Simultaneous feature selection and classification have been explored in the literature to extend the support vector machine (SVM) techniques by adding penalty terms to the loss function directly. However, it is the kernel function that controls the performance of the SVM, and an imbalance in the data will deteriorate the performance of an SVM. In this paper, we examine a new method of simultaneous feature selection and binary classification. Instead of incorporating the standard loss function of the SVM, a penalty is added to the data-adaptive kernel function directly to control the performance of the SVM, by firstly conformally transforming the kernel functions of the SVM, and then re-conducting an SVM classifier based on the sparse features selected. Both convex and non-convex penalties, such as least absolute shrinkage and selection (LASSO), moothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP) are explored, and the oracle property of the estimator is established accordingly. An iterative optimization procedure is applied as there is no analytic form of the estimated coefficients available. Numerical comparisons show that the proposed method outperforms the competitors considered when data are imbalanced, and it performs similarly to the competitors when data are balanced. The method can be easily applied in medical images from different platforms.

中文翻译：

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数据自适应核约束SVM的同时特征选择和分类

文献中已经探索了同时进行的特征选择和分类，以通过将惩罚项直接添加到损失函数来扩展支持向量机（SVM）技术。但是，内核功能控制着SVM的性能，数据不平衡会降低SVM的性能。在本文中，我们研究了一种同时特征选择和二进制分类的新方法。取代并入SVM的标准损失函数，首先通过共形变换SVM的内核函数，然后重新进行SVM分类器，将惩罚直接添加到数据自适应内核函数以控制SVM的性能。基于所选的稀疏特征。凸和非凸的惩罚，例如最小绝对收缩和选择（LASSO），探索了平滑修剪的绝对偏差（SCAD）和最小极大凹罚（MCP），并据此建立了估计器的预言性质。由于没有可用的估计系数的解析形式，因此应用了迭代优化过程。数值比较表明，该方法在数据不平衡的情况下优于竞争对手，并且在数据平衡时的性能与竞争对手相似。该方法可以轻松地应用于来自不同平台的医学图像。数值比较表明，该方法在数据不平衡的情况下优于竞争对手，并且在数据平衡时的性能与竞争对手相似。该方法可以轻松地应用于来自不同平台的医学图像。数值比较表明，该方法在数据不平衡的情况下优于竞争对手，并且在数据平衡时的性能与竞争对手相似。该方法可以轻松地应用于来自不同平台的医学图像。