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"Predicting graphs"
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Date: |
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Time: |
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Wednesday, 25 May 2022 |
Video-Recording for any system with MP4-support - Video.mp4 (ca. 486 Mb) |
15:15 – 16:30
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SMC Colloquium lecture
Aasa Feragen
(Technical University of Denmark)
Abstract:
Graphs are everywhere! In anatomy and
biology, they appear as transportation
systems
for air, water, nutrients, or signals, and are found both on the large scale
of arteries and airways, and
on the small scale of neurons in the brain.
The structure, geometry and state of the
networks affect their function, and
therefore
also the health of nearby tissue. Conversely, the state of surrounding
tissue
also affects the networks, making them both first and second order
reporters
of health, disease and dysfunction. As a consequence, networks are
studied
extensively in both biology and medicine — and as a proxy for these,
in imaging.
In this talk we first discuss a well known
space of graphs, where networks are
modelled
as equivalence classes of adjacency matrices modulo the action of the
node permutation group. We
derive geometric properties of this space and
discuss
the implications of those geometric properties for statistics such as
dimensionality
reduction and graph-valued regression. Next, we discuss the
potential
for carrying these geometric insights with us into the realm of deep
learning
on graphs.