Support Vector Machines (SVMs) are one of the most popular supervised learning models to classify using a hyperplane in an Euclidean space. Similar to SVMs, tropical SVMs classify data points using a tropical hyperplane under the tropical metric with the max-plus algebra. In this paper, first we show generalization error bounds of tropical SVMs over the tropical projective torus. While the generalization error bounds attained via Vapnik-Chervonenkis (VC) dimensions in a distribution-free manner still depend on the dimension, we also show numerically and theoretically by extreme value statistics that the tropical SVMs for classifying data points from two Gaussian distributions as well as empirical data sets of different neuron types are fairly robust against the curse of dimensionality. Extreme value statistics also underlie the anomalous scaling behaviors of the tropical distance between random vectors with additional noise dimensions. Finally, we define tropical SVMs over a function space with the tropical metric.

翻译：支持矢量机(SVMs)是使用超高飞机在赤道空间进行分类的最受欢迎的监管学习模型之一。与SVMs相似,热带SVMs在热带指标下使用热带高空数据点进行分类,使用最大增代数。在本文中,我们首先显示了热带SVMs在热带投影体上的概括误差。虽然通过Vapnik-Chervonenkis(VC)以无分布式方式实现的概括误差仍然取决于其尺寸,但我们从数字和理论上也显示了极值统计数据,表明用于从两个高山分布区对数据点进行分类的热带SVMs以及不同类型神经的经验数据集对维度的诅咒相当可靠。极端值统计数据也是以额外噪音维度测量的热带随机矢量之间热带距离的反常量行为的基础。最后,我们用热带指标来界定一个功能空间上的热带SVMs。