An Expectation–Maximization Method for Spatio–Temporal Blind Source Separation Using an AR-MOG Source Model

In this paper, we develop a maximum-likelihood (ML) spatio-temporal blind source separation (BSS) algorithm, where the temporal dependencies are explained by assuming that each source is an autoregressive (AR) process and the distribution of the associated independent identically distributed (i.i.d.) innovations process is described using a mixture of Gaussians. Unlike most ML methods, the proposed algorithm takes into account both spatial and temporal information, optimization is performed using the expectation-maximization (EM) method, the source model is adapted to maximize the likelihood, and the update equations have a simple, analytical form. The proposed method, which we refer to as autoregressive mixture of Gaussians (AR-MOG), outperforms nine other methods for artificial mixtures of real audio. We also show results for using AR-MOG to extract the fetal cardiac signal from real magnetocardiographic (MCG) data.     

Bayesian nonstationary source separation

A Bayesian nonstationary source separation algorithm is proposed in this paper to recover nonstationary sources from noisy mixtures. In order to exploit the temporal structure of the data, we use a time-varying autoregressive (TVAR) process to model each source signal. Then variational Bayesian (VB) learning is adopted to integrate the source model with blind source separation (BSS) in probabilistic form. Our separation algorithm makes full use of temporally correlated prior information and avoids overfitting in separation process. Experimental results demonstrate that our vbICA-TVAR algorithm learns the temporal structure of sources and acquires cleaner source reconstruction.     

Dual multivariate auto-regressive modeling in state space for temporal signal separation

Many existing independent component analysis (ICA) approaches result in deteriorated performance in temporal source separation because they have not taken into consideration of the underlying temporal structure of sources. In this paper, we model temporal sources as a general multivariate auto-regressive (AR) process whereby an underlying multivariate AR process in observation space is obtained. In this dual AR modeling, the mixing process from temporal sources to observations is the same as the mixture from the nontemporal residuals of the source AR (SAR) process to that of the observation AR (OAR) process. We can therefore avoid the source temporal effects in performing ICA by learning the demixing system on the independently distributed OAR residuals rather than the time-correlated observations. Particularly, we implement this approach by modeling each source signal as a finite mixture of generalized autoregressive conditional heteroskedastic (GARCH) process. The adaptive algorithms are proposed to extract the OAR residuals appropriately online, together with learning the demixing system via a nontemporal ICA algorithm. The experiments have shown its superior performance on temporal source separation.     

A Semi-supervised Learning Algorithm on Gaussian Mixture with Automatic Model Selection

In Gaussian mixture modeling, it is crucial to select the number of Gaussians for a sample set, which becomes much more difficult when the overlap in the mixture is larger. Under regularization theory, we aim to solve this problem using a semi-supervised learning algorithm through incorporating pairwise constraints into entropy regularized likelihood (ERL) learning which can make automatic model selection for Gaussian mixture. The simulation experiments further demonstrate that the presented semi-supervised learning algorithm (i.e., the constrained ERL learning algorithm) can automatically detect the number of Gaussians with a good parameter estimation, even when two or more actual Gaussians in the mixture are overlapped at a high degree. Moreover, the constrained ERL learning algorithm leads to some promising results when applied to iris data classification and image database categorization.     

Simplifying mixture models using the unscented transform

Mixture of Gaussians (MoG) model is a useful tool in statistical learning. In many learning processes that are based on mixture models, computational requirements are very demanding due to the large number of components involved in the model. We propose a novel algorithm for learning a simplified representation of a Gaussian mixture, that is based on the Unscented Transform which was introduced for filtering nonlinear dynamical systems. The superiority of the proposed method is validated on both simulation experiments and categorization of a real image database. The proposed categorization methodology is based on modeling each image using a Gaussian mixture model. A category model is obtained by learning a simplified mixture model from all the images in the category.     

基于自适应混合高斯模型的时空背景建模

提出了一种基于自适应混合髙斯模型的时空背景建模方法, 有效地融合了像素在时空域上的分布信息, 改善了传统的混合髙斯背景建模方法对非平稳场景较为敏感的缺点. 首先利用混合髙斯模型学习每个像素在时间域上的分布, 构造了基于像素的时间域背景模型, 在此基础上, 通过非参数密度估计方法统计每个像素邻域内表示背景的髙斯成分在空间上的分布, 构造了基于像素的空间域背景模型; 在决策层融合了基于时空背景模型的背景减除结果. 为了提高本文时空背景建模的效率, 提出了一种新的混合高斯模型髙斯成分个数的自适应选择策略, 并利用积分图实现了空间域背景模型的快速计算. 通过在不同的场景下与多个背景建模方法比较, 实验结果验证了本文算法的有效性.     

