Robust multilayer neural network based on median neuron model

Multilayer perceptron has been widely used in time series forecasting for last two decades. However, it is a well-known fact that the forecasting performance of multilayer perceptron is negatively affected when data have outliers and this is an important problem. In recent years, some alternative neuron models such as generalized-mean neuron, geometric mean neuron, and single multiplicative neuron have been also proposed in the literature. However, it is expected that forecasting performance of artificial neural network approaches based on these neuron models can be also negatively affected by outliers since the aggregation function employed in these models is based on mean value. In this study, a new multilayer feed forward neural network, which is called median neuron model multilayer feed forward (MNM-MFF) model, is proposed in order to deal with this problem caused by outliers and to reach high accuracy level. In the proposed model, unlike other models suggested in the literature, MNM which has median-based aggregation function is employed. MNM is also firstly defined in this study. MNM-MFF is a robust neural network method since aggregation functions in MNM-MFF are based on median, which is not affected much by outliers. In addition, to train MNM-MFF model, particle swarm optimization method was utilized. MNM-MFF was applied to two well-known time series in order to evaluate the performance of the proposed approach. As a result of the implementation, it was observed that the proposed MNM-MFF model has high forecasting accuracy and it is not affected by outlier as much as multilayer perceptron model. Proposed method brings improvement in 7 % for data without outlier, in 90 % for data with outlier, in 95 % for data with bigger outlier.     

The annealing robust backpropagation (ARBP) learning algorithm

Multilayer feedforward neural networks are often referred to as universal approximators. Nevertheless, if the used training data are corrupted by large noise, such as outliers, traditional backpropagation learning schemes may not always come up with acceptable performance. Even though various robust learning algorithms have been proposed in the literature, those approaches still suffer from the initialization problem. In those robust learning algorithms, the so-called M-estimator is employed. For the M-estimation type of learning algorithms, the loss function is used to play the role in discriminating against outliers from the majority by degrading the effects of those outliers in learning. However, the loss function used in those algorithms may not correctly discriminate against those outliers. In the paper, the annealing robust backpropagation learning algorithm (ARBP) that adopts the annealing concept into the robust learning algorithms is proposed to deal with the problem of modeling under the existence of outliers. The proposed algorithm has been employed in various examples. Those results all demonstrated the superiority over other robust learning algorithms independent of outliers. In the paper, not only is the annealing concept adopted into the robust learning algorithms but also the annealing schedule k/t was found experimentally to achieve the best performance among other annealing schedules, where k is a constant and t is the epoch number.     

Robust least squares twin support vector machine for human activity recognition

Human activity recognition is an active area of research in Computer Vision. One of the challenges of activity recognition system is the presence of noise between related activity classes along with high training and testing time complexity of the system. In this paper, we address these problems by introducing a Robust Least Squares Twin Support Vector Machine (RLS-TWSVM) algorithm. RLS-TWSVM handles the heteroscedastic noise and outliers present in activity recognition framework. Incremental RLS-TWSVM is proposed to speed up the training phase. Further, we introduce the hierarchical approach with RLS-TWSVM to deal with multi-category activity recognition problem. Computational comparisons of our proposed approach on four well-known activity recognition datasets along with real world machine learning benchmark datasets have been carried out. Experimental results show that our method is not only fast but, yields significantly better generalization performance and is robust in order to handle heteroscedastic noise and outliers.     

A hybrid robust system considering outliers for electric load series forecasting

Electric load forecasting has become crucial to the safe operation of power grids and cost reduction in the production of power. Although numerous electric load forecasting models have been proposed, most of them are still limited by poor effectiveness in the model training and a sensitivity to outliers. The limitations of current methods may lead to extra operational costs of a power system or even disrupt its power distribution and network safety. To this end, we propose a new hybrid load-forecasting model, which is based on a robust extreme-learning machine and an improved whale optimization algorithm. Specifically, Huber loss, which is insensitive to outliers, is proposed as the objective function in extreme learning machine (ELM) training. In addition, an improved whale optimization algorithm is designed for the robust ELM training, in which a cellular automaton mechanism is used to enhance the local search. To verify our improved whale optimization algorithm, some experiments were then conducted based on seven benchmark test functions. Due to the enhancement of the local search, the improved optimizer was around 7% superior to the basic. Finally, our proposed hybrid forecasting model was validated by two real electric load datasets (Nanjing and New South Wales), and the experimental results confirmed that the proposed hybrid load-forecasting model could achieve satisfying improvements in both datasets.

