A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit <a rel="external noopener" href="https://arxiv.org/pdf/2109.13213v2.pdf">the original URL</a>. The file type is <code>application/pdf</code>.
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We propose two multiscale comparisons of graphs using heat diffusion, allowing to compare graphs without node correspondence or even with different sizes. These multiscale comparisons lead to the definition of Lipschitz-continuous empirical processes indexed by a real parameter. The statistical properties of empirical means of such processes are studied in the general case. Under mild assumptions, we prove a functional Central Limit Theorem, as well as a Gaussian approximation with a rate<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2109.13213v2">arXiv:2109.13213v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a7o57i2k2zadhdvdowmtgqckey">fatcat:a7o57i2k2zadhdvdowmtgqckey</a> </span>
more »... ing only on the sample size. Once applied to our processes, these results allow to analyze data sets of pairs of graphs. More precisely, we are able to design consistent confidence bands around empirical means and consistent two-sample tests, using bootstrap methods. Their performances are evaluated by simulations on synthetic data sets.
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