Similar unlabeled (SU) classification is pervasive in many real-world applications, where only similar data pairs (two data points have the same label) and unlabeled data points are available to train a classifier. Recent work has identified a practical SU formulation and has derived the corresponding estimation error bound. It evaluated SU learning with linear classifiers on medium-sized datasets. However, in practice, we often need to learn nonlinear classifiers on large-scale datasets for superior predictive performance. How this could be done in an efficient manner is still an open problem for SU classification. In this paper, we propose a scalable kernel learning algorithm for SU classification using a triply stochastic optimization framework, called TSGSU. Specifically, in each iteration, our method randomly samples an instance from the similar pairs set, an instance from the unlabeled set, and their random features to calculate the stochastic functional gradient for the model update. Theoretically, we prove that our method can converge to a stationary point at the rate of \(O(1/\sqrt{T})\) after T iterations. Experiments on various benchmark datasets and high-dimensional datasets not only demonstrate the scalability of TSGSU but also show the efficiency of TSGSU compared with existing SU learning algorithms while retaining similar generalization performance.

类似的未标记 (SU) 分类在许多实际应用中很普遍，其中只有相似的数据对（两个数据点具有相同的标签）和未标记的数据点可用于训练分类器。最近的工作已经确定了一种实用的 SU 公式，并得出了相应的估计误差界限。它在中型数据集上使用线性分类器评估 SU 学习。然而，在实践中，我们经常需要在大规模数据集上学习非线性分类器以获得卓越的预测性能。如何以有效的方式做到这一点仍然是 SU 分类的一个悬而未决的问题。在本文中，我们使用称为 TSGSU 的三重随机优化框架提出了一种用于 SU 分类的可扩展内核学习算法。具体来说，在每次迭代中，我们的方法从相似对集合中随机采样一个实例，从未标记集合中随机采样一个实例，以及它们的随机特征来计算模型更新的随机函数梯度。从理论上讲，我们证明了我们的方法可以以\(O(1/\sqrt{T})\)经过T次迭代。在各种基准数据集和高维数据集上的实验不仅证明了 TSGSU 的可扩展性，而且还展示了 TSGSU 与现有 SU 学习算法相比的效率，同时保持了相似的泛化性能。