     

A robust learning algorithm based on support vector regression and robust fuzzy cerebellar model articulation controller

For real-world applications, the obtained data are always subject to noise or outliers. The learning mechanism of cerebellar model articulation controller (CMAC), a neurological model, is to imitate the cerebellum of human being. CMAC has an attractive property of learning speed in which a small subset addressed by the input space determines output instantaneously. For fuzzy cerebellar model articulation controller (FCMAC), the concept of fuzzy is incorporated into CMAC to improve the accuracy problem. However, the distributions of errors into the addressed hypercubes may cause unacceptable learning performance for input data with noise or outliers. For robust fuzzy cerebellar model articulation controller (RFCMAC), the robust learning of M-estimator can be embedded into FCMAC to degrade noise or outliers. Meanwhile, support vector machine (SVR) is a machine learning theory based algorithm which has been applied successfully to a number of regression problems when noise or outliers exist. Unfortunately, the practical application of SVR is limited to defining a set of parameters for obtaining admirable performance by the user. In this paper, a robust learning algorithm based on support SVR and RFCMAC is proposed. The proposed algorithm has both the advantage of SVR, the ability to avoid corruption effects, and the advantage of RFCMAC, the ability to obtain attractive properties of learning performance and to increase accurate approximation. Additionally, particle swarm optimization (PSO) is applied to obtain the best parameters setting for SVR. From simulation results, it shows that the proposed algorithm outperforms other algorithms.     

A New Multiplicative Seasonal Neural Network Model Based on Particle Swarm Optimization

In recent years, artificial neural networks (ANNs) have been commonly used for time series forecasting by researchers from various fields. There are some types of ANNs and feed forward neural networks model is one of them. This type has been used to forecast various types of time series in many implementations. In this study, a novel multiplicative seasonal ANN model is proposed to improve forecasting accuracy when time series with both trend and seasonal patterns is forecasted. This neural networks model suggested in this study is the first model proposed in the literature to model time series which contain both trend and seasonal variations. In the proposed approach, the defined neural network model is trained by particle swarm optimization. In the training process, local minimum traps are avoided by using this population based heuristic optimization method. The performance of the proposed approach is examined by using two real seasonal time series. The forecasts obtained from the proposed method are compared to those obtained from other forecasting techniques available in the literature. It is seen that the proposed forecasting model provides high forecasting accuracy.     

ARRBFNs with SVR for prediction of chaotic time series with outliers

In this article, annealing robust radial basis function networks (ARRBFNs), which consist of a radial basis function network and a support vector regression (SVR), and an annealing robust learning algorithm (ARLA) are proposed for the prediction of chaotic time series with outliers. In order to overcome the initial structural problems of the proposed neural networks, the SVR is utilized to determine the number of hidden nodes, the initial parameters of the kernel, and the initial weights for the proposed ARRBFNs. Then the ARLA that can conquer the outliers is applied to tune the parameters of the kernel and the weights in the proposed ARRBFNs under the initial structure with SVR. The simulation results of Mackey-Glass time series show that the proposed approach with different SVRs can cope with outliers and give a fast learning speed. The results of the simulation are also given to demonstrate the validity of proposed method for chaotic time series with outliers.     

PSO-based single multiplicative neuron model for time series prediction

Single multiplicative neuron model is a novel neural network model introduced recently, which has been used for time series prediction and function approximation. The model is based on a polynomial architecture that is the product of linear functions in different dimensions of the space. Particle swarm optimization (PSO), a global optimization method, is proposed to train the single neuron model in this paper. An improved version of the original PSO, cooperative random learning particle swarm optimization (CRPSO), is put forward to enhance the performance of the conventional PSO. The proposed CRPSO, PSO, back-propagation algorithm and genetic algorithm are employed to train the model for three well-known time series prediction problems. The experimental results demonstrate the superiority of CRPSO-based neuron model in efficiency and robustness over the other three algorithms.     