基于时变自回归模型的FAJD盲源分离算法

为实现多高斯源和相关源信号的盲分离,在快速近似联合对角化(FAJD)算法的基础上,将故障诊断领域的时变自回归理论成功地应用于相关源信号的盲分离和多高斯源信号的盲分离.首先采用时变自回归模型(TVAR)对源信号建模,并通过白化预处理使得建模后的源信号具有可联合对角化的结构;然后,通过基函数加权和的方法将时变参数近似为已知基函数的加权和的形式,将其变成时不变的参数,再通过递推最小二乘法求解出模型系数矩阵组;最后,将所求出的系数矩阵组作为快速近似联合对角化的目标矩阵组,通过FAJD算法实现混合信号的分离.Matlab仿真实验验证了所提出的算法对于相关源信号和多高斯源信号的分离是行之有效的.由于算法中TVAR模型的优良特性,此算法非常适用于混合通信信号的盲分离.     

Sparse Bayesian Learning for non-Gaussian sources

In this paper, we show that in the multiple measurement vector model we can take advantage of having multiple samples to learn the properties of the distributions of the sources as part of the recovery process and demonstrate that this improves the recovery performance. We propose a method to solve the simultaneous sparse approximation problem using a mixture of Gaussians prior, inspired by existing Sparse Bayesian Learning approaches. We justify our proposed prior by showing that there are a number of signals modelled better by a mixture of Gaussians prior than the standard zero-mean Gaussian prior, such as communications signals which often have a multimodal distribution. We further show that this method can be applied to data distributed according to an alpha-stable distribution. We also show that our proposed method can be applied to compressed sensing of ultrasound images and demonstrate an improvement over existing methods.     

一种基于区域的彩色图像分割方法

介绍了一种基于区域的彩色图像分割方法。该方法首先提取图像像素点的颜色、纹理等特征,然后采用Gaussian混合模型,通过EM算法学习,根据提出的选择最佳高斯混合模型参数K的准则,确定K,利用图像像素点特征的相似度在特征空间中粗略的将像素点划分为不同的组,最后在各个组内依据其位置信息对图像再进一步划分,得到图像的区域分割。实验结果表明,该分割方法具有较好的分割性能。     

Positive vectors clustering using inverted Dirichlet finite mixture models

In this work we present an unsupervised algorithm for learning finite mixture models from multivariate positive data. Indeed, this kind of data appears naturally in many applications, yet it has not been adequately addressed in the past. This mixture model is based on the inverted Dirichlet distribution, which offers a good representation and modeling of positive non-Gaussian data. The proposed approach for estimating the parameters of an inverted Dirichlet mixture is based on the maximum likelihood (ML) using Newton Raphson method. We also develop an approach, based on the minimum message length (MML) criterion, to select the optimal number of clusters to represent the data using such a mixture. Experimental results are presented using artificial histograms and real data sets. The challenging problem of software modules classification is investigated within the proposed statistical framework, also.     

MIMO-OFDM系统中一种改进的最大似然信道估计算法*

对MIMO-OFDM系统中的信道估计进行研究,提出了一种对最大似然（ML）算法的改进,该算法首先采用ML算法获得初始估计值,然后联合检测进行迭代信道估计,充分利用上了接收端联合数据检测得到的数据信号信息与信道估计进行信息交互来提高估计性能,仿真结果表明,相对于传统估计方法,这种改进方法能够得到更好的均方误差和误码率性能,尤其是在导频数量较少时,此改进算法的性能提升将更明显。     

Odor source localization using a mobile robot in outdoor airflow environments with a particle filter algorithm

This paper discusses odor source localization (OSL) using a mobile robot in an outdoor time-variant airflow environment. A novel OSL algorithm based on particle filters (PF) is proposed. When the odor plume clue is found, the robot performs an exploratory behavior, such as a plume-tracing strategy, to collect more information about the previously unknown odor source. In parallel, the information collected by the robot is exploited by the PF-based OSL algorithm to estimate the location of the odor source in real time. The process of the OSL is terminated if the estimated source locations converge within a given small area. The Bayesian-inference-based method is also performed for comparison. Experimental results indicate that the proposed PF-based OSL algorithm performs better than the Bayesian-inference-based OSL method.     

TOA source localization and DOA estimation algorithms using prior distribution for calibrated source

This paper presents an a priori probability density function (pdf)-based time-of-arrival (TOA) source localization algorithms. Range measurements are used to estimate the location parameter for TOA source localization. Previous information on the position of the calibrated source is employed to improve the existing likelihood-based localization method. The cost function where the prior distribution was combined with the likelihood function is minimized by the adaptive expectation maximization (EM) and space-alternating generalized expectation–maximization (SAGE) algorithms. The variance of the prior distribution does not need to be known a priori because it can be estimated using Bayes inference in the proposed adaptive EM algorithm. Note that the variance of the prior distribution should be known in the existing three-step WLS method [1]. The resulting positioning accuracy of the proposed methods was much better than the existing algorithms in regimes of large noise variances. Furthermore, the proposed algorithms can also effectively perform the localization in line-of-sight (LOS)/non-line-of-sight (NLOS) mixture situations.     

