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1<aside class=search-modal id=search><div class=container><section class=search-header><div class="row no-gutters justify-content-between mb-3"><div class=col-6><h1>Search</h1></div><div class="col-6 col-search-close"><a class=js-search href=# aria-label=Close><i class="fas fa-times-circle text-muted" aria-hidden=true></i></a></div></div><div id=search-box><input name=q id=search-query placeholder=Search... autocapitalize=off autocomplete=off autocorrect=off spellcheck=false type=search class=form-control aria-label=Search...></div></section><section class=section-search-results><div id=search-hits></div></section></div></aside><div class="page-header header--fixed"><header><nav class="navbar navbar-expand-lg navbar-light compensate-for-scrollbar" id=navbar-main><div class=container-xl><div class="d-none d-lg-inline-flex"><a class=navbar-brand href=/>Elena Wang</a></div><button type=button class=navbar-toggler data-toggle=collapse data-target=#navbar-content aria-controls=navbar-content aria-expanded=false aria-label="Toggle navigation">
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4<a href=# class="dropdown-item js-set-theme-auto"><span>Automatic</span></a></div></li></ul></div></nav></header></div><div class=page-body><div class=pub><div class="article-container pt-3"><h1>A Distance for Geometric Graphs via the Labeled Merge Tree Interleaving Distance</h1><div class=article-metadata><div><span>E. Chambers</span>, <span>E. Munch</span>, <span>S. Percival</span>, <span class=author-highlighted>Elena Xinyi Wang</span></div><span class=article-date>July, 2024</span></div><div class="btn-links mb-3"><a class="btn btn-outline-primary btn-page-header" href=https://arxiv.org/pdf/2407.09442 target=_blank rel=noopener>PDF</a>
5<a class="btn btn-outline-primary btn-page-header" href=https://github.com/elenawang93/Labeled-Merge-Tree-Transform target=_blank rel=noopener>Code</a>
6<a class="btn btn-outline-primary btn-page-header" href=https://arxiv.org/abs/2407.09442 target=_blank rel=noopener>arXiv</a></div></div><div class=article-container><h3>Abstract</h3><p class=pub-abstract>Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric graphs via merge trees. In order to preserve as much useful information as possible from the original data, we introduce a way of rotating the sublevel set to obtain the merge trees via the idea of the directional transform. We represent the merge trees using a surjective multi-labeling scheme and then compute the distance between two representative matrices. We show some theoretically desirable qualities and present two methods of computation - approximation via sampling and exact distance using a kinetic data structure, both in polynomial time. We illustrate its utility by implementing it on two data sets.</p><div class=row><div class=col-md-1></div><div class=col-md-10><div class=row><div class="col-12 col-md-3 pub-row-heading">Type</div><div class="col-12 col-md-9"><a href=/publication/#3>Preprint</a></div></div></div><div class=col-md-1></div></div><div class="d-md-none space-below"></div><div class=space-below></div><div class=article-style></div><div class=article-tags><a class="badge badge-light" href=/tag/geometric-graph/>Geometric Graph</a>
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