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Alternating Binary Classifier and Graph Learning from Partial Labels

机译：从部分标签交替进行二分类器和图学习

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Semi-supervised binary classifier learning is a fundamental machine learning task where only partial binary labels are observed, and labels of the remaining data need to be interpolated. Leveraging on the advances of graph signal processing (GSP), recently binary classifier learning is posed as a signal restoration problem regularized using a graph smoothness prior, where the undirected graph consists of a set of vertices and a set of weighted edges connecting vertices with similar features. In this paper, we improve the performance of such a graph-based classifier by simultaneously optimizing the feature weights used in the construction of the similarity graph. Specifically, we start by interpolating missing labels by first formulating a boolean quadratic program with a graph signal smoothness objective, then relax it to a convex semi-definite program, solvable in polynomial time. Next, we optimize the feature weights used for construction of the similarity graph by reusing the smoothness objective but with a convex set constraint for the weight vector. The reposed convex but non-differentiable problem is solved via an iterative proximal gradient descent algorithm. The two steps are solved alternately until convergence. Experimental results show that our alternating classifier / graph learning algorithm outperforms existing graph-based methods and support vector machines with various kernels1The work is partly funded by the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 734331..
机译：半监督二进制分类器学习是一项基本的机器学习任务，其中仅观察到部分二进制标签，并且需要对剩余数据的标签进行插值。借助图信号处理（GSP）的先进性，近来二进制分类器学习被提出为使用图平滑先验规则化的信号恢复问题，其中无向图由一组顶点和一组连接相似顶点的加权边组成特征。在本文中，我们通过同时优化构造相似图时使用的特征权重，提高了这种基于图的分类器的性能。具体来说，我们首先通过对带有图形信号平滑度目标的布尔二次程序进行公式化，然后再将其放宽为可在多项式时间内求解的凸半定程序来对缺失的标签进行插值。接下来，我们通过重用平滑度目标，但对权重向量具有凸集约束，来优化用于构建相似度图的特征权重。通过迭代的近端梯度下降算法解决了凸的但不可微的问题。交替求解这两个步骤，直到收敛为止。实验结果表明，我们的交替分类器/图学习算法优于现有的基于图的方法，并支持具有各种内核的向量机 1 这项工作部分由欧盟地平线2020研究与创新计划提供资金，该计划是根据玛丽·斯库多夫斯卡·居里（Marie Sklodowska-Curie）授予协议734331进行的。

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