44 lines
2.1 KiB
Org Mode
44 lines
2.1 KiB
Org Mode
* Topological Data Analysis of Temporal Networks
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Repository for my Master's thesis project. See the [[file:dissertation/dissertation.pdf][dissertation]].
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[[https://zenodo.org/badge/latestdoi/123611777][https://zenodo.org/badge/123611777.svg]]
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** Abstract
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Temporal networks are a mathematical model to represent interactions
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evolving over time. As such, they have a multitude of applications,
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from biology to physics to social networks. The study of dynamics on
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networks is an emerging field, with many challenges in modelling and
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data analysis.
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An important issue is to uncover meaningful temporal structure in a
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network. We focus on the problem of periodicity detection in
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temporal networks, by partitioning the time range of the network and
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clustering the resulting subnetworks.
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For this, we leverage methods from the field of topological data
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analysis and persistent homology. These methods have begun to be
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employed with static graphs in order to provide a summary of
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topological features, but applications to temporal networks have
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never been studied in detail.
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We cluster temporal networks by computing the evolution of
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topological features over time. Applying persistent homology to
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temporal networks and comparing various approaches has never been
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done before, and we examine their performance side-by-side with a
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simple clustering algorithm. Using a generative model, we show that
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persistent homology is able to detect periodicity in the topological
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structure of a network.
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We define two types of topological features, with and without
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aggregating the temporal networks, and multiple ways of embedding
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them in a feature space suitable for machine-learning
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applications. In particular, we examine the theoretical guarantees
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and empirical performance of kernels defined on topological
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features.
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Topological insights prove to be useful in statistical learning
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applications. Combined with the recent advances in network science,
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they lead to a deeper understanding of the structure of temporal
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networks.
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