IEEE Trans Neural Netw Learn Syst. 2017 May;28(5):1241-1248. doi: 10.1109/TNNLS.2016.2527796. Epub 2016 Feb 24.
The ν -support vector classification has the advantage of using a regularization parameter ν to control the number of support vectors and margin errors. Recently, a regularization path algorithm for ν -support vector classification ( ν -SvcPath) suffers exceptions and singularities in some special cases. In this brief, we first present a new equivalent dual formulation for ν -SVC and, then, propose a robust ν -SvcPath, based on lower upper decomposition with partial pivoting. Theoretical analysis and experimental results verify that our proposed robust regularization path algorithm can avoid the exceptions completely, handle the singularities in the key matrix, and fit the entire solution path in a finite number of steps. Experimental results also show that our proposed algorithm fits the entire solution path with fewer steps and less running time than original one does.
ν-支持向量分类具有使用正则化参数 ν 来控制支持向量和边界错误数量的优点。最近，ν-支持向量分类（ν-SvcPath）的正则化路径算法在某些特殊情况下会出现异常和奇异。在本文中，我们首先提出了 ν-SVC 的一种新的等价对偶公式，然后提出了一种基于部分选主元的上下分解的鲁棒 ν-SvcPath。理论分析和实验结果验证了我们提出的鲁棒正则化路径算法可以完全避免异常，处理关键矩阵中的奇点，并在有限的步骤内拟合整个解路径。实验结果还表明，与原始算法相比，我们提出的算法使用更少的步骤和更短的运行时间来拟合整个解路径。
