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DTSTART:20200329T030000
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DTSTART:20191027T020000
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DTSTAMP:20260403T220438Z
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\, ISTA
ORGANIZER:hwagner@ist.ac.at
SUMMARY:Alessandro Mella: GeomTop seminar: Non-Topological Persistence for 
 Computer Vision
URL:https://talks-calendar.ista.ac.at/events/2419
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