A Fast and Accurate Online Sequential Learning Algorithm for Feedforward Networks

In this paper, we develop an online sequential learning algorithm for single hidden layer feedforward networks (SLFNs) with additive or radial basis function (RBF) hidden nodes in a unified framework. The algorithm is referred to as online sequential extreme learning machine (OS-ELM) and can learn data one-by-one or chunk-by-chunk (a block of data) with fixed or varying chunk size. The activation functions for additive nodes in OS-ELM can be any bounded nonconstant piecewise continuous functions and the activation functions for RBF nodes can be any integrable piecewise continuous functions. In OS-ELM, the parameters of hidden nodes (the input weights and biases of additive nodes or the centers and impact factors of RBF nodes) are randomly selected and the output weights are analytically determined based on the sequentially arriving data. The algorithm uses the ideas of ELM of Huang developed for batch learning which has been shown to be extremely fast with generalization performance better than other batch training methods. Apart from selecting the number of hidden nodes, no other control parameters have to be manually chosen. Detailed performance comparison of OS-ELM is done with other popular sequential learning algorithms on benchmark problems drawn from the regression, classification and time series prediction areas. The results show that the OS-ELM is faster than the other sequential algorithms and produces better generalization performance     

Regularized online sequential learning algorithm for single-hidden layer feedforward neural networks

Online learning algorithms have been preferred in many applications due to their ability to learn by the sequentially arriving data. One of the effective algorithms recently proposed for training single hidden-layer feedforward neural networks (SLFNs) is online sequential extreme learning machine (OS-ELM), which can learn data one-by-one or chunk-by-chunk at fixed or varying sizes. It is based on the ideas of extreme learning machine (ELM), in which the input weights and hidden layer biases are randomly chosen and then the output weights are determined by the pseudo-inverse operation. The learning speed of this algorithm is extremely high. However, it is not good to yield generalization models for noisy data and is difficult to initialize parameters in order to avoid singular and ill-posed problems. In this paper, we propose an improvement of OS-ELM based on the bi-objective optimization approach. It tries to minimize the empirical error and obtain small norm of network weight vector. Singular and ill-posed problems can be overcome by using the Tikhonov regularization. This approach is also able to learn data one-by-one or chunk-by-chunk. Experimental results show the better generalization performance of the proposed approach on benchmark datasets.     

基于核映射极限学习机的入口氮氧化物预测

针对在线贯序极限学习机(OS-ELM)算法隐含层输出不稳定、易产生奇异矩阵和在线贯序更新时没有考虑训练样本时效性的问题,提出一种基于核函数映射的正则化自适应遗忘因子(FFOS-RKELM)算法.该算法利用核函数代替隐含层,能够产生稳定的输出结果.在初始阶段加入正则化方法,通过构造非奇异矩阵提高模型的泛化能力;在贯序更新阶段,通过新到的数据自动更新遗忘因子.将FFOS-RKELM算法应用到混沌时间序列预测和入口氮氧化物时间序列预测中,相比于OS-ELM、FFOS-RELM、OS-RKELM算法,可有效地提高预测精度和泛化能力.     

极限学习机在机场旅客吞吐量预测中的应用

极限学习机(ELM)是一种新型单馈层神经网络算法,在训练过程中只需要设置合适的隐藏层节点个数,随机赋值输入权值和隐藏层偏差,一次完成无需迭代.结合遗传算法在预测模型参数寻优方面的优势,找到极限学习机的最优参数取值,建立成都双流国际机场旅客吞吐量预测模型,通过对比支持向量机、BP神经网络,分析遗传-极限学习机算法在旅客吞吐量预测中的可行性和优势.仿真结果表明遗传-极限学习机算法不仅可行,并且与原始极限学习机算法相比,在预测精度和训练速度上具有比较明显的优势.     

Fast learning network: a novel artificial neural network with a fast learning speed

This paper proposes a novel artificial neural network called fast learning network (FLN). In FLN, input weights and hidden layer biases are randomly generated, and the weight values of the connection between the output layer and the input layer and the weight values connecting the output node and the input nodes are analytically determined based on least squares methods. In order to test the FLN validity, it is applied to nine regression applications, and experimental results show that, compared with support vector machine, back propagation, extreme learning machine, the FLN with much more compact networks can achieve very good generalization performance and stability at a very fast training speed and a quick reaction of the trained network to new observations. In addition, in order to further test the FLN validity, it is applied to model the thermal efficiency and NO _x emissions of a 330 WM coal-fired boiler and achieves very good prediction precision and generalization ability at a high learning speed.     

