IEEE Trans Cybern. 2014 Oct;44(10):1898-909. doi: 10.1109/TCYB.2014.2299291.
In this paper, the well known stagewise additive modeling using a multiclass exponential (SAMME) boosting algorithm is extended to address problems where there exists a natural order in the targets using a cost-sensitive approach. The proposed ensemble model uses an extreme learning machine (ELM) model as a base classifier (with the Gaussian kernel and the additional regularization parameter). The closed form of the derived weighted least squares problem is provided, and it is employed to estimate analytically the parameters connecting the hidden layer to the output layer at each iteration of the boosting algorithm. Compared to the state-of-the-art boosting algorithms, in particular those using ELM as base classifier, the suggested technique does not require the generation of a new training dataset at each iteration. The adoption of the weighted least squares formulation of the problem has been presented as an unbiased and alternative approach to the already existing ELM boosting techniques. Moreover, the addition of a cost model for weighting the patterns, according to the order of the targets, enables the classifier to tackle ordinal regression problems further. The proposed method has been validated by an experimental study by comparing it with already existing ensemble methods and ELM techniques for ordinal regression, showing competitive results.
在本文中，使用一种代价敏感方法，将使用多类指数的知名分阶段加法建模（SAMME）增强算法扩展到解决存在目标自然顺序的问题。所提出的集成模型使用极限学习机（ELM）模型作为基本分类器（具有高斯核和附加正则化参数）。提供了导出的加权最小二乘问题的封闭形式解，并在增强算法的每次迭代中，通过它分析地估计连接隐藏层到输出层的参数。与最先进的增强算法，特别是那些使用 ELM 作为基本分类器的算法相比，所建议的技术不需要在每次迭代时生成新的训练数据集。提出了问题的加权最小二乘公式作为已有 ELM 增强技术的无偏和替代方法。此外，根据目标的顺序为模式添加成本模型进行加权，使分类器能够进一步解决有序回归问题。通过将其与现有的用于有序回归的集成方法和 ELM 技术进行比较，通过实验研究验证了所提出的方法，结果具有竞争力。
