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Persistent homology of time-dependent functional networks constructed from coupled time series | | Bernadette J. Stolz
; Heather A. Harrington
; Mason A. Porter
; | | Date: |
2 May 2016 | | Abstract: | We use topological data analysis to study "functional networks" that we
construct from time-series data from both experimental and synthetic sources.
Specifically, we use persistent homology in combination with a weight rank
clique filtration to gain insights into these functional networks, and we use
persistence landscapes to interpret our results. Our first example consists of
biological data in the form of functional magnetic resonance imaging (fMRI)
data that was acquired from human subjects during a simple motor-learning task.
Our second example uses time-series output from networks of coupled Kuramoto
oscillators. With these examples, we demonstrate that (1) using persistent
homology to study functional networks provides fascinating insights into their
properties and (2) the position of the features in a filtration can play a more
vital role than persistence in the interpretation of topological features, even
though the latter is used more commonly to distinguish between signal and
noise. We find that in particular, persistent homology can detect differences
in synchronisation patterns in our data sets over time giving insight on
changes in community structure in the networks, and on increased
synchronisation between brain regions forming loops in the functional network
during motor-learning. For the motor-learning data we also observe that
persistence landscapes reveal that the majority of changes in the loops of the
network takes place on the second of three days of the learning process. | | Source: | arXiv, 1605.0562 | | Services: | Forum | Review | PDF | Favorites | |
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