Evolutionary extreme learning machine

Extreme learning machine (ELM) [G.-B. Huang, Q.-Y. Zhu, C.-K. Siew, Extreme learning machine: a new learning scheme of feedforward neural networks, in: Proceedings of the International Joint Conference on Neural Networks (IJCNN2004), Budapest, Hungary, 25-29 July 2004], a novel learning algorithm much faster than the traditional gradient-based learning algorithms, was proposed recently for single-hidden-layer feedforward neural networks (SLFNs). However, ELM may need higher number of hidden neurons due to the random determination of the input weights and hidden biases. In this paper, a hybrid learning algorithm is proposed which uses the differential evolutionary algorithm to select the input weights and Moore-Penrose (MP) generalized inverse to analytically determine the output weights. Experimental results show that this approach is able to achieve good generalization performance with much more compact networks.     

基于结合混沌纵横交叉的粒子群算法优化极限学习机的短期负荷预测

为了解决传统的单一负荷预测模型精度低以及常规智能算法在解决高维、多模复杂问题时容易陷入局部最优的问题,提出了一种结合混沌纵横交叉的粒子群算法（CC-PSO）优化极限学习机(ELM)的短期负荷预测模型。ELM的泛化能力与其输入权值和隐含层偏置密切相关,采用结合混沌纵横交叉的粒子群算法优化ELM的输入权值与隐含层偏置,提高了ELM的泛化能力和预测精度。选择广东某地区实际电网负荷数据进行分析,研究结果表明,相对于BP神经网络和支持向量机,ELM具有更高的泛化能力和预测精度;CC-PSO相对于粒子群和遗传算法具有更高的全局搜索能力,CC-PSO-ELM模型具有较高的负荷预测精度。     

Ensemble of online sequential extreme learning machine

Liang et al. [A fast and accurate online sequential learning algorithm for feedforward networks, IEEE Transactions on Neural Networks 17 (6) (2006), 1411–1423] has proposed an online sequential learning algorithm called online sequential extreme learning machine (OS-ELM), which can learn the data one-by-one or chunk-by-chunk with fixed or varying chunk size. It has been shown [Liang et al., A fast and accurate online sequential learning algorithm for feedforward networks, IEEE Transactions on Neural Networks 17 (6) (2006) 1411–1423] that OS-ELM runs much faster and provides better generalization performance than other popular sequential learning algorithms. However, we find that the stability of OS-ELM can be further improved. In this paper, we propose an ensemble of online sequential extreme learning machine (EOS-ELM) based on OS-ELM. The results show that EOS-ELM is more stable and accurate than the original OS-ELM.     

Dynamic ensemble extreme learning machine based on sample entropy

Extreme learning machine (ELM) as a new learning algorithm has been proposed for single-hidden layer feed-forward neural networks, ELM can overcome many drawbacks in the traditional gradient-based learning algorithm such as local minimal, improper learning rate, and low learning speed by randomly selecting input weights and hidden layer bias. However, ELM suffers from instability and over-fitting, especially on large datasets. In this paper, a dynamic ensemble extreme learning machine based on sample entropy is proposed, which can alleviate to some extent the problems of instability and over-fitting, and increase the prediction accuracy. The experimental results show that the proposed approach is robust and efficient.     

面向贯序不均衡数据的混合采样极限学习机

针对现有机器学习算法难以有效提高贯序不均衡数据分类问题中少类样本分类精度的问题,提出一种基于混合采样策略的在线贯序极限学习机。该算法可在提高少类样本分类精度的前提下,减少多类样本的分类精度损失,主要包括离线和在线两个阶段:离线阶段采用均衡采样策略,利用主曲线分别构建多类和少类样本的可信区域,在不改变样本分布特性的前提下,利用可信区域扩充少类样本和削减多类样本,进而得到均衡的离线样本集,建立初始模型;在线阶段仅对贯序到达的多类数据进行欠采样,根据样本重要度挑选最具价值的多类样本,进而动态更新网络权值。通过理论分析证明所提算法在理论上存在损失信息上界。采用UCI标准数据集和实际的澳门空气污染预报数据进行仿真实验,结果表明,与现有在线贯序极限学习机(OS-ELM)、极限学习机(ELM)和元认知在线贯序极限学习机(MCOS-ELM)算法相比,所提算法对少类样本的预测精度更高,且数值稳定性良好。     

