Model selection of extreme learning machine based on multi-objective optimization

As a novel learning algorithm for single-hidden-layer feedforward neural networks, extreme learning machines (ELMs) have been a promising tool for regression and classification applications. However, it is not trivial for ELMs to find the proper number of hidden neurons due to the nonoptimal input weights and hidden biases. In this paper, a new model selection method of ELM based on multi-objective optimization is proposed to obtain compact networks with good generalization ability. First, a new leave-one-out (LOO) error bound of ELM is derived, and it can be calculated with negligible computational cost once the ELM training is finished. Furthermore, the hidden nodes are added to the network one-by-one, and at each step, a multi-objective optimization algorithm is used to select optimal input weights by minimizing this LOO bound and the norm of output weight simultaneously in order to avoid over-fitting. Experiments on five UCI regression data sets are conducted, demonstrating that the proposed algorithm can generally obtain better generalization performance with more compact network than the conventional gradient-based back-propagation method, original ELM and evolutionary ELM.     

Improved Meta-ELM with error feedback incremental ELM as hidden nodes

Liao et al. (Neurocomputing 128:81–87, 2014) proposed a meta-learning approach to extreme learning machine (Meta-ELM), which can obtain good generalization performance by training multiple ELMs. However, one of its open problems is overfitting when minimizing training error. In this paper, we propose an improved meta-learning model of ELM (improved Meta-ELM) to handle the problem. The improved Meta-ELM architecture is composed of some base ELMs which are error feedback incremental extreme learning machine (EFI-ELM) and the top ELM. The improved Meta-ELM includes two stages. First, each base ELM with EFI-ELM is trained on a subset of training data. Then, the top ELM learns with the base ELMs as hidden nodes. Simulation results on some artificial and benchmark datasets show that the proposed improved Meta-ELM model is more feasible and effective than Meta-ELM.

     

Local coupled extreme learning machine

Due to the significant efficiency and simple implementation, extreme learning machine (ELM) algorithms enjoy much attention in regression and classification applications recently. Many efforts have been paid to enhance the performance of ELM from both methodology (ELM training strategies) and structure (incremental or pruned ELMs) perspectives. In this paper, a local coupled extreme learning machine (LC-ELM) algorithm is presented. By assigning an address to each hidden node in the input space, LC-ELM introduces a decoupler framework to ELM in order to reduce the complexity of the weight searching space. The activated degree of a hidden node is measured by the membership degree of the similarity between the associated address and the given input. Experimental results confirm that the proposed approach works effectively and generally outperforms the original ELM in both regression and classification applications.     

Uncertainty evaluation and model selection of extreme learning machine based on Riemannian metric

Considering the uncertainty of hidden neurons, choosing significant hidden nodes, called as model selection, has played an important role in the applications of extreme learning machines(ELMs). How to define and measure this uncertainty is a key issue of model selection for ELM. From the information geometry point of view, this paper presents a new model selection method of ELM for regression problems based on Riemannian metric. First, this paper proves theoretically that the uncertainty can be characterized by a form of Riemannian metric. As a result, a new uncertainty evaluation of ELM is proposed through averaging the Riemannian metric of all hidden neurons. Finally, the hidden nodes are added to the network one by one, and at each step, a multi-objective optimization algorithm is used to select optimal input weights by minimizing this uncertainty evaluation and the norm of output weight simultaneously in order to obtain better generalization performance. Experiments on five UCI regression data sets and cylindrical shell vibration data set are conducted, demonstrating that the proposed method can generally obtain lower generalization error than the original ELM, evolutionary ELM, ELM with model selection, and multi-dimensional support vector machine. Moreover, the proposed algorithm generally needs less hidden neurons and computational time than the traditional approaches, which is very favorable in engineering applications.     

基于蚁群优化的极限学习机选择性集成学习算法

针对现有极限学习机集成学习算法分类精度低、泛化能力差等缺点,提出了一种基于蚁群优化思想的极限学习机选择性集成学习算法。该算法首先通过随机分配隐层输入权重和偏置的方法生成大量差异的极限学习机分类器,然后利用一个二叉蚁群优化搜索算法迭代地搜寻最优分类器组合,最终使用该组合分类测试样本。通过12个标准数据集对该算法进行了测试,该算法在9个数据集上获得了最优结果,在另3个数据集上获得了次优结果。采用该算法可显著提高分类精度与泛化性能。     