基于Rescaled Hinge损失函数的多子支持向量机

针对多分类学习模型性能会受异常值影响的问题，提出基于Rescaled Hinge损失函数的多子支持向量机（RHMBSVM）。首先，该方法通过引入有界、非凸的Rescaled Hinge损失函数来构建相应的优化问题；然后，利用共轭函数理论将优化问题作等价变换；最后，使用变量交替策略形成一个迭代算法来求解非凸优化问题，该方法在求解的过程中可自动调节每个样本点的惩罚权重，从而削弱了异常值对K个超平面的影响，增强了鲁棒性。使用5折交叉验证的方法进行数值实验，实验结果表明，在数据集无异常值的情况下，该方法的正确率比多子支持向量机（MBSVM）提升了1.11个百分点，比基于Rescaled Hinge损失函数的鲁棒支持向量机（RSVM-RHHQ）提升了0.74个百分点；在数据集有异常值的情况下，该方法的正确率比MBSVM提升了2.10个百分点，比RSVM-RHHQ提升了1.47个百分点。实验结果证明了所提方法在解决有异常值的多分类问题上的鲁棒性。     

基于Rescaled Hinge损失函数的多子支持向量机

针对多分类学习模型性能会受异常值影响的问题,提出基于Rescaled Hinge损失函数的多子支持向量机（RHMBSVM）。首先,该方法通过引入有界、非凸的Rescaled Hinge损失函数来构建相应的优化问题;然后,利用共轭函数理论将优化问题作等价变换;最后,使用变量交替策略形成一个迭代算法来求解非凸优化问题,该方法在求解的过程中可自动调节每个样本点的惩罚权重,从而削弱了异常值对K个超平面的影响,增强了鲁棒性。使用5折交叉验证的方法进行数值实验,实验结果表明,在数据集无异常值的情况下,该方法的正确率比多子支持向量机（MBSVM）提升了1.11个百分点,比基于Rescaled Hinge损失函数的鲁棒支持向量机（RSVM-RHHQ）提升了0.74个百分点;在数据集有异常值的情况下,该方法的正确率比MBSVM提升了2.10个百分点,比RSVM-RHHQ提升了1.47个百分点。实验结果证明了所提方法在解决有异常值的多分类问题上的鲁棒性。     

Robust exponential smoothing of multivariate time series

Multivariate time series may contain outliers of different types. In the presence of such outliers, applying standard multivariate time series techniques becomes unreliable. A robust version of multivariate exponential smoothing is proposed. The method is affine equivariant, and involves the selection of a smoothing parameter matrix by minimizing a robust loss function. It is shown that the robust method results in much better forecasts than the classic approach in the presence of outliers, and performs similarly when the data contain no outliers. Moreover, the robust procedure yields an estimator of the smoothing parameter less subject to downward bias. As a byproduct, a cleaned version of the time series is obtained, as is illustrated by means of a real data example.     

Efficient and robust deep learning with Correntropy-induced loss function

Deep learning systems aim at using hierarchical models to learning high-level features from low-level features. The progress in deep learning is great in recent years. The robustness of the learning systems with deep architectures is however rarely studied and needs further investigation. In particular, the mean square error (MSE), a commonly used optimization cost function in deep learning, is rather sensitive to outliers (or impulsive noises). Robust methods are needed to improve the learning performance and immunize the harmful influences caused by outliers which are pervasive in real-world data. In this paper, we propose an efficient and robust deep learning model based on stacked auto-encoders and Correntropy-induced loss function (CLF), called CLF-based stacked auto-encoders (CSAE). CLF as a nonlinear measure of similarity is robust to outliers and can approximate different norms (from \(l_0\) to \(l_2\)) of data. Essentially, CLF is an MSE in reproducing kernel Hilbert space. Different from conventional stacked auto-encoders, which use, in general, the MSE as the reconstruction loss and KL divergence as the sparsity penalty term, the reconstruction loss and sparsity penalty term in CSAE are both built with CLF. The fine-tuning procedure in CSAE is also based on CLF, which can further enhance the learning performance. The excellent and robust performance of the proposed model is confirmed by simulation experiments on MNIST benchmark dataset.     

