules are further simplified to correlation-based BSS algorithms. In addition, an initialization strategy is proposed for improving the convergence of the learning rules. Simulation results are given to demonstrate the validity and performance of the algorithms.      

基于宽带聚焦矩阵和高阶累积量的OFDM信号的来波方向估计

为了解决正交频分复用(OFDM)宽带信号处理的问题,研究了基于宽带聚焦矩阵和高阶累积量的波达方向(DOA)估计方法。前者是通过傅里叶变换将宽带阵列数据分解为若干窄带信号,再利用一种聚焦矩阵将不同频带下的方向矩阵变换到同一参考频率下,然后用多重信号分类(MUSIC)算法来估计DOA;高阶累积量算法是通过聚焦操作,把各个窄带频率处的阵列输出矢量变换到聚焦频率处,然后求其累积量矩阵。对各个累积量矩阵进行加权平均并特征值分解,再应用MUSIC算法估计DOA。理论分析和仿真结果表明,两种方法都能够精确地估计OFDM信号的DOA,四阶累积量方法的空间分辨率比聚焦矩阵方法有所提高。四阶累积量算法扩展了阵列孔径,信噪比(SNR)较低的时候也有很好的适应性。     

近场源DOA、距离、极化参数及频率联合估计算法

文章研究了近场情况下多信源到达角(DOA)、距离、极化参数及频率的四维参数联合估计问题,建立了近场源在极化域的参数估计模型。文中所考虑的极化敏感阵列由和坐标轴方向一致的偶极子对构成,分别感应x轴方向和y轴方向的电场分量。该算法不需要谱峰搜索,直接给出各参数的闭式解。由于使用了四阶累积量,因此该算法适用于任意高斯噪声环境。仿真结果验证了该文方法的有效性。     

An Efficient Measure of Signal Temporal Predictability for Blind Source Separation

An efficient measure of signal temporal predictability is proposed, which is referred to as difference measure. We can prove that the difference measure of any signal mixture is between the maximal and minimal difference measure of the source signals. Previous blind source separation (BSS) problem is changed to a generalized eigenproblem by using Stone’s measure. However, by using difference measure, the BSS problem is furthermore simplified to a standard symmetric eigenproblem. And the separation matrix is the eigenvector matrix, which can be solved by using principal component analysis (PCA) method. Based on difference measure, a few efficient algorithms have been proposed, which are either in batch mode or in on-line mode. Simulations show that difference measure is competitive with Stone’s measure. Especially, the on-line algorithms derived from difference measure have better performance than those derived from Stone’s measure.     

主成分分析与神经网络的结合在多变量序列预测中的应用

目前预测方法的研究主要集中在单变量时间序列上,本文建立起一种针对多元变量非线性时间序列建模和预测的方法框架.首先,同时考虑序列状态间的线性相关性和非线性相关性,建立初始延迟窗以包含充分的预测信息;然后,利用主成分分析(PCA)方法寻找不同变量在数据空间中的最大方差方向,扩展PCA应用于提取多个变量的综合信息,重构多元变量输入状态相空间;最后,利用神经网络逼近不同变量之间以及当前状态和将来状态之间的函数映射关系,实现多元变量预测.对Ro¨ssler混沌方程和大连降雨、气温序列的预测仿真说明了本文方法的有效性,为多元变量时间序列分析提供了一条新的途径.     

Statistical control of control-affine nonlinear systems with nonquadratic cost functions: HJB and verification theorems

In statistical control, the cost function is viewed as a random variable and one optimizes the distribution of the cost function through the cost cumulants. We consider a statistical control problem for a control-affine nonlinear system with a nonquadratic cost function. Using the Dynkin formula, the Hamilton-Jacobi-Bellman equation for the nth cost moment case is derived as a necessary condition for optimality and corresponding sufficient conditions are also derived. Utilizing the nth moment results, the higher order cost cumulant Hamilton-Jacobi-Bellman equations are derived. In particular, we derive HJB equations for the second, third, and fourth cost cumulants. Even though moments and cumulants are similar mathematically, in control engineering higher order cumulant control shows a greater promise in contrast to cost moment control. We present the solution for a control-affine nonlinear system using the derived Hamilton-Jacobi-Bellman equation, which we solve numerically using a neural network method.     

Hammerstein模型的记忆效应盲辨识方法

针对未知记忆深度的Hammerstein模型,提出一种基于高阶累积量的Hammerstein模型记忆效应盲辨识方法。将Hammerstein模型中对记忆深度的确定转换为对模型输出信号高阶累积量扩展矩阵的求秩问题,给出对角元素乘积(NPODE)方法以确定记忆深度,分别比较该方法与GM直接定阶法、拐点法的鲁棒性。结合提出的记忆深度估计算法,给出线性记忆模块系数的提取方法。理论推导与仿真结果表明,线性记忆模块系数的提取过程不受无记忆非线性效应的影响。