Manifold regularized extreme learning machine

Extreme learning machine (ELM) works for generalized single-hidden-layer feedforward networks (SLFNs), and its essence is that the hidden layer of SLFNs need not be tuned. But ELM only utilizes labeled data to carry out the supervised learning task. In order to exploit unlabeled data in the ELM model, we first extend the manifold regularization (MR) framework and then demonstrate the relation between the extended MR framework and ELM. Finally, a manifold regularized extreme learning machine is derived from the proposed framework, which maintains the properties of ELM and can be applicable to large-scale learning problems. Experimental results show that the proposed semi-supervised extreme learning machine is the most cost-efficient method. It tends to have better scalability and achieve satisfactory generalization performance at a relatively faster learning speed than traditional semi-supervised learning algorithms.     

极限学习机与支持向量机在储层渗透率预测中的对比研究

极限学习机ELM是一种简单易用、有效的单隐层前馈神经网络SLFNs学习算法。传统的神经网络学习算法(如BP算法)需要人为设置大量的网络训练参数,并且很容易产生局部最优解。极限学习机只需要设置网络的隐层节点个数,在算法执行过程中不需要调整网络的输入权值以及隐元的偏置,并且产生唯一的最优解,因此具有学习速度快且泛化性能好的优点。本文将极限学习机引入到储层渗透率的预测中,通过对比支持向量机,分析其在储层渗透率预测中的可行性和优势。实验结果表明,极限学习机与支持向量机有近似的预测精度,但在参数选择以及学习速度上极限学习机具有明显的优势。     

基于改进KH算法优化ELM的目标威胁估计

为了提高目标威胁度估计的精确度,建立了反向学习磷虾群算法（OKH）优化极限学习机的目标威胁估计模型（OKH-ELM）,提出基于此模型的算法。该模型使用反向学习策略优化磷虾群算法,并通过改进后的磷虾群算法优化极限学习机初始输入权重和偏置,使优化后的极限学习机能够对威胁度测试样本集做更好的预测。实验结果显示,OKH算法能够更好地优化极限学习机的权值与阈值,使建立的极限学习机目标威胁估计模型具有更高的预测精度和更强的泛化能力,能够精准、有效地实现目标威胁估计。     

基于径向基神经网络和正则化极限学习机的多标签学习模型*

相比径向基(RBF)神经网络,极限学习机(ELM)训练速度更快,泛化能力更强.同时,近邻传播聚类算法(AP)可以自动确定聚类个数.因此,文中提出融合AP聚类、多标签RBF(ML-RBF)和正则化ELM(RELM)的多标签学习模型(ML-AP-RBF-RELM).首先,在该模型中输入层使用ML-RBF进行映射,且通过AP聚类算法自动确定每一类标签的聚类个数,计算隐层节点个数.然后,利用每类标签的聚类个数通过K均值聚类确定隐层节点RBF函数的中心.最后,通过RELM快速求解隐层到输出层的连接权值.实验表明,ML-AP-RBF-RELM效果较好.     

Symmetric extreme learning machine

Extreme learning machine (ELM) can be considered as a black-box modeling approach that seeks a model representation extracted from the training data. In this paper, a modified ELM algorithm, called symmetric ELM (S-ELM), is proposed by incorporating a priori information of symmetry. S-ELM is realized by transforming the original activation function of hidden neurons into a symmetric one with respect to the input variables of the samples. In theory, S-ELM can approximate N arbitrary distinct samples with zero error. Simulation results show that, in the applications where there exists the prior knowledge of symmetry, S-ELM can obtain better generalization performance, faster learning speed, and more compact network architecture.     

