Sparse SVM for Sufficient Data Reduction
Sparse SVM for Sufficient Data Reduction
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DOI：
10.1109/tpami.2021.3075339
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发表时间：
2020-05
影响因子：
23.6
通讯作者：
Shenglong Zhou
中科院分区：
文献类型：
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作者：
Shenglong Zhou
支持向量机（SVM）的基于核的方法在各种应用中表现出非常有利的性能。然而，对于大规模的样本数据集，它们可能会产生令人望而却步的计算成本。因此，数据精简（减少支持向量的数量）似乎是必要的，这引起了稀疏SVM的话题。针对这一问题，本文提出了一种稀疏约束核支持向量机优化方法，以控制支持向量的个数。基于所建立的最优性条件与固定方程，牛顿型方法来处理稀疏约束优化。该方法被发现享受一步收敛性能，如果选择的起始点是接近一个局部区域的一个稳定点，从而导致超高的计算速度。与几个强大的求解器的数值比较表明，所提出的方法性能非常好，特别是对于大规模数据集，因为支持向量的数量要少得多，计算时间更短。
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.