基于Ginzburg-Landau函数极小化的多类图半监督学习
Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization
摘要：
我们提出了一个基于图的变分算法分类的高维数据，推广的二元扩散界面模型的情况下，多个类。受全变分技术的启发，该方法涉及最小化由三项组成的能量泛函。前两个术语促进了类之间具有急剧过渡的逐步连续分类函数，同时保持类标签之间的对称性。第三项是数据保真度项，允许我们在半监督框架中将先验信息纳入模型。该算法在合成数据以及COIL和MNIST基准数据集上的性能与最先进的基于图形的多类分割方法具有竞争力。
英文摘要：
We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification function with sharp transitions between classes, while preserving symmetry among the class labels. The third term is a data fidelity term, allowing us to incorporate prior information into the model in a semi-supervised framework. The performance of the algorithm on synthetic data, as well as on the COIL and MNIST benchmark datasets, is competitive with state-of-the-art graph-based multiclass segmentation methods.
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