What will be new in GUDHI library version 2.0.0
|
|
|
- Leona Elliott
- 5 years ago
- Views:
Transcription
1 What will be new in GUDHI library version Jean-Daniel Boissonnat, Paweł Dłotko, Marc Glisse, François Godi, Clément Jamin, Siargey Kachanovich, Clément Maria, Vincent Rouvreau and David Salinas DataShape, Inria Saclay and Sophia-Antipolis
2 GUDHI is a five years project supported by a Grant of the European Research Council and hosted by INRIA - develop and understand geometrical data structures - develop associated statistical, geometric and topological functions
3 Wikipedia - TDA workflow
4 Point cloud Geometric filtered complex builds the filtered simplicial complex Distance matrix
5 Point cloud Geometric filtered complex Data structure Persistent homology Distance matrix - Stores the filtered simplicial complex - Interfaces with persistence modules
6 Point cloud Geometric filtered complex Data structure Persistent homology Persistence intervals Distance matrix Bar code Diagram Betti numbers Bottleneck distance Statistic tools...
7 Point cloud Geometric filtered complex Data structure Persistent homology Persistence intervals Distance matrix Bar code Diagram Betti numbers Bottleneck distance Statistic tools...
8 Point cloud Geometric filtered complex Geometric filtered complex Rips from a point cloud by Clément Maria
9 Distance matrix Geometric filtered complex Geometric filtered complex Rips from a distance matrix by Paweł Dłotko
10 Point cloud Geometric non filtered complex CGAL Geometric non filtered complex Tangential complex - Suppose we have a set of points sampled from a manifold. - For every point construct tangent space at that every p L. - For every p L, construct its star and glue the stars of neighbouring points if they agree. - Based on Jean-Daniel Boissonnat and Arijit Ghosh Manifold reconstruction using Tangential Delaunay Complexes. by Clément Jamin
11 Distance matrix Geometric filtered complex CGAL Geometric filtered complex Witness complex - For large point clouds, select small, representative collection of points L called landmarks. - Build a complex on landmark points. Add a simplex if a witness exists. - Version with and without filtration. by Siargey Kachanovich
12 Point cloud Geometric filtered complex CGAL Geometric filtered complex Alpha from a point cloud + Periodic, exact and weighted alpha complexes in dimension 3. by Marc Glisse & Vincent Rouvreau
13 Point cloud Geometric filtered complex CGAL Geometric filtered complex - Delaunay from a point cloud by Marc Glisse & Vincent Rouvreau
14 Point cloud Geometric filtered complex Data structure Persistent homology Persistence intervals Distance matrix Bar code Diagram Betti numbers Bottleneck distance Statistic tools...
15 Data structure Cubical complexes bitmap - Represented as a vector of filtration values. - (Co)boundary computed based on the position in this vector. - Used in analysis of grid-type data. by Paweł Dłotko
16 Data structure Filtered simplicial complexes Simplex tree - Memory and time efficient data structure to store simplicial complexes. - Every simplex is a word stored in the tree. - The nodes corresponding to simplices of the same dimension having the same maximal vertex are stored in a cyclic list. - It is a base of all algorithms to compute persistence of weighted simplicial complexes in GUDHI. by Clément Maria
17 Data structure Simplicial complexes Skeleton blocker - A data structure for very large simplicial complexes. - We store the 1 skeleton and the minimal simplices which are not present in the complex. - The rest is generated from cliques in the 1 skeleton. - Used in edge contraction toolbox (details later). by David Salinas
18 Point cloud Geometric filtered complex Data structure Edge contraction Distance matrix
19 Edge contraction Toolbox edge contraction - Efficient on a skeleton blocker data structure. by David Salinas
20 Point cloud Geometric filtered complex Data structure Persistent homology Persistence intervals Distance matrix Bar code Diagram Betti numbers Bottleneck distance Statistic tools...
21 Persistent homology Persistence intervals Toolbox Persistence cohomology - Standard persistence cohomology computations by using compressed annotation matrix. - Multi field persistence (detection of torsion coefficients). by Clément Maria
22 Point cloud Geometric filtered complex Data structure Persistent homology Persistence intervals Distance matrix Bar code Diagram Betti numbers Bottleneck distance Statistic tools...