基于深度极限学习机的危险源识别算法HIELM

危险源识别是民用航空管理的重要环节之一,危险源识别结果必须高度准确才能确保飞行的安全。为此,提出了一种基于深度极限学习机的危险源识别算法HIELM(Hazard Identification Algorithm Based on Extreme Lear-ning Machine),设计了一种由多个深层栈式极限学习机(S-ELM)和一个单隐藏层极限学习机(ELM)构成的深层网络结构。算法中,多个深层S-ELM使用平行结构,各自可以拥有不同的隐藏结点个数,按照危险源领域分类接受危险源状态信息完成预学习,并结合识别特征改进网络输入权重的产生方式。在单隐藏层ELM中,深层ELM的预学习结果作为其输入,改进了反向传播算法,提高了网络识别的精确度。同时,分别训练各深层S-ELM,缓解了高维数据训练的内存压力和节点过多产生的过拟合现象。     

GPU-accelerated and parallelized ELM ensembles for large-scale regression

The paper presents an approach for performing regression on large data sets in reasonable time, using an ensemble of extreme learning machines (ELMs). The main purpose and contribution of this paper are to explore how the evaluation of this ensemble of ELMs can be accelerated in three distinct ways: (1) training and model structure selection of the individual ELMs are accelerated by performing these steps on the graphics processing unit (GPU), instead of the processor (CPU); (2) the training of ELM is performed in such a way that computed results can be reused in the model structure selection, making training plus model structure selection more efficient; (3) the modularity of the ensemble model is exploited and the process of model training and model structure selection is parallelized across multiple GPU and CPU cores, such that multiple models can be built at the same time. The experiments show that competitive performance is obtained on the regression tasks, and that the GPU-accelerated and parallelized ELM ensemble achieves attractive speedups over using a single CPU. Furthermore, the proposed approach is not limited to a specific type of ELM and can be employed for a large variety of ELMs.     

Extreme learning machine with errors in variables

Extreme learning machine (ELM) is widely used in training single-hidden layer feedforward neural networks (SLFNs) because of its good generalization and fast speed. However, most improved ELMs usually discuss the approximation problem for sample data with output noises, not for sample data with noises both in input and output values, i.e., error-in-variable (EIV) model. In this paper, a novel algorithm, called (regularized) TLS-ELM, is proposed to approximate the EIV model based on ELM and total least squares (TLS) method. The proposed TLS-ELM uses the idea of ELM to choose the hidden weights, and applies TLS method to determine the output weights. Furthermore, the perturbation quantities of hidden output matrix and observed values are given simultaneously. Comparison experiments of our proposed TLS-ELM with least square method, TLS method and ELM show that our proposed TLS-ELM has better accuracy and less training time.     

A fast incremental extreme learning machine algorithm for data streams classification

Data streams classification is an important approach to get useful knowledge from massive and dynamic data. Because of concept drift, traditional data mining techniques cannot be directly applied in data streams environment. Extreme learning machine (ELM) is a single hidden layer feedforward neural network (SLFN), comparing with the traditional neural network (e.g. BP network), ELM has a faster speed, so it is very suitable for real-time data processing. In order to deal with the challenge in data streams classification, a new approach based on extreme learning machine is proposed in this paper. The approach utilizes ELMs as base classifiers and adaptively decides the number of the neurons in hidden layer, in addition, activation functions are also randomly selected from a series of functions to improve the performance of the approach. Finally, the algorithm trains a series of classifiers and the decision results for unlabeled data are made by weighted voting strategy. When the concept in data streams keeps stable, every classifier is incrementally updated by using new data; if concept drift is detected, the classifiers with weak performance will be cleared away. In the experiment, we used 7 artificial data sets and 9 real data sets from UCI repository to evaluate the performance of the proposed approach. The testing results showed, comparing with the conventional classification methods for data streams such as ELM, BP, AUE2 and Learn++.MF, on most data sets, the new approach could not only be simplest in the structure, but also get a higher and more stable accuracy with lower time consuming.     

Multiple-kernel-learning-based extreme learning machine for classification design

The extreme learning machine (ELM) is a new method for using single hidden layer feed-forward networks with a much simpler training method. While conventional kernel-based classifiers are based on a single kernel, in reality, it is often desirable to base classifiers on combinations of multiple kernels. In this paper, we propose the issue of multiple-kernel learning (MKL) for ELM by formulating it as a semi-infinite linear programming. We further extend this idea by integrating with techniques of MKL. The kernel function in this ELM formulation no longer needs to be fixed, but can be automatically learned as a combination of multiple kernels. Two formulations of multiple-kernel classifiers are proposed. The first one is based on a convex combination of the given base kernels, while the second one uses a convex combination of the so-called equivalent kernels. Empirically, the second formulation is particularly competitive. Experiments on a large number of both toy and real-world data sets (including high-magnification sampling rate image data set) show that the resultant classifier is fast and accurate and can also be easily trained by simply changing linear program.     

