On the complex backpropagation algorithm

A recursive algorithm for updating the coefficients of a neural network structure for complex signals is presented. Various complex activation functions are considered and a practical definition is proposed. The method, associated to a mean-square-error criterion, yields the complex form of the conventional backpropagation algorithm     

Extended backpropagation algorithm

A fast learning algorithm for feedforward neural networks is described. This algorithm is based on modifications to the backpropagation algorithm, The learning rate and momentum coefficient are adapted according to the coefficient of correlation between the downhill gradient and the previous weight update.<>     

Modified backpropagation algorithm for fast learning in neural networks

A fast learning rule for artificial neural systems which is based on modifications to a backpropagation algorithm is described. The rule minimises the error function along the direction of the gradient and backpropagates the error pattern according to a constant error energy approach.<>     

The complex LMS algorithm

A least-mean-square (LMS) adaptive algorithm for complex signals is derived. The original Widrow-Hoff LMS algorithm is Wj+l= Wj+ 2µεjXj. The complex form is shown to be Wj+1= Wj+ 2µεjX^-j, where the boldfaced terms represent complex (phasor) signals and the bar above Xjdesignates complex conjugate.     

Fluctuation analysis of a two-layer backpropagation algorithm usedfor modeling nonlinear memoryless channels

Neural networks have been used to model the nonlinear characteristics of memoryless nonlinear channels using the backpropagation learning (BP) with experimental training data. The mean transient and convergence behavior of a simplified two-layer neural network has been studied previously in order to better understand this neural network application. The network was trained with zero mean Gaussian data. This paper extends these results to include the effects of the weight fluctuations on the mean square error (MSE). A new methodology is presented that can be extended to other nonlinear learning problems. The new mathematical model is able to predict the MSE learning behavior as a function of the algorithm step size μ. The performance analysis is based on the derivation of linear recursions for the variance and covariance of the weights that depend nonlinearly on the mean weights. These linear recursions can be used to predict the local mean-square stability of the weights. As in linear gradient search problems (LMS, etc.), it is shown that there exists an optimum p (minimizing the MSE), which is the result of the tradeoff between fast learning and small weight fluctuations. Monte Carlo simulations display excellent agreement between the actual behavior and the predictions of the theoretical model over a wide range of μ values     

Rapid backpropagation learning algorithms

One of the major drawbacks of the backpropagation algorithm is its slow rate of convergence. Researchers have tried several different approaches to speed up the convergence of backpropagation learning. In this paper, we present those rapid learning methods as three categories, and implement the representative methods of each category: (1) for the numerical method based approach, the Aitken's ² process, (2) for the heuristics based approach, the dynamic adaptation of learning rate, and (3) for the learning strategy based approach, the selective presentation of learning samples. Based on these implementations, the performance is evaluated with experiments and the merits and demerits are briefly discussed.This work was supported in part by a grant from the Korea Science and Engineering Foundation (KOSEF) and the Center for Artificial Intelligence Research (CAIR), the Engineering Research Center (ERC) of Excellence Program.     

Single-step digital backpropagation for nonlinearity mitigation

Nonlinearity mitigation based on the enhanced split-step Fourier method (ESSFM) for the implementation of low-complexity digital backpropagation (DBP) is investigated and experimentally demonstrated. After reviewing the main computational aspects of DBP and of the conventional split-step Fourier method (SSFM), the ESSFM for dual-polarization signals is introduced. Computational complexity, latency, and power consumption of DBP based on the SSFM and ESSFM algorithms are estimated and compared. Effective low-complexity nonlinearity mitigation in a 112 Gb/s polarization-multiplexed QPSK system is experimentally demonstrated by using a single-step DBP based on the ESSFM. The proposed DBP implementation requires only a single step of the ESSFM algorithm to achieve a transmission distance of 3200 km over a dispersion-unmanaged link. In comparison, a conventional DBP implementation requires 20 steps of the SSFM algorithm to achieve the same performance. An analysis of the computational complexity and structure of the two algorithms reveals that the overall complexity and power consumption of DBP are reduced by a factor of 16 with respect to a conventional implementation, while the computation time is reduced by a factor of 20. Similar complexity reductions can be obtained at longer distances if higher error probabilities are acceptable. The results indicate that the proposed algorithm enables a practical and effective implementation of DBP in real-time optical receivers, with only a moderate increase in the computational complexity, power consumption, and latency with respect to a simple feed-forward equalizer for bulk dispersion compensation.     

Statistical analysis of a two-layer backpropagation algorithm usedfor modeling nonlinear memoryless channels: the single neuron case

Neural networks have been used for modeling the nonlinear characteristics of memoryless nonlinear channels using backpropagation (BP) learning with experimental training data. In order to better understand this neural network application, this paper studies the transient and convergence properties of a simplified two-layer neural network that uses the BP algorithm and is trained with zero mean Gaussian data. The paper studies the effects of the neural net structure, weights, initial conditions, and algorithm step size on the mean square error (MSE) of the neural net approximation. The performance analysis is based on the derivation of recursions for the mean weight update that can be used to predict the weights and the MSE over time. Monte Carlo simulations display good to excellent agreement between the actual behavior and the predictions of the theoretical model     

