Yang Liming, Ren Zhuo, Wang Yidan, Dong Hongwei
College of Science, China Agricultural University, Beijing, 100083, China
Neural Comput. 2017 Nov;29(11):3014-3039. doi: 10.1162/neco_a_01002. Epub 2017 Aug 4.
This work proposes a robust regression framework with nonconvex loss function. Two regression formulations are presented based on the Laplace kernel-induced loss (LK-loss). Moreover, we illustrate that the LK-loss function is a nice approximation for the zero-norm. However, nonconvexity of the LK-loss makes it difficult to optimize. A continuous optimization method is developed to solve the proposed framework. The problems are formulated as DC (difference of convex functions) programming. The corresponding DC algorithms (DCAs) converge linearly. Furthermore, the proposed algorithms are applied directly to determine the hardness of licorice seeds using near-infrared spectral data with noisy input. Experiments in eight spectral regions show that the proposed methods improve generalization compared with the traditional support vector regressions (SVR), especially in high-frequency regions. Experiments on several benchmark data sets demonstrate that the proposed methods achieve better results than the traditional regression methods in most of data sets we have considered.
本文提出了一种具有非凸损失函数的稳健回归框架。基于拉普拉斯核诱导损失（LK损失）给出了两种回归公式。此外，我们说明了LK损失函数是对零范数的良好近似。然而，LK损失的非凸性使其难以优化。开发了一种连续优化方法来求解所提出的框架。这些问题被表述为DC（凸函数之差）规划。相应的DC算法（DCAs）线性收敛。此外，所提出的算法直接应用于利用带有噪声输入的近红外光谱数据来确定甘草种子的硬度。在八个光谱区域的实验表明，与传统支持向量回归（SVR）相比，所提出的方法提高了泛化能力，尤其是在高频区域。在几个基准数据集上的实验表明，在所考虑的大多数数据集中，所提出的方法比传统回归方法取得了更好的结果。
