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DTSTART:20200329T030000
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DTSTART:20191027T020000
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DTSTAMP:20200122T211215Z
UID:5dd3c5f3ef5e4019965797@ist.ac.at
DTSTART:20191120T163000
DTEND:20191120T173000
DESCRIPTION:Speaker: Alessandro Mella\nhosted by Herbert Edelsbrunner\nAbst
ract: Persistent Homology (PH) provides a mathematical description of a da
ta set that captures its internal structure (relations) at multiple scales
in a robust manner [3]. These properties made of PH a widely used tool in
applications [4] However\, PH requires the dataset to be represented as a
topological space\, usually as a simplicial complex whose homology group
can be computed via efficient algorithms. In this talk\, we will build on
the non-topological persistence framework introduced in [1\,2]\, which al
lows us to define persistence diagrams (PDs) in other categories than FinS
imp (e.g.\, weighted graphs\, quivers\, metric spaces) and arbitrary funct
ors (e.g.\, edge-block and clique communities). We will discuss two genera
l ways for producing persistence functions\, and some examples coming from
graph theory and image processing. We will introduce a non-topological pe
rsistence construction that allows for the detection of the boundary of ob
jects in images\, and that is robust to noise\, e.g. salt and pepper\, and
Gaussian noise. We will use this construction\, that we named persistence
pooling\, to define a new pooling layer for Convolutional Neural Networks
. The persistence pooling layer associates a PD to each patch. The pixels
will be consequently sorted in a list following their lifetime. The final
output will be obtained averaging this list with a list of learnable weigh
ts. Preliminary results will be presented showing the performances of this
layer on the Fashion-MNIST dataset [5].[1] Bergomi\, M.G.\, Ferri\, M.\,
Vertechi\, P.\, Zuffi\, L. (2019)\, Beyond topological persistence: Starti
ng from networks\, arXiv.[2] Bergomi\, M.G.\, Vertechi\, P. (2019)\, Rank-
based persistence\, arXiv.[3] Cohen-Steiner\, D.\, Edelsbrunner\, H.\, & H
arer\, J. (2007). Stability of persistence diagrams. Discrete & Computatio
nal Geometry\, 37(1)\, 103-120.[4] Ferri\, M. (2017). Persistent topology
for natural data analysisA survey. In Towards Integrative Machine Learning
and Knowledge Extraction (pp. 117-133). Springer\, Cham.[5] Xiao\, H.\, R
asul\, K.\, Vollgraf R. (2017)\, Fashion-MNIST: a Novel Image Dataset for
Benchmarking Machine Learning Algorithms\, arXiv
LOCATION:Mondi Seminar Room 3\, Central Building\, IST Austria
ORGANIZER:hwagner@ist.ac.at
SUMMARY:GeomTop seminar: Non-Topological Persistence for Computer Vision
URL:https://talks-calendar.app.ist.ac.at/events/2419
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