The Wasserstein distance is a powerful metric based on the theory of optimal mass transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common divergences on distributions such as Kullback-Leibler or Jensen-Shannon, it is (weakly) continuous, and thus ideal for analyzing corrupted and noisy data. Until recently, however, no kernel methods for dealing with nonlinear data have been proposed via the Wasserstein distance. In this work, we develop a novel method to compute the L2-Wasserstein distance in reproducing kernel Hilbert spaces (RKHS) called kernel L2-Wasserstein distance, which is implemented using the kernel trick. The latter is a general method in machine learning employed to handle data in a nonlinear manner. We evaluate the proposed approach in identifying computed tomography (CT) slices with dental artifacts in head and neck cancer, performing unsupervised hierarchical clustering on the resulting Wasserstein distance matrix that is computed on imaging texture features extracted from each CT slice. We further compare the performance of kernel Wasserstein distance with alternatives including kernel Kullback-Leibler divergence we previously developed. Our experiments show that the kernel approach outperforms classical non-kernel approaches in identifying CT slices with artifacts.

中文翻译：

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一种基于高斯测度的新颖的核Wasserstein距离：在头颈部计算机断层扫描中识别牙齿伪像的应用。

Wasserstein距离是基于最佳质量传输理论的强大度量。它给出了两种分布之间距离的自然度量，具有广泛的应用范围。与许多常见的分布差异（例如Kullback-Leibler或Jensen-Shannon）不同，它是（弱）连续的，因此非常适合分析损坏和嘈杂的数据。但是，直到最近，还没有提出通过Wasserstein距离来处理非线性数据的核方法。在这项工作中，我们开发了一种新的方法来计算再现内核希尔伯特空间（RKHS）中的L2-Wasserstein距离，称为内核L2-Wasserstein距离，该方法是使用内核技巧实现的。后者是机器学习中用于以非线性方式处理数据的通用方法。我们评估提出的方法，以识别头颈癌中带有牙齿伪影的计算机断层摄影（CT）切片，对由此产生的Wasserstein距离矩阵执行无监督的层次聚类，该矩阵是根据从每个CT切片提取的成像纹理特征计算得出的。我们进一步将核Wasserstein距离的性能与包括我们先前开发的核Kullback-Leibler发散在内的其他方案进行比较。我们的实验表明，在识别带有伪影的CT切片时，内核方法优于传统的非内核方法。我们进一步将核Wasserstein距离的性能与包括我们先前开发的核Kullback-Leibler发散在内的其他方案进行比较。我们的实验表明，在识别带有伪影的CT切片时，内核方法优于传统的非内核方法。我们进一步将核Wasserstein距离的性能与包括我们先前开发的核Kullback-Leibler发散在内的其他方案进行比较。我们的实验表明，在识别带有伪影的CT切片时，内核方法优于传统的非内核方法。