23 Persistence intervals Bottleneck distance CGAL Toolbox Bottleneck distance by François Godi
24 Our website: Documentation will be available here: BETA
25 Third party libraries GUDHI Boost CGAL GMP MPFR Eigen3 TBB Installing GUDHI: BETA
26 If you want to join the GUDHI users community: BETA
27 GUDHI downloads:
28 GUDHI is open to external contributions. - Examples driven development - Documentation is required - Unitary tests are required - Some conventions to write code - Peer review process - All the packages come with the names of their authors
29
30 Interfaces Library TDA GUDHI Boost CGAL GMP MPFR Eigen3 TBB
31 Interfaces Library TDA Cython GUDHI Boost CGAL GMP MPFR Eigen3 TBB
32 Dim2: random cubical complex to , dx = 400 Dim3: random cubical complex to , dx = 20
33 Cython - Documentation will be available here: BETA - Documentation will be available here: BETA
34 What will arrive after GUDHI 2.0.0? - S.A.L. - GUDHI stat - Zig zag persistence - Phat persistence interface - Graph induced complex - Nearest neighbor
35 Thank you!
A roadmap for the computation of persistent homology
A roadmap for the computation of persistent homology Nina Otter Mathematical Institute, University of Oxford (joint with Mason A. Porter, Ulrike Tillmann, Peter Grindrod, Heather A. Harrington) 2nd School
The Gudhi Library: Simplicial Complexes and Persistent Homology
The Gudhi Library: Simplicial Complexes and Persistent Homology Clément Maria, Jean-Daniel Boissonnat, Marc Glisse, Mariette Yvinec To cite this version: Clément Maria, Jean-Daniel Boissonnat, Marc Glisse,
Computational Geometry Learning
Computational Geometry Learning Jean-Daniel Boissonnat Frédéric Chazal Geometrica, INRIA http://www-sop.inria.fr/geometrica Lectures at MPRI MPRI Computational Geometry Learning Lectures at MPRI 1 / 14
Tutorial on the R package TDA
Tutorial on the R package TDA Jisu Kim Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clément Maria, Vincent Rouvreau Abstract This tutorial gives an introduction to the R package TDA, which provides some
The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes
The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes Jean-Daniel Boissonnat, Clément Maria To cite this version: Jean-Daniel Boissonnat, Clément Maria. The Simplex Tree: An Efficient
Goodies in Statistic and ML. DataShape, Inria Saclay
Goodies in Statistic and ML. DataShape, Inria Saclay Gudhi is in Statistic and ML. DataShape, Inria Saclay Where did I start playing with statistics? Analysis of time varying patterns from dynamical systems,
topological data analysis and stochastic topology yuliy baryshnikov waikiki, march 2013
topological data analysis and stochastic topology yuliy baryshnikov waikiki, march 2013 Promise of topological data analysis: extract the structure from the data. In: point clouds Out: hidden structure
JPlex Software Demonstration. AMS Short Course on Computational Topology New Orleans Jan 4, 2011 Henry Adams Stanford University
JPlex Software Demonstration AMS Short Course on Computational Topology New Orleans Jan 4, 2011 Henry Adams Stanford University What does JPlex do? Input: a filtered simplicial complex or finite metric
3. Persistence. CBMS Lecture Series, Macalester College, June Vin de Silva Pomona College
Vin de Silva Pomona College CBMS Lecture Series, Macalester College, June 2017 o o The homology of a planar region Chain complex We have constructed a diagram of vector spaces and linear maps @ 0 o 1 C
Recent Advances and Trends in Applied Algebraic Topology
Recent Advances and Trends in Applied Algebraic Topology Mikael Vejdemo-Johansson School of Computer Science University of St Andrews Scotland July 8, 2012 M Vejdemo-Johansson (St Andrews) Trends in applied
JPlex. CSRI Workshop on Combinatorial Algebraic Topology August 29, 2009 Henry Adams
JPlex CSRI Workshop on Combinatorial Algebraic Topology August 29, 2009 Henry Adams Plex: Vin de Silva and Patrick Perry (2000-2006) JPlex: Harlan Sexton and Mikael Vejdemo- Johansson (2008-present) JPlex