Improving Dendritic Neuron Model With Dynamic Scale-Free Network-Based Differential Evolution

Some recent research reports that a dendritic neuron model (DNM) can achieve better performance than traditional artificial neuron networks (ANNs) on classification, prediction, and other problems when its parameters are well-tuned by a learning algorithm. However, the back-propagation algorithm (BP), as a mostly used learning algorithm, intrinsically suffers from defects of slow convergence and easily dropping into local minima. Therefore, more and more research adopts non-BP learning algorithms to train ANNs. In this paper, a dynamic scale-free network-based differential evolution (DSNDE) is developed by considering the demands of convergent speed and the ability to jump out of local minima. The performance of a DSNDE trained DNM is tested on 14 benchmark datasets and a photovoltaic power forecasting problem. Nine meta-heuristic algorithms are applied into comparison, including the champion of the 2017 IEEE Congress on Evolutionary Computation (CEC2017) benchmark competition effective butterfly optimizer with covariance matrix adapted retreat phase (EBOwithCMAR). The experimental results reveal that DSNDE achieves better performance than its peers.      

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     

CPBUM neural networks for modeling with outliers and noise

In this study, CPBUM neural networks with annealing robust learning algorithm (ARLA) are proposed to improve the problems of conventional neural networks for modeling with outliers and noise. In general, the obtained training data in the real applications maybe contain the outliers and noise. Although the CPBUM neural networks have fast convergent speed, these are difficult to deal with outliers and noise. Hence, the robust property must be enhanced for the CPBUM neural networks. Additionally, the ARLA can be overcome the problems of initialization and cut-off points in the traditional robust learning algorithm and deal with the model with outliers and noise. In this study, the ARLA is used as the learning algorithm to adjust the weights of the CPBUM neural networks. It tunes out that the CPBUM neural networks with the ARLA have fast convergent speed and robust against outliers and noise than the conventional neural networks with robust mechanism. Simulation results are provided to show the validity and applicability of the proposed neural networks.     

竞争式模糊聚类学习在函数逼近中的应用

本文通过对RCA算法中遗忘函数的修正,抑制了类间竞争迭代中的病态发散,从而实现了算法的稳健收敛。用该算法分析数据,采用TSK模糊模型对函数进行逼近,仿真表明该方法能有效地排除噪声及孤立点对系统逼近的干扰。     

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。     

Robust Learning Algorithm Based on Iterative Least Median of Squares

Outliers and gross errors in training data sets can seriously deteriorate the performance of traditional supervised feedforward neural networks learning algorithms. This is why several learning methods, to some extent robust to outliers, have been proposed. In this paper we present a new robust learning algorithm based on the iterative Least Median of Squares, that outperforms some existing solutions in its accuracy or speed. We demonstrate how to minimise new non-differentiable performance function by a deterministic approximate method. Results of simulations and comparison with other learning methods are demonstrated. Improved robustness of our novel algorithm, for data sets with varying degrees of outliers, is shown.     

一种基于聚类提升的不平衡数据分类算法

不平衡数据分类是机器学习研究领域中的一个热点问题。针对传统分类算法处理不平衡数据的少数类识别率过低问题,文章提出了一种基于聚类的改进AdaBoost分类算法。算法首先进行基于聚类的欠采样,在多数类样本上进行K均值聚类,之后提取聚类质心,与少数类样本数目一致的聚类质心和所有少数类样本组成新的平衡训练集。为了避免少数类样本数量过少而使训练集过小导致分类精度下降,采用少数过采样技术过采样结合聚类欠采样。然后,借鉴代价敏感学习思想,对AdaBoost算法的基分类器分类误差函数进行改进,赋予不同类别样本非对称错分损失。实验结果表明,算法使模型训练样本具有较高的代表性,在保证总体分类性能的同时提高了少数类的分类精度。     

A genetic algorithm based robust learning credit assignment cerebellar model articulation controller

In this paper, a novel approach of genetic algorithm based robust learning credit assignment cerebellar model articulation controller (GCA-CMAC) is proposed. The cerebellar model articulation controller (CMAC) is a neurological model, which has an attractive property of learning speed. However, the distributions of errors into the addressed hypercubes of CMAC are not proportional to their credibility and may cause unacceptable learning performance. The credit assignment CMAC (CA-CMAC) can solve this problem by using the creditability of hypercubes that the calculated errors are assigned proportional to the inverse of learning times. Afterward, the obtained learning times can be optimized by genetic algorithm (GA) to increase its accuracy. In this paper, the proposed algorithm is to combine credit assignment ideas and GA to provide accurate learning for CMAC. Moreover, we embed the robust learning approach into the GCA-CMAC and dynamically adjust the learning constant for training data with noise or outliers. From simulation results, it shows that the proposed algorithm outperforms other CMACs.