论文标题
Wasserstein指数核
Wasserstein Exponential Kernels
论文作者
论文摘要
在内核方法的上下文中，数据点之间的相似性是由内核函数编码的，内核函数通常得益于欧几里得距离，这是一个常见的示例，是平方的指数核。最近，其他依靠最佳运输理论的距离（例如概率分布之间的Wasserstein距离）已经显示了它们与不同机器学习技术的实际相关性。在本文中，我们研究了定义的指数内核的使用，这要归功于正规化的瓦斯汀距离并讨论了它们的积极确定性。更具体地说，我们定义了Wasserstein的特征图，并说明了他们对涉及形状和图像的监督学习问题的兴趣。从经验上讲，与使用欧几里得距离的类似分类器相比，在小训练集的形状训练集上，瓦斯恒星平方的指数核被证明会产生较小的分类误差。
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances relying on optimal transport theory - such as the Wasserstein distance between probability distributions - have shown their practical relevance for different machine learning techniques. In this paper, we study the use of exponential kernels defined thanks to the regularized Wasserstein distance and discuss their positive definiteness. More specifically, we define Wasserstein feature maps and illustrate their interest for supervised learning problems involving shapes and images. Empirically, Wasserstein squared exponential kernels are shown to yield smaller classification errors on small training sets of shapes, compared to analogous classifiers using Euclidean distances.
