论文标题
稀疏的SVM以减少数据
Sparse SVM for Sufficient Data Reduction
论文作者
论文摘要
基于内核的支持向量机（SVM）的方法在各种应用中显示出非常有利的性能。但是，它们可能会为大规模样本数据集而产生高度的计算成本。因此，似乎有必要减少数据（减少支持向量的数量），这引起了稀疏SVM的主题。在此问题的激励下，本文考虑了稀疏性内核SVM优化，以控制支持向量的数量。基于与固定方程相关的既定最佳条件，开发了一种牛顿型方法来处理稀疏性约束优化。如果选择起点靠近固定点的局部区域，则发现此方法可以享受一步收敛属性，从而导致超高的计算速度。与几个功能强大的求解器的数值比较表明，所提出的方法的性能非常出色，特别是对于大规模数据集而言，就支持向量和较短的计算时间而言。
Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction (reducing the number of support vectors) appears to be necessary, which gives rise to the topic of the sparse SVM. Motivated by this problem, the sparsity constrained kernel SVM optimization has been considered in this paper in order to control the number of support vectors. Based on the established optimality conditions associated with the stationary equations, a Newton-type method is developed to handle the sparsity constrained optimization. This method is found to enjoy the one-step convergence property if the starting point is chosen to be close to a local region of a stationary point, thereby leading to a super-high computational speed. Numerical comparisons with several powerful solvers demonstrate that the proposed method performs exceptionally well, particularly for large-scale datasets in terms of a much lower number of support vectors and shorter computational time.