The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes
The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes Jean-Daniel Boissonnat, Clément Maria To cite this version: Jean-Daniel Boissonnat, Clément Maria. The Simplex Tree: An Efficient
A Practical Guide to Persistent Homology
A Practical Guide to Persistent Homology Dmitriy Morozov Lawrence Berkeley National Lab A Practical Guide to Persistent Code snippets available at: http://hg.mrzv.org/dionysus-tutorial Homology (Dionysus
Homology and Persistent Homology Bootcamp Notes 2017
Homology and Persistent Homology Bootcamp Notes Summer@ICERM 2017 Melissa McGuirl September 19, 2017 1 Preface This bootcamp is intended to be a review session for the material covered in Week 1 of Summer@ICERM
Topological Data Analysis
Proceedings of Symposia in Applied Mathematics Topological Data Analysis Afra Zomorodian Abstract. Scientific data is often in the form of a finite set of noisy points, sampled from an unknown space, and
Lecture 1 Discrete Geometric Structures
Lecture 1 Discrete Geometric Structures Jean-Daniel Boissonnat Winter School on Computational Geometry and Topology University of Nice Sophia Antipolis January 23-27, 2017 Computational Geometry and Topology
Topological estimation using witness complexes. Vin de Silva, Stanford University
Topological estimation using witness complexes, Acknowledgements Gunnar Carlsson (Mathematics, Stanford) principal collaborator Afra Zomorodian (CS/Robotics, Stanford) persistent homology software Josh
Package TDA. December 9, 2017
Type Package Package TDA December 9, 2017 Title Statistical Tools for Topological Data Analysis Version 1.6 Date 2017-12-09 Author Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clement Maria, Vincent Rouvreau.
Analyse Topologique des Données
Collège de France 31 mai 2017 Analyse Topologique des Données Frédéric Chazal DataShape team INRIA Saclay - Ile-de-France frederic.chazal@inria.fr Introduction [Shape database] [Galaxies data] [Scanned
Topological Inference via Meshing
Topological Inference via Meshing Benoit Hudson, Gary Miller, Steve Oudot and Don Sheehy SoCG 2010 Mesh Generation and Persistent Homology The Problem Input: Points in Euclidean space sampled from some
The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes
The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes Jean-Daniel Boissonnat, Clément Maria To cite this version: Jean-Daniel Boissonnat, Clément Maria. The Simplex Tree: An Efficient
4. Simplicial Complexes and Simplicial Homology
MATH41071/MATH61071 Algebraic topology Autumn Semester 2017 2018 4. Simplicial Complexes and Simplicial Homology Geometric simplicial complexes 4.1 Definition. A finite subset { v 0, v 1,..., v r } R n
R Package TDA for Statistical Inference on Topological Data Analysis and Lessons from its Maintenance
R Package TDA for Statistical Inference on Topological Data Analysis and Lessons from its Maintenance Jisu KIM Carnege Mellon University October 11, 2018 1 / 59 R Package TDA for Statistical Inference
New Results on the Stability of Persistence Diagrams
New Results on the Stability of Persistence Diagrams Primoz Skraba Jozef Stefan Institute TAGS - Linking Topology to Algebraic Geometry and Statistics joint work with Katharine Turner and D. Yogeshwaran
Persistent Homology and Nested Dissection
Persistent Homology and Nested Dissection Don Sheehy University of Connecticut joint work with Michael Kerber and Primoz Skraba A Topological Data Analysis Pipeline A Topological Data Analysis Pipeline
A Multicover Nerve for Geometric Inference. Don Sheehy INRIA Saclay, France
A Multicover Nerve for Geometric Inference Don Sheehy INRIA Saclay, France Computational geometers use topology to certify geometric constructions. Computational geometers use topology to certify geometric
A Geometric Perspective on Sparse Filtrations
CCCG 2015, Kingston, Ontario, August 10 12, 2015 A Geometric Perspective on Sparse Filtrations Nicholas J. Cavanna Mahmoodreza Jahanseir Donald R. Sheehy Abstract We present a geometric perspective on
