AATRN Networks seminar, Tuesday, May 7, at 5pm CEST by Sarah Percival
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Daniela Egas
May 6, 2024, 5:38:20 PMMay 6
to AATRN Networks, Percival, Sarah, Jason Smith, Henri Riihimäki
Dear AATRN Networks members,
Our next online seminar will be Tuesday, May 7, at 5pm CEST / 11am Eastern Time.
Speaker: Sarah Percival
Title: Bounding the Interleaving Distance for Mapper Graphs with a Loss Function
Abstract: Data consisting of a graph with a function mapping into R^d arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such objects is required in a data analysis pipeline, leading to a need for distances between them. In this work, we study the interleaving distance on discretization of these objects, R^d-mapper graphs, where functor representations of the data can be compared by finding pairs of natural transformations between them. However, in many cases, computation of the interleaving distance is NP-hard. For this reason, we take inspiration from recent work by Robinson to find quality measures for families of maps that do not rise to the level of a natural transformation, called assignments. We then endow the functor images with the extra structure of a metric space and define a loss function which measures how far an assignment is from making the required diagrams of an interleaving commute. Finally, we show that the computation of the loss function is polynomial with a given assignment. We believe this idea is both powerful and translatable, with the potential to provide approximations and bounds on interleavings in a broad array of contexts.
We will meet in the following coordinates (which differ from the previous zoom link):
https://epfl.zoom.us/j/66322742056?pwd=VnlFcU9kWTlERG9pQTRjVVVOa29TZz09
Meeting ID: 663 2274 2056
Passcode: 712373
Our seminar occurs on the first Tuesday of every month, and you can follow our future planned list of speakers on our website sites.google.com/view/aatrn-networks-seminar.
You may also be interested in adding AATRN’s Google calendar (link), which contains other seminar information.
Best,
The AATRN Networks organizers
Daniela Egas Santander, Henri Riihimäki, Jason Smith
Our next online seminar will be Tuesday, May 7, at 5pm CEST / 11am Eastern Time.
Speaker: Sarah Percival
Title: Bounding the Interleaving Distance for Mapper Graphs with a Loss Function
Abstract: Data consisting of a graph with a function mapping into R^d arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such objects is required in a data analysis pipeline, leading to a need for distances between them. In this work, we study the interleaving distance on discretization of these objects, R^d-mapper graphs, where functor representations of the data can be compared by finding pairs of natural transformations between them. However, in many cases, computation of the interleaving distance is NP-hard. For this reason, we take inspiration from recent work by Robinson to find quality measures for families of maps that do not rise to the level of a natural transformation, called assignments. We then endow the functor images with the extra structure of a metric space and define a loss function which measures how far an assignment is from making the required diagrams of an interleaving commute. Finally, we show that the computation of the loss function is polynomial with a given assignment. We believe this idea is both powerful and translatable, with the potential to provide approximations and bounds on interleavings in a broad array of contexts.
We will meet in the following coordinates (which differ from the previous zoom link):
https://epfl.zoom.us/j/66322742056?pwd=VnlFcU9kWTlERG9pQTRjVVVOa29TZz09
Meeting ID: 663 2274 2056
Passcode: 712373
Our seminar occurs on the first Tuesday of every month, and you can follow our future planned list of speakers on our website sites.google.com/view/aatrn-networks-seminar.
You may also be interested in adding AATRN’s Google calendar (link), which contains other seminar information.
Best,
The AATRN Networks organizers
Daniela Egas Santander, Henri Riihimäki, Jason Smith
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