Abstract:Persistence diagrams do not admit an inner product structure compatible with any Wasserstein metric. Hence, when applying kernel methods to persistence diagrams, the underlying feature map necessarily causes distortion. We prove that persistence diagrams with the -Wasserstein metric do not admit a coarse embedding into a Hilbert space when .

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中文翻译：

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sistence> 2 Wasserstein度量的余辉图的不可嵌入性

摘要：持续性图不允许内部产品结构与任何Wasserstein指标兼容。因此，当将内核方法应用于持久性图时，基础特征图必然会导致变形。我们证明了，当-时，具有-Wasserstein度量的余辉图不允许进入Hilbert空间。

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