Birdsong recognition using backpropagation and multivariatestatistics

An investigation has been made of bird species recognition using recordings of birdsong. Six species of birds native to Manitoba were chosen: song sparrows, fox sparrows, marsh wrens, sedge wrens, yellow warblers, and red-winged blackbirds. These species exhibit overlapping characteristics in terms of frequency content, song components, and length of songs. Songs from multiple individuals in each of these species were employed, with discernible recording noise such as tape hiss and, in some cases, other competing songs in the background. These songs were analyzed using backpropagation learning in two-layer perceptrons, as well as methods from multivariate statistics that included principal components and quadratic discriminant analysis. Preprocessing methods included linear predictive coding and windowed Fourier transforms. Generalization performance ranged from 82-93 % correct identification, with the lower figures corresponding to smaller networks employing more preprocessing for dimensionality reduction. At the same time, the computational requirements were significantly reduced in this case     

复杂数据的异常检测算法

随着信息技术的快速发展,不同领域产生越来越多的数据,大量的数据形式多种多样,其中有一些数据用图表示更合适,异常数据会对相关领域造成一定危害,如何检测复杂数据中的异常有着重要的意义。传统的异常检测算法大都针对向量型数据提出,不能直接运用于这些复杂的数据中,因此利用图核的方法先将这些数据进行转化接着降维,再利用单类支持向量机训练模型提出了复杂数据的异常检测算法,在数据集上的实验结果验证了算法的有效性。     

求解三维问题的区域分解时域有限差分方法

该文提出一种用于三维复杂问题的区域分解时域有限差分算法(DD-FDTD)。依据待解三维复杂问题的特点,将其分解为几个子区域。每个子域中的问题相对简单,可采用适合于该区域的共形网格进行划分计算,通过插值再修正误差的办法,把各个子区域综合起来,获得原问题的解。这样,应用区域分解的思想,简化了复杂的问题。修正误差的方法,使本算法得以实现并大幅度提高了计算精度。采用本算法对三维口径天线问题进行了分析计算并与实测数据进行了比对,验证了算法的正确性。     

Algebraical algorithm for computing complex systems reliability

This paper describes the use of a graph theoretical approach called Latin Multiplication, for finding the success paths for any reliability network whose elements are statistically independent.     

Fast algorithm for computer complex number-theoretic transforms

A high-radix f.f.t. algorithm for computing transforms over GF(q2), where q is a Mersenne prime, is developed to implement fast circular convolutions. This new algorithm requires substantially fewer multiplications than the conventional f.f.t.     

一种有效的双树复小波-Wiener滤波去噪算法

为了有效恢复被高斯白噪声污染的图像,将双树复小波变换和自适应Wiener滤波结合起来,提出了一种双树复小波-Wiener滤波去噪算法.仿真结果表明,利用该算法去噪后恢复的图像主观质量和峰值信噪比比基于正交小波变换的门限法和Wiener滤波法都要好.     

CMAS: an associative neural network alternative to backpropagation

The CMAC (cerebellar model arithmetic computer) neural network, an alternative to backpropagated multilayer networks, is described. The following advantages of CMAC are discussed: local generalization, rapid algorithmic computation based on LMS (least-mean-square) training, incremental training, functional representation, output superposition, and a fast practical hardware realization. A geometrical explanation of how CMAC works is provided, and applications in robot control, pattern recognition, and signal processing are briefly described. Possible disadvantages of CMAC are that it does not have global generalization and that it can have noise due to hash coding. Care must be exercised (as with all neural networks) to assure that a low error solution will be learned     

A complex algorithm for linearly constrained adaptive arrays

A linearly constrained least mean squares (lms) algorithm for complex signals is derived to minimize noise power in the array output. The original algorithm for real signals isW(k + 1) = P[W(k) - mu y(k)X(k)] + F. The complex form is shown to beW(k + 1) = P[W(k) - mu y(k)bar{X}(k)] + F, where the bar abovebar{X}denotes complex conjugate.W, y, X, andFare complex.Pandmuare real.     

基于时域相位思想的复自相关算法的研究

根据ADCP流速测量的需要,研究了利用复自相关法估计回波信号多普勒频移的算法.通过对比FFT法和复自相关法在频率估计量的偏差和标准差,以及算法运算量,表明复自相关算法是频率估计算法的一个合适选择.     

复杂环境下基于ROI的车牌提取算法

感兴趣区域（ROI）是最能体现图像内容的区域,基于ROI的图像特征提取技术有效提高了图像处理和分析的效率,在图像处理与分析领域有着重要的应用.首先简要介绍现有的车牌提取方法,针对目前复杂环境下的车牌ROI提取算法提取效果不明显、计算繁琐、漏检率高等缺点,提出一种采用颜色特征和模板匹配的车牌ROI提取算法,该算法避免大量运算,具有相对于图像平移、尺度变化的低敏感性,并且取得了较好的实验效果.     

复合形遗传算法求解功率优化分配研究

传统遗传算法存在过早收敛及局部搜索能力差的缺点,在求解无线网络协作通信功率优化分配等NP难问题时难以求得最优解。通过小生境策略解决遗传算法过早收敛问题,引入复合形法提高局部搜索能力,构造了兼顾广度搜索与深度搜索的高性能混合算法,并对上述问题进行求解。实验结果表明,所提算法与已有算法相比有一定优势,有效延长了协作网络寿命,稳定性较好,分配的功率波动范围小。