New robust forecasting models for exchange rates prediction

This paper introduces two robust forecasting models for efficient prediction of different exchange rates for future months ahead. These models employ Wilcoxon artificial neural network (WANN) and Wilcoxon functional link artificial neural network (WFLANN). The learning algorithms required to train the weights of these models are derived by minimizing a robust norm called Wilcoxon norm. These models offer robust exchange rate predictions in the sense that the training of weight parameters of these models are not influenced by outliers present in the training samples. The Wilcoxon norm considers the rank or position of an error value rather than its amplitude. Simulation based experiments have been conducted using real life data and the results indicate that both models, unlike conventional models, demonstrate consistently superior prediction performance under different densities of outliers present in the training samples. Further, comparison of performance between the two proposed models reveals that both provide almost identical performance but the later involved low computational complexity and hence is preferable over the WANN model.     

Robust error measure for supervised neural network learning withoutliers

Most supervised neural networks (NNs) are trained by minimizing the mean squared error (MSE) of the training set. In the presence of outliers, the resulting NN model can differ significantly from the underlying system that generates the data. Two different approaches are used to study the mechanism by which outliers affect the resulting models: influence function and maximum likelihood. The mean log squared error (MLSE) is proposed as the error criteria that can be easily adapted by most supervised learning algorithms. Simulation results indicate that the proposed method is robust against outliers.     

A robust evolutionary feedforward active noise control system using Wilcoxon norm and particle swarm optimization algorithm

The conventional filtered-x least mean square (FxLMS) algorithm commonly employed for active noise control (ANC) is sensitive to disturbances acquired by the error microphone and yields poor performance in such scenario. To circumvent this problem, in this paper, a Wilcoxon FxLMS (WFxLMS) algorithm is proposed and used in the design of an efficient ANC which is robust to outliers in the secondary path and immune to burst noise acquired by the error microphone. It is demonstrated through simulation study that under such situation the proposed algorithm outperforms the traditional FxLMS algorithm. A particle swarm optimization (PSO) algorithm based robust ANC system, which does not require the modeling of the secondary path is also derived in the paper. Improved performance of the robust evolutionary ANC system over L2 norm based evolutionary ANC system is also shown.     

自步稀疏最优均值主成分分析

主成分分析(PCA)是一种无监督降维方法。然而现有的方法没有考虑样本的差异性,且不能联合地提取样本的重要信息,从而影响了方法的性能。针对以上问题,提出自步稀疏最优均值主成分分析方法。模型以 $ {{L}_{{2,1}}}$ 范数定义损失函数,同时用 $ {L_{{\rm{2,1}}}}$ 范数约束投影矩阵作为正则化项,且将均值作为在迭代中优化的变量,这样可一致地选择重要特征,提高方法对异常值的鲁棒性;考虑到训练样本的差异性,利用自步学习机制实现训练样本由“简单”到“复杂”的学习过程,有效地降低异常值的影响。理论分析和实验结果表明,以上方法能更有效地降低异常值对分类精度的影响,提高分类精度。     

Robust TSK fuzzy modeling for function approximation with outliers

The Takagi-Sugeno-Kang (TSK) type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications. Most approaches for modeling TSK fuzzy rules define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions. Besides, training data sets algorithms often contain outliers, which seriously affect least-square error minimization clustering and learning algorithms. A robust TSK fuzzy modeling approach is presented. In the approach, a clustering algorithm termed as robust fuzzy regression agglomeration (RFRA) is proposed to define fuzzy subspaces in a fuzzy regression manner with robust capability against outliers. To obtain a more precision model, a robust fine-tuning algorithm is then employed. Various examples are used to verify the effectiveness of the proposed approach. From the simulation results, the proposed robust TSK fuzzy modeling indeed showed superior performance over other approaches     

The C-loss function for pattern classification

This paper presents a new loss function for neural network classification, inspired by the recently proposed similarity measure called Correntropy. We show that this function essentially behaves like the conventional square loss for samples that are well within the decision boundary and have small errors, and L₀ or counting norm for samples that are outliers or are difficult to classify. Depending on the value of the kernel size parameter, the proposed loss function moves smoothly from convex to non-convex and becomes a close approximation to the misclassification loss (ideal 0–1 loss). We show that the discriminant function obtained by optimizing the proposed loss function in the neighborhood of the ideal 0–1 loss function to train a neural network is immune to overfitting, more robust to outliers, and has consistent and better generalization performance as compared to other commonly used loss functions, even after prolonged training. The results also show that it is a close competitor to the SVM. Since the proposed method is compatible with simple gradient based online learning, it is a practical way of improving the performance of neural network classifiers.     