Mixing matrix estimation using discriminative clustering for blind source separation

Mixing matrix estimation in instantaneous blind source separation (BSS) can be performed by exploiting the sparsity and disjoint orthogonality of source signals. As a result, approaches for estimating the unknown mixing process typically employ clustering algorithms on the mixtures in a parametric domain, where the signals can be sparsely represented. In this paper, we propose two algorithms to perform discriminative clustering of the mixture signals for estimating the mixing matrix. For the case of overdetermined BSS, we develop an algorithm to perform linear discriminant analysis based on similarity measures and combine it with K-hyperline clustering. Furthermore, we propose to perform discriminative clustering in a high-dimensional feature space obtained by an implicit mapping, using the kernel trick, for the case of underdetermined source separation. Using simulations on synthetic data, we demonstrate the improvements in mixing matrix estimation performance obtained using the proposed algorithms in comparison to other clustering methods. Finally we perform mixing matrix estimation from speech mixtures, by clustering single source points in the time-frequency domain, and show that the proposed algorithms achieve higher signal to interference ratio when compared to other baseline algorithms.     

基于Delaunay四面体剖分的网格分割算法

为了构建有意义曲面分片,提出一种基于Delaunay四面体剖分的网格分割算法.首先根据Delaunay四面体剖分得到多边形网格内部的四面体,求出每个面上反映网格内部信息的Delaunay体距离;然后对Delaunay体距离进行平滑处理,再对网格上面的Delaunay体距离进行聚类,用高斯混合模型对Delaunay体距离作柱状图的拟合,利用期望最大化算法来快速求得拟合结果;最后结合图切分技术,同时考虑聚类的结果、分割区域的边界平滑和视觉认知中的最小规则,得到最终的网格分割结果.实验结果表明,采用文中算法可以有效地实现有意义的网格分割.     

Background subtraction using finite mixtures of asymmetric Gaussian distributions and shadow detection

Foreground segmentation of moving regions in image sequences is a fundamental step in many vision systems including automated video surveillance, human-machine interface, and optical motion capture. Many models have been introduced to deal with the problems of modeling the background and detecting the moving objects in the scene. One of the successful solutions to these problems is the use of the well-known adaptive Gaussian mixture model. However, this method suffers from some drawbacks. Modeling the background using the Gaussian mixture implies the assumption that the background and foreground distributions are Gaussians which is not always the case for most environments. In addition, it is unable to distinguish between moving shadows and moving objects. In this paper, we try to overcome these problem using a mixture of asymmetric Gaussians to enhance the robustness and flexibility of mixture modeling, and a shadow detection scheme to remove unwanted shadows from the scene. Furthermore, we apply this method to real image sequences of both indoor and outdoor scenes. The results of comparing our method to different state of the art background subtraction methods show the efficiency of our model for real-time segmentation.     

MISEP method for postnonlinear blind source separation

In this letter, a standard postnonlinear blind source separation algorithm is proposed, based on the MISEP method, which is widely used in linear and nonlinear independent component analysis. To best suit a wide class of postnonlinear mixtures, we adapt the MISEP method to incorporate a priori information of the mixtures. In particular, a group of three-layered perceptrons and a linear network are used as the unmixing system to separate sources in the postnonlinear mixtures, and another group of three-layered perceptron is used as the auxiliary network. The learning algorithm for the unmixing system is then obtained by maximizing the output entropy of the auxiliary network. The proposed method is applied to postnonlinear blind source separation of both simulation signals and real speech signals, and the experimental results demonstrate its effectiveness and efficiency in comparison with existing methods.     

Consistency of modified LS estimation method for identifying 2-Dnoncausal SAR model parameters

Least squares (LS) and maximum likelihood (ML) are the two main methods for parameter estimation of two-dimensional (2D) noncausal simultaneous autoregressive (SAR) models. ML is asymptotically consistent and unbiased but computationally unattractive. On the other hand, conventional LS is computationally efficient but does not produce accurate parameter estimates for noncausal models. Recently, Zhao-Yu (1993) proposed a modified LS estimation method and was shown to be unbiased. In this paper we prove that, under certain assumptions, the method introduced by Zhao-Yu is also consistent     

A parametric density model for blind source separation

In this paper, a parametric mixture density model is employed to be the source prior in blind source separation (BSS). A strict lower bound on the source prior is derived by using a variational method, which naturally enables the intractable posterior to be represented as a gaussian form. An expectation-maximization (EM) algorithm in closed form is therefore derived for estimating the mixing matrix and inferring the sources. Simulation results show that the proposed variational expectation-maximization algorithm can perform blind separation of not only speech source of more sources than mixtures, but also binary source of more sources than mixtures.     

Exchange rate prediction using hybrid neural networks and trading indicators

This paper describes a hybrid model formed by a mixture of various regressive neural network models, such as temporal self-organising maps and support vector regressions, for modelling and prediction of foreign exchange rate time series. A selected set of influential trading indicators, including the moving average convergence/divergence and relative strength index, are also utilised in the proposed method. A genetic algorithm is applied to fuse all the information from the mixture regression models and the economical indicators. Experimental results and comparisons show that the proposed method outperforms the global modelling techniques such as generalised autoregressive conditional heteroscedasticity in terms of profit returns. A virtual trading system is built to examine the performance of the methods under study.