Topological Persistence
Topological Persistence Topological Persistence (in a nutshell) X topological space f : X f persistence X Dg f signature: persistence diagram encodes the topological structure of the pair (X, f) 1 Topological
Clustering algorithms and introduction to persistent homology
Foundations of Geometric Methods in Data Analysis 2017-18 Clustering algorithms and introduction to persistent homology Frédéric Chazal INRIA Saclay - Ile-de-France frederic.chazal@inria.fr Introduction
arxiv: v7 [math.at] 12 Sep 2017
![arxiv: v7 [math.at] 12 Sep 2017](/thumbs/83/87225858.jpg "arxiv: v7 [math.at] 12 Sep 2017")
A Roadmap for the Computation of Persistent Homology arxiv:1506.08903v7 [math.at] 12 Sep 2017 Nina Otter (otter@maths.ox.ac.uk) Mason A. Porter (mason@math.ucla.edu) Ulrike Tillmann (tillmann@maths.ox.ac.uk)
Statistical properties of topological information inferred from data
Saclay, July 8, 2014 DataSense Research day Statistical properties of topological information inferred from data Frédéric Chazal INRIA Saclay Joint works with B.T. Fasy (CMU), M. Glisse (INRIA), C. Labruère
Topological Data Analysis - I. Afra Zomorodian Department of Computer Science Dartmouth College
Topological Data Analysis - I Afra Zomorodian Department of Computer Science Dartmouth College September 3, 2007 1 Acquisition Vision: Images (2D) GIS: Terrains (3D) Graphics: Surfaces (3D) Medicine: MRI
Homological Reconstruction and Simplification in R3
Homological Reconstruction and Simplification in R3 Dominique Attali, Ulrich Bauer, Olivier Devillers, Marc Glisse, André Lieutier To cite this version: Dominique Attali, Ulrich Bauer, Olivier Devillers,
Discrete Exterior Calculus
Discrete Exterior Calculus Peter Schröder with Mathieu Desbrun and the rest of the DEC crew 1 Big Picture Deriving a whole Discrete Calculus first: discrete domain notion of chains and discrete representation
Simplicial Complexes: Second Lecture
Simplicial Complexes: Second Lecture 4 Nov, 2010 1 Overview Today we have two main goals: Prove that every continuous map between triangulable spaces can be approximated by a simplicial map. To do this,
The Arithmetic Toolbox in
The Arithmetic Toolbox in Computational Geometry Algorithms Library Sylvain Pion Mini-workshop on irram/mpc/mpfr Schloß Dagstuhl April 18-20, 2018 Talk outline Brief overview of CGAL Robustness issues
Package TDA. April 27, 2017
Type Package Package TDA April 27, 2017 Title Statistical Tools for Topological Data Analysis Version 1.5.1 Date 2017-04-27 Author Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clement Maria, Vincent Rouvreau.
Clique homological simplification problem is NP-hard
Clique homological simplification problem is NP-hard NingNing Peng Department of Mathematics, Wuhan University of Technology pnn@whut.edu.cn Foundations of Mathematics September 9, 2017 Outline 1 Homology
A persistence landscapes toolbox for topological statistics
A persistence landscapes toolbox for topological statistics Peter Bubenik, Dlotko Pawel To cite this version: Peter Bubenik, Dlotko Pawel. A persistence landscapes toolbox for topological statistics. Journal
Stratified Structure of Laplacian Eigenmaps Embedding
Stratified Structure of Laplacian Eigenmaps Embedding Abstract We construct a locality preserving weight matrix for Laplacian eigenmaps algorithm used in dimension reduction. Our point cloud data is sampled
Lecture 0: Reivew of some basic material
Lecture 0: Reivew of some basic material September 12, 2018 1 Background material on the homotopy category We begin with the topological category TOP, whose objects are topological spaces and whose morphisms
Topological Inference via Meshing
Topological Inference via Meshing Don Sheehy Theory Lunch Joint work with Benoit Hudson, Gary Miller, and Steve Oudot Computer Scientists want to know the shape of data. Clustering Principal Component
Random Simplicial Complexes
Random Simplicial Complexes Duke University CAT-School 2015 Oxford 8/9/2015 Part I Random Combinatorial Complexes Contents Introduction The Erdős Rényi Random Graph The Random d-complex The Random Clique