基于健壮主成分分类器的无监督异常检测方法研究

入侵检测系统在训练过程中需要大量有标识的监督数据进行学习,不利于其应用和推广,经典主成分分析方法对离群数据非常敏感,进而导致分类准确性的下降。为了解决该问题,提出了一种基于健壮主成分分类器的方法,得到被离群数据干扰较少的主成分。根据主成分空间距离和数据重构误差构建异常检测模型。实验表明：该方法能够有效检测未知入侵,在检测率、误警率方面都达到较满意的结果。     

Internal model based robust inversion feedforward and feedback 2DOF control for LPV system with disturbance

To reduce the adverse effects on the control performance and disturbance rejection caused by system uncertainty, a novel internal model based robust inversion feedforward and feedback 2DOF control approach was proposed for LPV system with disturbance. The proposed control approach combines the internal model control and robust inversion based 2DOF control, it utilizes internal model based control to reject external disturbance, utilizes robust inversion 2DOF control to enhance the control resolution and guarantee the system control performance. At first, a LMI synthesis approach for LPV system model identification and a disturbance compensator optimization design method which could minimize H_∞ norm of output error caused by disturbance are presented. Then, combined with internal loop for disturbance compensation, a robust inversion feedforward controller is designed by robust inversion approach and the feedback controller which could render the requirements of reference signal tracking performance and robustness satisfied is obtained by the H_∞ mixed sensitivity synthesis approach. Finally, atomic force microscopy (AFM) vertical positioning simulation experiments are conducted and the experiment results showed that the proposed control approach could achieve better output performance and disturbance rejection compared with conventional internal model based control and robust inversion based 2DOF control approach.     

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.     

时空RPCA在复杂场景下的运动目标检测

在复杂动态背景下,鲁棒主成分分析模型(RPCA)容易将背景中动态背景误判为前景运动目标,导致运动目标检测精度不高。为解决该问题,提出一种基于非凸加权核范数的时空低秩RPCA算法。使用非凸加权核范数替代传统的核范数进行低秩约束,在观测矩阵上通过拉普拉斯特征映射得到时空图拉普拉斯矩阵,将得到的时空图拉普拉斯矩阵嵌入低秩背景矩阵以保持背景对噪声和离群值的鲁棒性。实验结果表明,所提模型在复杂场景中能较准确检测出运动目标。     

Distributed and robust parameter estimation of IIR systems using incremental particle swarm optimization

In recent years because of substantial use of wireless sensor network the distributed estimation has attracted the attention of many researchers. Two popular learning algorithms: incremental least mean square (ILMS) and diffusion least mean square (DLMS) have been reported for distributed estimation using the data collected from sensor nodes. But these algorithms, being derivative based, have a tendency of providing local minima solution particularly for minimization of multimodal cost function. Hence for problems like distributed parameters estimation of IIR systems, alternative distributed algorithms are required to be developed. Keeping this in view the present paper proposes two population based incremental particle swarm optimization (IPSO) algorithms for estimation of parameters of noisy IIR systems. But the proposed IPSO algorithms provide poor performance when the measured data is contaminated with outliers in the training samples. To alleviate this problem the paper has proposed a robust distributed algorithm (RDIPSO) for IIR system identification task. The simulation results of benchmark IIR systems demonstrate that the proposed algorithms provide excellent identification performance in all cases even when the training samples are contaminated with outliers.     

Robust real-time identification for a class of linear time-varying discrete systems

The problem of robust real-time identification of linear single-input-single-output dynamic systems with stochastically time-varying parameters is considered. Two ways of constructing robust algorithms that are able to handle outliers contaminating the gaussian observation disturbance samples are discussed. The first way is based on the general formulation of dynamic stochastic approximation schemes characterized by an adequate non-linear residual transformation, as well as the step-by-step optimization with respect to the weighting matrix of the algorithm. The second way is based on the formulation of one-step optimal estimates. Monte Carlo simulation results illustrate the discussion and show the efficiency of the proposed algorithms in the presence of outliers.     

基于局部保持投影的鲁棒稀疏子空间学习

传统的子空间学习算法包含投影学习和分类两个过程,但是这两个过程分离,且对离群点较敏感,可能导致算法无法获得整体最优解。为此,提出了一种基于局部保持投影的鲁棒稀疏子空间学习算法。该算法将特征学习和分类模型相结合,使学习得到的子空间特征更具有判别性;利用L2,1范数的行稀疏性质,剔除冗余特征,同时在算法模型中考虑数据样本的局部关系来提高对离群点的鲁棒性;最后采用交替迭代方法来求解该模型。在不同数据集上的实验结果表明该算法具有较好的识别效果。     

鲁棒最小二乘孪生支持向量机及其稀疏算法

最小二乘孪生支持向量机通过求解两个线性规划问题来代替求解复杂的二次规划问题,具有计算简单和训练速度快的优势。然而,最小二乘孪生支持向量机得到的超平面易受异常点影响且解缺乏稀疏性。针对这一问题,基于截断最小二乘损失提出了一种鲁棒最小二乘孪生支持向量机模型,并从理论上验证了模型对异常点具有鲁棒性。为使模型可处理大规模数据,基于表示定理和不完全Cholesky分解得到了新模型的稀疏解,并提出了适合处理带异常点的大规模数据的稀疏鲁棒最小二乘孪生支持向量机算法。数值实验表明,新算法比已有算法分类准确率、稀疏性、收敛速度分别提高了1.97%~37.7%、26~199倍和6.6~2 027.4倍。     

