多用户干扰信道下建模于流形上的联合干扰对齐预编码

首先从子空间对齐的角度将干扰信号功率和有用信号功率联合优化的问题建模于Grassmannian流形上,有约束的最优化问题被转化为降维的无约束的最优化问题。然后利用Grassmannian流形的几何特性,提出了一种基于Grassmannian 流形上共轭梯度算法的联合干扰对齐预编码方案。计算机仿真表明,该算法兼顾干扰信号功率的最小化和有用信号功率的最大化,可以有效提高系统的和速率性能,而且该算法可以有效解决Grassmannian流形上最陡下降算法每次寻优的 90°转折问题,具有更高的收敛速度。     

一种基于特征空间的盲波束形成算法

绝大多数通信信号都具有周期平稳信号特性。利用信号的周期平稳特性可以进行真正的盲自适应波束形成,因而受到了广泛关注。ＣＡＢ类算法就是其中的一种。它的运算量较小,但鲁棒性不够强。本文针对其不足,提出了一种基于特征空间的盲波束形成算法。该算法将估计的导引矢量约束在信号子空间,降低了目标信号含于自相关估计矩阵和有限次快拍相关阵引起的子空间扰动的影响,提高了算法的收敛速度和鲁棒性。同时,目前用于进行子空间分解的新算法层出不穷,运算量不断降低。因此,本文提出的盲算法具有很强的实用性和广阔的应用前景。计算机仿真验证了理论分析。     

一种非平稳环境下的自适应变步长盲源分离算法

提出一种基于不完整自然梯度的变步长约束算法,用来处理非平稳环境下的瞬时盲源分离问题.该算法利用系统上的扰动对代价函数进行约束,对算法中的约束因子采用自适应形式,根据分离情况对约束因子进行自适应调整,以加快收敛速度.同时,引入基于代价函数梯度的变步长,使其具有更好的跟踪性能.仿真结果表明,在非平稳环境下,所提出的算法在提高收敛速度的同时可以有效分离源信号而不产生严重的稳态误差.     

基于自组织神经网络的非平稳信号盲分离

针对具有二阶非平稳特性的源信号盲分离问题,提出一种基于自组织神经网络的在线盲源分离新算法.利用自组织神经网络构建一种多层盲分离网络模型,以网络输出层信号的相关性为代价函数,采用自然梯度原理对网络参数进行学习,最小化该代价函数从而实现信号分离.将多层自组织神经网络和自然梯度原理相结合,提高了分离算法的灵活性和性能.最后将该算法与其他算法进行了仿真对比,仿真结果表明该算法具有较好的收敛精度及稳定性.     

采用过采样技术的Infomax盲源分离算法

针对混合平稳信号的盲分离问题,提出了一种基于过采样技术的新盲源分离算法。对接收混合信号进行过采样,使接收平稳信号具有循环平稳特性。根据信息最大化算法,以输出信号的熵作为目标函数,将信号的循环相关函数和循环频率应用到分离矩阵的寻优中,实现信号的盲分离。仿真结果表明,该算法比传统的Infomax盲分离算法收敛速度快,收敛精度高。     

NGA实现互信息量最小化的盲源分离

提出了一种新的盲源分离算法,该算法通过自然梯度算法实现互信息量最小化,从而达到盲源分离的最佳效果。由于互信息量具有度量分离信号的循环相关矩阵和单位阵的相似程度的特性,最小互信量标志着分离矩阵最佳的状态。通过自然梯度寻优算法来实现互信息量的最小化,从而得到理想的分离矩阵。仿真结果表明算法对具有循环平稳特性的源信号分离效果显著,且收敛速度快。     

一种基于核函数的杂系盲源分离算法

本文提出了一种基于核函数的杂系盲源分离算法,即KFBSS算法。该算法通过引入非线性核函数和平滑参数h,将分离信号进行非线性核映射,最优化平滑参数h,同时更新混合分离矩阵,通过不断迭代学习,对混合信号进行盲源分离。仿真结果表明,与EASI算法、白化算法、自然梯度算法相比,本文方法能更有效的分离同系混合或杂系混合信号,收敛速度更快,且能够适应于非平稳环境,具有一定的实用性。     