Persistence stability for geometric complexes
Lake Tahoe - December, 8 2012 NIPS workshop on Algebraic Topology and Machine Learning Persistence stability for geometric complexes Frédéric Chazal Joint work with Vin de Silva and Steve Oudot (+ on-going
Coxeter triangulations have good quality
Coxeter triangulations have good quality Aruni Choudhary, Siargey Kachanovich, and Mathijs Wintraecken Max Planck Institute for Informatics, Saarland Informatics Campus Saarbrücken, Germany Université
Homological Reconstruction and Simplification in R3
Homological Reconstruction and Simplification in R3 Dominique Attali, Ulrich Bauer, Olivier Devillers, Marc Glisse, André Lieutier To cite this version: Dominique Attali, Ulrich Bauer, Olivier Devillers,
An introduction to Topological Data Analysis through persistent homology: Intro and geometric inference
Sophia-Antipolis, January 2016 Winter School An introduction to Topological Data Analysis through persistent homology: Intro and geometric inference Frédéric Chazal INRIA Saclay - Ile-de-France frederic.chazal@inria.fr
Introduction to the R package TDA
Introduction to the R package TDA Brittany T. Fasy Computer Science Department,Tulane University Jisu Kim arxiv:1411.1830v2 [cs.ms] 29 Jan 2015 Abstract Department of Statistics, Carnegie Mellon University
Simplicial Complexes of Networks and Their Statistical Properties
Simplicial Complexes of Networks and Their Statistical Properties Slobodan Maletić, Milan Rajković*, and Danijela Vasiljević Institute of Nuclear Sciences Vinča, elgrade, Serbia *milanr@vin.bg.ac.yu bstract.
Computational Statistics and Mathematics for Cyber Security
and Mathematics for Cyber Security David J. Marchette Sept, 0 Acknowledgment: This work funded in part by the NSWC In-House Laboratory Independent Research (ILIR) program. NSWCDD-PN--00 Topics NSWCDD-PN--00
Lecture 5: Simplicial Complex
Lecture 5: Simplicial Complex 2-Manifolds, Simplex and Simplicial Complex Scribed by: Lei Wang First part of this lecture finishes 2-Manifolds. Rest part of this lecture talks about simplicial complex.
An algorithm for calculating top-dimensional bounding chains
An algorithm for calculating top-dimensional bounding chains J. Frederico Carvalho Corresp., 1, Mikael Vejdemo-Johansson 2, Danica Kragic 1, Florian T. Pokorny 1 1 CAS/RPL, KTH, Royal Institute of Technology,
Topological Data Analysis
Mikael Vejdemo-Johansson School of Computer Science University of St Andrews Scotland 22 November 2011 M Vejdemo-Johansson (St Andrews) TDA 22 November 2011 1 / 32 e Shape of Data Outline 1 e Shape of
66 III Complexes. R p (r) }.
66 III Complexes III.4 Alpha Complexes In this section, we use a radius constraint to introduce a family of subcomplexes of the Delaunay complex. These complexes are similar to the Čech complexes but differ
Random Simplicial Complexes
Random Simplicial Complexes Duke University CAT-School 2015 Oxford 9/9/2015 Part II Random Geometric Complexes Contents Probabilistic Ingredients Random Geometric Graphs Definitions Random Geometric Complexes
TOPOLOGICAL DATA ANALYSIS
TOPOLOGICAL DATA ANALYSIS BARCODES Ghrist, Barcodes: The persistent topology of data Topaz, Ziegelmeier, and Halverson 2015: Topological Data Analysis of Biological Aggregation Models 1 Questions in data
Topological Inference for Modern Data Analysis
Topological Inference for Modern Data Analysis An Introduction to Persistent Homology Giancarlo Sanchez A project presented for the degree of Master s of Science in Mathematics Department of Mathematics
Discrete Exterior Calculus How to Turn Your Mesh into a Computational Structure. Discrete Differential Geometry
Discrete Exterior Calculus How to Turn Your Mesh into a Computational Structure Discrete Differential Geometry Big Picture Deriving a whole Discrete Calculus you need first a discrete domain will induce
Detection and approximation of linear structures in metric spaces
