The extreme learning machine (ELM) is a type of machine learning algorithm for training a single hidden layer feedforward neural network. Randomly initializing the weight between the input layer and the hidden layer and the threshold of each hidden layer neuron, the weight matrix of the hidden layer can be calculated by the least squares method. The efficient learning ability in ELM makes it widely applicable in classification, regression, and more. However, owing to some unutilized information in the residual, there are relatively huge prediction errors involving ELM. In this paper, a deep residual compensation extreme learning machine model (DRC‐ELM) of multilayer structures applied to regression is presented. The first layer is the basic ELM layer, which helps in obtaining an approximation of the objective function by learning the characteristics of the sample. The other layers are the residual compensation layers in which the learned residual is corrected layer by layer to the predicted value obtained in the previous layer by constructing a feature mapping between the input layer and the output of the upper layer. This model is applied to two practical problems: gold price forecasting and airfoil self‐noise prediction. We used the DRC‐ELM with 50, 100, and 200 residual compensation layers respectively for experiments, which show that DRC‐ELM does better in generalization and robustness than classical ELM, improved ELM models such as GA‐RELM and OS‐ELM, and other traditional machine learning algorithms such as support vector machine (SVM) and back‐propagation neural network (BPNN).

中文翻译：

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一种深度残差补偿极限学习机及其应用

极限学习机（ELM）是一种用于训练单个隐藏层前馈神经网络的机器学习算法。随机初始化输入层和隐藏层之间的权重以及每个隐藏层神经元的阈值，可以通过最小二乘法计算隐藏层的权重矩阵。ELM的高效学习能力使其广泛应用于分类，回归等方面。但是，由于残差中有一些未利用的信息，因此涉及ELM的预测误差相对较大。本文提出了一种用于回归的多层结构的深度残差补偿极限学习机模型（DRC‐ELM）。第一层是基本的ELM层，通过学习样本的特性，这有助于获得目标函数的近似值。其他层是残差补偿层，其中，通过在输入层和上层输出之间构建特征映射，将学习到的残差逐层校正为上一层中获得的预测值。该模型适用于两个实际问题：黄金价格预测和机翼自噪声预测。我们分别使用具有50、100和200个剩余补偿层的DRC‐ELM进行了实验，这表明DRC‐ELM的泛化性和鲁棒性比经典ELM，改进的ELM模型（如GA‐RELM和OS‐ELM）好，并且其他传统的机器学习算法，例如支持向量机（SVM）和反向传播神经网络（BPNN）。