主奇异子空间跟踪算法与性能分析

主奇异子空间分析是一种自适应的神经网络信号处理技术,广泛应用于现代信号处理中.本文提出一种新的主奇异子空间跟踪信息准则,并以此为基础推导出一种在线的梯度流神经网络算法.理论分析表明,信息准则具有唯一的全局最小值,且最小值对应的状态矩阵能够恰好张成输入信号的主奇异子空间.该算法具有良好的收敛能力,强大的自稳定性能,且当输入信号呈现出奇异互相关特性时,仍呈现出良好的跟踪效果.分别采用李雅普诺夫函数方法和常微分方程方法分析算法的收敛性能和自稳定性. MATLAB仿真算例验证了算法的性能.     

基于遗传-狮群算法优化的独立分量分析算法

针对传统独立分量分析算法存在过度依赖梯度信息、容易陷入局部最优等缺陷,提出一种基于遗传-狮群算法(GA_LSO)优化的独立分量分析算法。以信号的峭度绝对值之和作为目标函数,结合遗传算法较强的全局搜索能力和狮群算法良好的进化机制,对目标函数进行求解,提高了独立分量分析算法的精度,实现了对混叠信号的盲分离。仿真实验结果表明,该算法在收敛精度和速度上均较其他智能算法有较大提升,在解决盲源信号分离问题时,具有更高的收敛精度和更好的全局搜索能力,能有效地分离出各个源信号。     

基于时频分布的非平稳信号盲分离算法

针对传统的盲源分离方法往往忽略信号非平稳性的问题,基于从瞬时线性混合模型的观测信号中分离出相互独立的源信号,并针对信号具有非平稳性,结合时频分析和盲源分离各自的特点,对非平稳信号盲分离进行了研究,并提出了一种新的具有不同空间时频分布的非平稳盲分离算法.仿真实验表明,通过采用维纳全时频域搜索来寻找局部最大值的平滑伪Wigner-Ville分布,该算法可以抑制交叉项而且能够保持时频聚集性,并达到了很好的分离效果.     

基于复杂性寻踪的非独立图像盲分离

复杂性寻踪是近期发展起来的一种结合非高斯性和时间相关的投影寻踪方法,目的是在多元数据中找到一个投影方向,使得数据在该方向上的投影具有最令人感兴趣的结构。它是投影寻踪方法在时间序列应用上的扩展,相似于依赖时间的信号源盲分离和独立分离分析。由相互独立的图像混合而成的混合图像的盲分离技术已经相当成熟,但对非独立混合的图像的盲分离仍然是个难题。从时间序列的复杂性寻踪出发,推导出一个复杂性寻踪的定点算法。该算法是经典的快速独立分量分析算法（FastICA）的扩展,继承了FastICA的优点,简单易行,不需要用户选择学习率,并且算法具有快速稳定收敛的性质。该算法应用到非独立图像的混合图像的盲分离时,取得了较好的分离结果。     

Complexity Pursuit for Unifying Model

Complexity pursuit is an extension of projection pursuit to time series data and the method is closely related to blind separation of time-dependent source signals and independent component analysis. The goal is to find projections of time series that have interesting structure, defined using criteria related to Kolmogoroff complexity or coding length. In this paper, we first derive a simple approximation of coding length for unifying model that takes into account nongaussianity of sources, their autocorrelations and their smoothly changing nonstationary variances. Next, a fixed-point algorithm is proposed by using approximate Newton method. Finally, simulations verify the fixed-point algorithm converges faster than the existing gradient algorithm and it is more simple to implement due to it does not need any learning rate.     

Self-stabilized gradient algorithms for blind source separation with orthogonality constraints.

Developments in self-stabilized algorithms for gradient adaptation of orthonormal matrices have resulted in simple but powerful principal and minor subspace analysis methods. We extend these ideas to develop algorithms for instantaneous prewhitened blind separation of homogeneous signal mixtures. Our algorithms are proven to be self-stabilizing to the Stiefel manifold of orthonormal matrices, such that the rows of the adaptive demixing matrix do not need to be periodically reorthonormalized. Several algorithm forms are developed, including those that are equivariant with respect to the prewhitened mixing matrix. Simulations verify the excellent numerical properties of the proposed methods for the blind source separation task.     