采用凹二次正则项的弹性点匹配算法

现有的采用l1范数正则项的点匹配算法,其l1范数优化问题可等价为一个线性规划问题,但约束不满足完全的单模性,这导致解出的对应关系不是整数,需要后续的取整过程,这会给计算结果带来额外误差并使算法复杂化。为解决该问题,基于鲁棒点匹配算法的最新成果,提出一种新的正则项。该正则项是凹的,可以证明目标函数具有整数的最优解,所以算法无须后续处理,实现起来更简单。实验结果表明：相比采用l1范数正则项的算法,所提算法对于各种干扰均有更好的鲁棒性,特别对于野点干扰,误差只有对比算法的一半。     

基于ISDAE模型的复杂工业过程运行状态评价方法及应用

工业过程的运行状态评价对保证产品质量及提升企业综合经济效益具有重要意义. 针对工业过程中存在强非线性、信息冗余以及不确定性因素影响而难以建立稳健可靠的运行状态评价模型问题, 提出一种基于综合经济指标驱动的稀疏降噪自编码器模型(Comprehensive economic index driven sparse denoising autoencoder, ISDAE)的复杂工业过程运行状态评价方法. 首先, 在SDAE (Sparse denoising autoencoder)模型中引入综合经济指标预测误差项, 迫使SDAE学习与综合经济指标相关的数据特征, 建立ISDAE特征提取模型. 其次, 将ISDAE模型所学特征作为输入训练运行状态识别模型, 级联特征提取模型和运行状态识别模型并通过微调网络结构参数获得运行状态评价模型. 另外, 针对非优状态, 提出一种基于自编码器贡献图算法的非优因素追溯方法, 通过计算变量的贡献率识别非优因素. 最后, 将所提方法应用于重介质选煤过程, 验证所提方法的有效性和实用性.     

Applying Dynamic Training‐Subset Selection Methods Using Genetic Programming for Forecasting Implied Volatility

Volatility is a key variable in option pricing, trading, and hedging strategies. The purpose of this article is to improve the accuracy of forecasting implied volatility using an extension of genetic programming (GP) by means of dynamic training‐subset selection methods. These methods manipulate the training data in order to improve the out‐of‐sample patterns fitting. When applied with the static subset selection method using a single training data sample, GP could generate forecasting models, which are not adapted to some out‐of‐sample fitness cases. In order to improve the predictive accuracy of generated GP patterns, dynamic subset selection methods are introduced to the GP algorithm allowing a regular change of the training sample during evolution. Four dynamic training‐subset selection methods are proposed based on random, sequential, or adaptive subset selection. The latest approach uses an adaptive subset weight measuring the sample difficulty according to the fitness cases' errors. Using real data from S&P500 index options, these techniques are compared with the static subset selection method. Based on mean squared error total and percentage of non‐fitted observations, results show that the dynamic approach improves the forecasting performance of the generated GP models, especially those obtained from the adaptive‐random training‐subset selection method applied to the whole set of training samples.     

利用矢量基学习和自适应迭代算法改进LSSVR

针对最小二乘支持向量回归缺乏传统SVR的稀疏性和鲁棒性等问题,综合矢量基学习和自适应迭代算法的优势,提出了一种改进的加权最小二乘支持向量回归算法（LSSVR）。该算法通过引入用矢量基学习和自适应迭代相结合的方式得到一个小的支持向量集,可以避免递推时可能出现的误差积累问题,有效提高算法的稀疏性和稳定性;同时采用加权方法确定权值系数以减小训练样本中非高斯噪声的影响。实验结果表明,改进的LSSVR具有较好的鲁棒性、支持向量稀疏性和动态建模实时性。     

基于改进的LSSVM辨识动态非线性时变系统

针对非线性时变系统难以辨识的问题,提出了一种基于改进最小二乘支持向量机的辨识新方法。该方法在加权最小二乘支持向量机的基础上,引入用矢量基学习和自适应迭代相结合的方式得到一个小的支持向量,同时采用加权方法确定权值系数以减小训练样本中非高斯噪声的影响。通过对动态非线性时变系统的仿真,结果表明该算法具有较好的鲁棒性、支持向量稀疏性和动态建模实时性。     

孤立点检测改进径向基神经网络动态预测模型

提出一种基于凝聚层次聚类消除孤立点的新方法,借助聚类树识别孤立点。去除孤立点后,利用RBF网络建立动态预测模型,实验结果表明,网络的训练和泛化性能较消除孤立点前有明显提高。说明凝聚层次聚类方法用在孤立点检测方面是有效可行的,消除孤立点后建立的模型收敛速度快,泛化能力更优。