基于径向基函数的多目标回归特征构建算法

多目标回归（MTR）是一种针对单个样本同时具有多个连续型输出的回归问题。现有的多目标回归算法都基于同一个特征空间学习回归模型，而忽略了各输出目标本身的特殊性质。针对这一问题，提出基于径向基函数的多目标回归特征构建算法。首先，将各目标的输出作为额外的特征对各输出目标进行聚类，根据聚类中心在原始特征空间构成了目标特定特征空间的基；然后，通过径向基函数将原始特征空间映射到目标特定特征空间，构造目标特定的特征，并基于这些目标特定特征构建各输出目标的基回归模型；最后，用基回归模型的输出组成隐藏空间，采用低秩学习算法在其中发掘和利用输出目标之间的关联。在18个多目标回归数据集上进行实验，并把所提算法与层叠单目标回归（SST）、回归器链集成（ERC）、多层、多目标回归（MMR）等经典的多目标回归算法进行对比，结果表明所提算法在14个数据集上都取得了最好的性能，并且在18个数据集上的平均性能排序居第一位。可见所提算法构建的目标特定特征能够提高各输出目标的预测准确性，并结合低秩学习得到输出目标间的关联性以从整体上提升多目标回归的预测性能。

Feature construction algorithm for multi-target regression via radial basis function

Multi-Target Regression (MTR) is a regression problem of single samples with multiple continuous outputs. The existing multi-target regression algorithms learn regression models based on a same feature space, and ignore the specific characteristics of each output target. To solve the problem, a feature construction algorithm for multi-target regression via radial basis function was proposed. Firstly, clustering was applied to each output target with the output of each target as the additional feature, and according to the centers of clusters, the bases of target specific feature space were constructed in the original feature space. Secondly, the radial basis function was utilized to map the original feature space into the target specific feature space, constructing the target specific features, and then a base regression model was built for each target based on these target specific features. Finally, the low-rank learning method was applied to explore and utilize the correlation between the output targets from the latent space formed by the outputs of base regression models. Experiments were conducted on 18 multi-target regression datasets, and the proposed algorithm was compared with some classical regression algorithms, such as Stacked Single-Target (SST), Ensemble of Regressor Chains (ERC) and Multi-layer Multi-target Regression (MMR). The results show that the proposed algorithm outperforms the comparison algorithms on 14 datasets and achieves the best average performance on 18 datasets. It can be seen that the target specific features can improve the prediction accuracy of each output target and improve the overall prediction performance of multi-target regression by combining the low-rank learning to learn and obtain the correlation between the output targets.