核岭回归的邻域保持最大间隔分析的人脸识别

邻域保持嵌入是局部线性嵌入的线性近似,强调保持数据流形的局部结构.改进的最大间隔准则重视数据流形的判别和几何结构,提高了对数据的分类性能.文中提出的核岭回归的邻域保持最大间隔分析既保持流形的局部结构,又使不同类别的数据保持最大间隔,以此构建算法的目标函数.为了解决数据流形高度非线性化的问题,算法采用核岭回归计算特征空间的变换矩阵.先求解数据样本在核子空间中降维映射的结果,再解得核子空间.在标准人脸数据库上的实验表明该算法正确有效,并且识别性能优于普通的流形学习算法.     

A non-monotone linear search algorithm with mixed direction on Stiefel manifold

In this paper, we propose a non-monotone line search method for solving optimization problems on Stiefel manifold. The main novelty of our approach is that our method uses a search direction based on a linear combination of descent directions and a Barzilai–Borwein line search. The feasibility is guaranteed by projecting each iterate on the Stiefel manifold through SVD (singular value decomposition) factorizations. Some theoretical results for analysing the algorithm are presented. Finally, we provide numerical experiments for comparing our algorithm with other state-of-the-art procedures. The code is available online. The experimental results show that the proposed algorithm is competitive with other approaches and for particular problems, the computational performance is better than the state-of-the-art algorithms.     

Natural gradient learning for over- and under-complete bases In ICA

Independent component analysis or blind source separation is a new technique of extracting independent signals from mixtures. It is applicable even when the number of independent sources is unknown and is larger or smaller than the number of observed mixture signals. This article extends the natural gradient learning algorithm to be applicable to these overcomplete and undercomplete cases. Here, the observed signals are assumed to be whitened by preprocessing, so that we use the natural Riemannian gradient in Stiefel manifolds.     

An approximate approach to H2 optimal model reduction

Deals with the problem of computing an H₂ optimal reduced-order model for a given stable multivariable linear system. By way of orthogonal projection, the problem is formulated as that of minimizing the H₂ model-reduction cost over the Stiefel manifold so that the stability constraint on reduced-order models is automatically satisfied and thus totally avoided in the new problem formulation. The closed form expression for the gradient of the cost over the manifold is derived, from which a gradient flow results as an ordinary differential equation (ODE). A number of nice properties about such a flow are established. Furthermore, two explicit iterative convergent algorithms are developed from the flow; one has a constant step-size and the other has a varying step-size and is much more efficient. Both of them inherit the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model reduction cost is decreasing to minima along the iterates. A procedure for closing the gap between the original and modified problem is proposed. In the symmetric case, the two problems are shown to be equivalent. Numerical examples are presented to illustrate the effectiveness of the proposed algorithms as well as convergence     

An unconstrained H 2 model order reduction optimisation algorithm based on the Stiefel manifold for bilinear systems

In this paper, the optimal H ₂ model order reduction (MOR) problem for bilinear systems is explored. The orthogonality constraint of the cost function generated by the H ₂ MOR error makes it is posed not on the Euclidean space, but can be discussed on the Stiefel manifold. Then, the H ₂ optimal MOR problem of bilinear systems is turned into the unconstrained optimisation on the Stiefel manifold. The explicit expression of the gradient for the cost function on this manifold is derived. Full use of the geometry properties of this Stiefiel manifold, we propose a feasible and effective iterative algorithm to solve the unconstrained H ₂ minimisation problem. Moreover, the convergence of our algorithm is rigorously proved. Finally, two practical examples related to bilinear systems demonstrate the effectiveness of our algorithm.     

Stochastic Backward Euler: An Implicit Gradient Descent Algorithm for <Emphasis Type="Italic">k</Emphasis>-Means Clustering

In this paper, we propose an implicit gradient descent algorithm for the classic k-means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-point iteration, in which we randomly sample a mini-batch gradient in every iteration. It is the average of the fixed-point trajectory that is carried over to the next gradient step. We draw connections between the proposed stochastic backward Euler and the recent entropy stochastic gradient descent for improving the training of deep neural networks. Numerical experiments on various synthetic and real datasets show that the proposed algorithm provides better clustering results compared to k-means algorithms in the sense that it decreased the objective function (the cluster) and is much more robust to initialization.