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Successive Overrelaxation for Laplacian Support Vector Machine

机译：拉普拉斯支持向量机的连续超松弛

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摘要

Semisupervised learning (SSL) problem, which makes use of both a large amount of cheap unlabeled data and a few unlabeled data for training, in the last few years, has attracted amounts of attention in machine learning and data mining. Exploiting the manifold regularization (MR), Belkin proposed a new semisupervised classification algorithm: Laplacian support vector machines (LapSVMs), and have shown the state-of-the-art performance in SSL field. To further improve the LapSVMs, we proposed a fast Laplacian SVM (FLapSVM) solver for classification. Compared with the standard LapSVM, our method has several improved advantages as follows: 1) FLapSVM does not need to deal with the extra matrix and burden the computations related to the variable switching, which make it more suitable for large scale problems; 2) FLapSVM's dual problem has the same elegant formulation as that of standard SVMs. This means that the kernel trick can be applied directly into the optimization model; and 3) FLapSVM can be effectively solved by successive overrelaxation technology, which converges linearly to a solution and can process very large data sets that need not reside in memory. In practice, combining the strategies of random scheduling of subproblem and two stopping conditions, the computing speed of FLapSVM is rigidly quicker to that of LapSVM and it is a valid alternative to PLapSVM.
机译：在过去的几年中，半监督学习（SSL）问题同时利用大量廉价的未标记数据和一些未标记的数据进行训练，在机器学习和数据挖掘中引起了广泛的关注。利用流形正则化（MR），Belkin提出了一种新的半监督分类算法：Laplacian支持向量机（LapSVM），并展示了SSL领域的最新性能。为了进一步改善LapSVM，我们提出了一种快速的Laplacian SVM（FLapSVM）求解器进行分类。与标准的LapSVM相比，我们的方法具有以下几个改进的优点：1）FLapSVM不需要处理额外的矩阵，并且不需要负担与变量切换相关的计算，这使其更适合于大规模问题； 2）FLapSVM的双重问题具有与标准SVM相同的优雅表述。这意味着可以将内核技巧直接应用于优化模型。 3）可以通过连续的超松弛技术有效地解决FLapSVM，该技术可以线性收敛到一个解决方案，并且可以处理不需要驻留在内存中的非常大的数据集。在实践中，结合子问题的随机调度和两个停止条件的策略，FLapSVM的计算速度比LapSVM的速度快得多，并且是PLapSVM的有效替代方案。

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