Generalized extreme learning machine acting on a metric space

Functional data learning is an extension of traditional data learning, that is, learning the data chosen from the Euclidean space ${\mathbb{R}^{n}}$ to a metric space. This paper focuses on the functional data learning with generalized single-hidden layer feedforward neural networks (GSLFNs) acting on some metric spaces. In addition, three learning algorithms, named Hilbert parallel overrelaxation backpropagation (H-PORBP) algorithm, ν-generalized support vector regression (ν-GSVR) and generalized extreme learning machine (G-ELM) are proposed to train the GSLFNs acting on some metric spaces. The experimental results on some metric spaces indicate that GELM with additive/RBF hidden-nodes has a faster learning speed, a better accuracy, and a better stability than HPORBP algorithm and ν-GSVR for training the functional data. The idea of GELM can be used to extend those improved extreme learning machines (ELMs) that act on the Euclidean space ${\mathbb{R}^{n}, }$ such as online sequential ELM, incremental ELM, pruning ELM and so on, to some metric spaces.     

逐层可加的急速学习机

已有的急速学习机（Extreme Learning Machine）的学习精度受隐节点数目的影响很大。无论是已提出的单隐层急速学习机还是多隐层神经网络,都是先确定隐藏层数,再通过增加每一层的神经元个数来提高精度。但当训练集规模很大时,往往需要引入很多的隐节点,导致违逆矩阵计算复杂度大,从而不利于学习效率的提高。提出逐层可加的急速学习机MHL-ELM（Extreme Learning Machine with Incremental Hidden Layers）,其思想是首先对当前隐藏层神经元（数目不大且不寻优,因而复杂度小）的权值进行随机赋值,用ELM思想求出逼近误差;若误差达不到要求,再增加一个隐含层。然后运用ELM的思想对当前隐含层优化。逐渐增加隐含层,直至满足误差精度为止。除此以外,MHL-ELM的算法复杂度为[l=1MO(N3l)]。实验使用10个UCI,keel真实数据集,通过与BP,OP-ELM等传统方法进行比较,表明MHL-ELM学习方法具有更好的泛化性,在学习精度和学习速度方面都有很大的提升。     

A scalable, incremental learning algorithm for classification problems

In this paper a novel data mining algorithm, Clustering and Classification Algorithm-Supervised (CCA-S), is introduced. CCA-S enables the scalable, incremental learning of a non-hierarchical cluster structure from training data. This cluster structure serves as a function to map the attribute values of new data to the target class of these data, that is, classify new data. CCA-S utilizes both the distance and the target class of training data points to derive the cluster structure. In this paper, we first present problems with many existing data mining algorithms for classification problems, such as decision trees, artificial neural networks, in scalable and incremental learning. We then describe CCA-S and discuss its advantages in scalable, incremental learning. The testing results of applying CCA-S to several common data sets for classification problems are presented. The testing results show that the classification performance of CCA-S is comparable to the other data mining algorithms such as decision trees, artificial neural networks and discriminant analysis.     

基于极限学习机的无监督领域适应分类器

在构建基于极限学习机的无监督自适应分类器时, 隐含层的参数通常都是随机选取的, 而随机选取的参数不具备领域适应能力. 为了增强跨领域极限学习机的知识迁移能力,提出一种新的基于极限学习机的无监督领域适应分类器学习方法, 该方法主要利用自编码极限学习机对源域和目标域数据进行重构学习, 从而可以获得具有领域不变特性的隐含层参数. 进一步, 结合联合概率分布匹配和流形正则的思想, 对输出层权重进行自适应调整. 所提出算法能对极限学习机的两层参数均赋予领域适应能力,在字符数据集和对象识别数据集上的实验结果表明其具有较高的跨领域分类精度.     

