Abstract: Regression problem is one of the basic problems in the field of pattern recognition and machine learning. Twin support vector regression (TSVR) is a new algorithm to deal with regression problems developed on the basis of support vector regression (SVR). It has good performance in dealing with noiseless data, but poor performance in dealing with noisy data.?In order to reduce the influence of noise on the performance of TSVR, the mixed Hε loss function is constructed by combining ε -insensitive loss function and Huber loss function, which can be effectively adapted to the noise of different distributions. Then, a robust twin support vector regression (Hε-TSVR) is proposed based on the mixed [Hε] loss function and the principle of structural risk minimization (SRM), and the model is solved by Newton iterative method in the primal space. Experiments are carried out on some noisy and noiseless artificial datasets and UCI datasets respectively, and the experimental results verify the effectiveness of the proposed algorithm compared with SVR and TSVR, etc.

Key words: pattern recognition, support vector regression (SVR), twin support vector regression (TSVR), loss function

摘要： 回归问题是模式识别与机器学习领域的基本问题之一，孪生支持向量回归机（TSVR）是在支持向量回归机（SVR）基础上发展而来的一种处理回归问题的新算法，它在处理无噪声数据时表现出较好的性能，但在处理有噪声数据时往往性能不佳。为了降低噪声对孪生支持向量回归机性能的影响，结合[ε]-不敏感损失函数与Huber损失函数构造了混合[Hε]损失函数，该损失函数可以有效地适应于不同分布类型的噪声；然后基于混合[Hε]损失函数和结构风险最小化（SRM）原则提出了一种鲁棒的孪生支持向量回归机（[Hε]-TSVR），并在原始空间中利用牛顿迭代法求解模型。分别在有噪声和无噪声的人工数据集、UCI数据集上进行实验，与支持向量回归机和孪生支持向量回归机等算法比较，实验结果验证了所提算法的有效性。

关键词: 模式识别, 支持向量回归机（SVR）, 孪生支持向量回归机（TSVR）, 损失函数