Extreme learning machine and its applications

Recently, a novel learning algorithm for single-hidden-layer feedforward neural networks (SLFNs) named extreme learning machine (ELM) was proposed by Huang et al. The essence of ELM is that the learning parameters of hidden nodes, including input weights and biases, are randomly assigned and need not be tuned while the output weights can be analytically determined by the simple generalized inverse operation. The only parameter needed to be defined is the number of hidden nodes. Compared with other traditional learning algorithms for SLFNs, ELM provides extremely faster learning speed, better generalization performance and with least human intervention. This paper firstly introduces a brief review of ELM, describing the principle and algorithm of ELM. Then, we put emphasis on the improved methods or the typical variants of ELM, especially on incremental ELM, pruning ELM, error-minimized ELM, two-stage ELM, online sequential ELM, evolutionary ELM, voting-based ELM, ordinal ELM, fully complex ELM, and symmetric ELM. Next, the paper summarized the applications of ELM on classification, regression, function approximation, pattern recognition, forecasting and diagnosis, and so on. In the last, the paper discussed several open issues of ELM, which may be worthy of exploring in the future.     

A study on random weights between input and hidden layers in extreme learning machine

Extreme learning machine (ELM), as an emergent technique for training feed-forward neural networks, has shown good performances on various learning domains. This paper investigates the impact of random weights during the training of ELM. It focuses on the randomness of weights between input and hidden layers, and the dimension change from input layer to hidden layer. The direct motivation is to verify as to whether during the training of ELM, the randomly assigned weights exert some positive effects. Experimentally we show that for many classification and regression problems, the dimension increase caused by random weights in ELM has a performance better than the dimension increase caused by some kernel mappings. We assume that via the random transformation, output-samples are more concentrate than input-samples which will make the learning more efficient.     

An integrated PSO for parameter determination and feature selection of ELM and its application in classification of power system disturbances

This paper presents a performance enhancement scheme for the recently developed extreme learning machine (ELM) for classifying power system disturbances using particle swarm optimization (PSO). Learning time is an important factor while designing any computational intelligent algorithms for classifications. ELM is a single hidden layer neural network with good generalization capabilities and extremely fast learning capacity. In ELM, the input weights are chosen randomly and the output weights are calculated analytically. However, ELM may need higher number of hidden neurons due to the random determination of the input weights and hidden biases. One of the advantages of ELM over other methods is that the parameter that the user must properly adjust is the number of hidden nodes only. But the optimal selection of its parameter can improve its performance. In this paper, a hybrid optimization mechanism is proposed which combines the discrete-valued PSO with the continuous-valued PSO to optimize the input feature subset selection and the number of hidden nodes to enhance the performance of ELM. The experimental results showed the proposed algorithm is faster and more accurate in discriminating power system disturbances.     

基于可拓聚类的极限学习机神经网络

针对极限学习机(ELM)算法随机选择输入层权值的问题,借鉴第2类型可拓神经网络(ENN-2)聚类的思想,提出了一种基于可拓聚类的ELM(EC-ELM)神经网络。该神经网络是以隐含层神经元的径向基中心向量作为输入层权值,采用可拓聚类算法动态调整隐含层节点数目和径向基中心,并根据所确定的输入层权值,利用Moore-Penrose广义逆快速完成输出层权值的求解。同时,对标准的Friedman#1回归数据集和Wine分类数据集进行测试,结果表明,EC-ELM提供了一种简便的神经网络结构和参数学习方法,并且比基于可拓理论的径向基函数(ERBF)、ELM神经网络具有更高的建模精度和更快的学习速度,为复杂过程的建模提供了新思路。     

Performance enhancement of extreme learning machine for multi-category sparse data classification problems

This paper presents a performance enhancement scheme for the recently developed extreme learning machine (ELM) for multi-category sparse data classification problems. ELM is a single hidden layer neural network with good generalization capabilities and extremely fast learning capacity. In ELM, the input weights are randomly chosen and the output weights are analytically calculated. The generalization performance of the ELM algorithm for sparse data classification problem depends critically on three free parameters. They are, the number of hidden neurons, the input weights and the bias values which need to be optimally chosen. Selection of these parameters for the best performance of ELM involves a complex optimization problem.In this paper, we present a new, real-coded genetic algorithm approach called ‘RCGA-ELM’ to select the optimal number of hidden neurons, input weights and bias values which results in better performance. Two new genetic operators called ‘network based operator’ and ‘weight based operator’ are proposed to find a compact network with higher generalization performance. We also present an alternate and less computationally intensive approach called ‘sparse-ELM’. Sparse-ELM searches for the best parameters of ELM using K-fold validation. A multi-class human cancer classification problem using micro-array gene expression data (which is sparse), is used for evaluating the performance of the two schemes. Results indicate that the proposed RCGA-ELM and sparse-ELM significantly improve ELM performance for sparse multi-category classification problems.