ELM-based gene expression classification with misclassification cost

Cost-sensitive learning is a crucial problem in machine learning research. Traditional classification problem assumes that the misclassification for each category has the same cost, and the target of learning algorithm is to minimize the expected error rate. In cost-sensitive learning, costs of misclassification for samples of different categories are not the same; the target of algorithm is to minimize the sum of misclassification cost. Cost-sensitive learning can meet the actual demand of real-life classification problems, such as medical diagnosis, financial projections, and so on. Due to fast learning speed and perfect performance, extreme learning machine (ELM) has become one of the best classification algorithms, while voting based on extreme learning machine (V-ELM) makes classification results more accurate and stable. However, V-ELM and some other versions of ELM are all based on the assumption that all misclassifications have same cost. Therefore, they cannot solve cost-sensitive problems well. To overcome the drawback of ELMs mentioned above, an algorithm called cost-sensitive ELM (CS-ELM) is proposed by introducing misclassification cost of each sample into V-ELM. Experimental results on gene expression data show that CS-ELM is effective in reducing misclassification cost.     

Length-Changeable Incremental Extreme Learning Machine

Extreme learning machine (ELM) is a learning algorithm for generalized single-hidden-layer feed-forward networks (SLFNs). In order to obtain a suitable network architecture, Incremental Extreme Learning Machine (I-ELM) is a sort of ELM constructing SLFNs by adding hidden nodes one by one. Although kinds of I-ELM-class algorithms were proposed to improve the convergence rate or to obtain minimal training error, they do not change the construction way of I-ELM or face the over-fitting risk. Making the testing error converge quickly and stably therefore becomes an important issue. In this paper, we proposed a new incremental ELM which is referred to as Length-Changeable Incremental Extreme Learning Machine (LCI-ELM). It allows more than one hidden node to be added to the network and the existing network will be regarded as a whole in output weights tuning. The output weights of newly added hidden nodes are determined using a partial error-minimizing method. We prove that an SLFN constructed using LCI-ELM has approximation capability on a universal compact input set as well as on a finite training set. Experimental results demonstrate that LCI-ELM achieves higher convergence rate as well as lower over-fitting risk than some competitive I-ELM-class algorithms.     

改进式混合增量极限学习机算法

针对增量型极限学习机(I-ELM) 中存在大量降低学习效率及准确性的冗余节点的问题, 提出一种基于Delta 检验(DT) 和混沌优化算法(COA) 的改进式增量型核极限学习算法. 利用COA的全局搜索能力对I-ELM 中的隐含层节点参数进行寻优, 结合DT 算法检验模型输出误差, 确定有效的隐含层节点数量, 从而降低网络复杂程度, 提高算法的学习效率; 加入核函数可增强网络的在线预测能力. 仿真结果表明, 所提出的DCI-ELMK 算法具有较好的预测精度和泛化能力, 网络结构更为紧凑.

     

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.     

Parallel Chaos Search Based Incremental Extreme Learning Machine

Recently, a simple and efficient learning steps referred to as extreme learning machine (ELM), was proposed by Huang et al. , which has shown that compared to some conventional methods, the training time of neural networks can be reduced even by thousands of times. However, recent study showed that some of random hidden nodes may paly a very minion role in the network output and thus eventually increase the network complexity. This paper proposes a parallel chaos search based incremental extreme learning machine (PC-ELM) with additional steps to obtain a more compact network architecture. At each learning step, optimal parameters of hidden node that are selected by parallel chaos optimization algorithm will be added to exist network in order to minimize the residual error between target function and network output. The optimization method is proposed parallel chaos optimization method. We prove the convergence of PC-ELM both in increased network architecture and fixed network architecture. Then we apply this approach to several regression and classification problems. Experiment of 19 benchmark testing data sets are used to test the performance of PC-ELM. Simulation results demonstrate that the proposed method provides better generalization performance and more compact network architecture.     

Efficient and effective algorithms for training single-hidden-layer neural networks

Recently there have been renewed interests in single-hidden-layer neural networks (SHLNNs). This is due to its powerful modeling ability as well as the existence of some efficient learning algorithms. A prominent example of such algorithms is extreme learning machine (ELM), which assigns random values to the lower-layer weights. While ELM can be trained efficiently, it requires many more hidden units than is typically needed by the conventional neural networks to achieve matched classification accuracy. The use of a large number of hidden units translates to significantly increased test time, which is more valuable than training time in practice. In this paper, we propose a series of new efficient learning algorithms for SHLNNs. Our algorithms exploit both the structure of SHLNNs and the gradient information over all training epochs, and update the weights in the direction along which the overall square error is reduced the most. Experiments on the MNIST handwritten digit recognition task and the MAGIC gamma telescope dataset show that the algorithms proposed in this paper obtain significantly better classification accuracy than ELM when the same number of hidden units is used. For obtaining the same classification accuracy, our best algorithm requires only 1/16 of the model size and thus approximately 1/16 of test time compared with ELM. This huge advantage is gained at the expense of 5 times or less the training cost incurred by the ELM training.