Stanford - July 12, 2012 MMDS 2012 Detection and approximation of linear structures in metric spaces Frédéric Chazal Geometrica group INRIA Saclay Joint work with M. Aanjaneya, D. Chen, M. Glisse, L. Guibas,
arxiv: v2 [cs.cg] 8 Feb 2010 Abstract
![arxiv: v2 [cs.cg] 8 Feb 2010 Abstract](/thumbs/74/70185799.jpg "arxiv: v2 [cs.cg] 8 Feb 2010 Abstract")
Topological De-Noising: Strengthening the Topological Signal Jennifer Kloke and Gunnar Carlsson arxiv:0910.5947v2 [cs.cg] 8 Feb 2010 Abstract February 8, 2010 Topological methods, including persistent
Kernel Methods for Topological Data Analysis
Kernel Methods for Topological Data Analysis Toward Topological Statistics Kenji Fukumizu The Institute of Statistical Mathematics (Tokyo Japan) Joint work with Genki Kusano and Yasuaki Hiraoka (Tohoku
Coxeter Groups and CAT(0) metrics
Peking University June 25, 2008 http://www.math.ohio-state.edu/ mdavis/ The plan: First, explain Gromov s notion of a nonpositively curved metric on a polyhedral complex. Then give a simple combinatorial
Data Analysis, Persistent homology and Computational Morse-Novikov theory
Data Analysis, Persistent homology and Computational Morse-Novikov theory Dan Burghelea Department of mathematics Ohio State University, Columbuus, OH Bowling Green, November 2013 AMN theory (computational
Observing Information: Applied Computational Topology.
Observing Information: Applied Computational Topology. Bangor University, and NUI Galway April 21, 2008 What is the geometric information that can be gleaned from a data cloud? Some ideas either already
Topological Classification of Data Sets without an Explicit Metric
Topological Classification of Data Sets without an Explicit Metric Tim Harrington, Andrew Tausz and Guillaume Troianowski December 10, 2008 A contemporary problem in data analysis is understanding the
Analysis of high dimensional data via Topology. Louis Xiang. Oak Ridge National Laboratory. Oak Ridge, Tennessee
Analysis of high dimensional data via Topology Louis Xiang Oak Ridge National Laboratory Oak Ridge, Tennessee Contents Abstract iii 1 Overview 1 2 Data Set 1 3 Simplicial Complex 5 4 Computation of homology
Periodic meshes for the CGAL library
Periodic meshes for the CGAL library Aymeric Pellé, Monique Teillaud To cite this version: Aymeric Pellé, Monique Teillaud. Periodic meshes for the CGAL library. International Meshing Roundtable, Oct 2014,
On the Local Behavior of Spaces of Natural Images
On the Local Behavior of Spaces of Natural Images Gunnar Carlsson Tigran Ishkhanov Vin de Silva Afra Zomorodian Abstract In this study we concentrate on qualitative topological analysis of the local behavior
arxiv: v1 [math.st] 11 Oct 2017
![arxiv: v1 [math.st] 11 Oct 2017](/thumbs/83/87139311.jpg "arxiv: v1 [math.st] 11 Oct 2017")
An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists Frédéric Chazal and Bertrand Michel October 12, 2017 arxiv:1710.04019v1 [math.st] 11 Oct 2017 Abstract
Western TDA Learning Seminar. June 7, 2018
The The Western TDA Learning Seminar Department of Mathematics Western University June 7, 2018 The The is an important tool used in TDA for data visualization. Input point cloud; filter function; covering
A fast and robust algorithm to count topologically persistent holes in noisy clouds
A fast and robust algorithm to count topologically persistent holes in noisy clouds Vitaliy Kurlin Durham University Department of Mathematical Sciences, Durham, DH1 3LE, United Kingdom vitaliy.kurlin@gmail.com,
PERSISTENT HOMOLOGY OF FINITE TOPOLOGICAL SPACES
PERSISTENT HOMOLOGY OF FINITE TOPOLOGICAL SPACES HANEY MAXWELL Abstract. We introduce homology and finite topological spaces. From the basis of that introduction, persistent homology is applied to finite
Classifying Spaces and Spectral Sequences
Classifying Spaces and Spectral Sequences Introduction Christian Carrick December 2, 2016 These are a set of expository notes I wrote in preparation for a talk given in the MIT Kan Seminar on December
Tutorial 3 Comparing Biological Shapes Patrice Koehl and Joel Hass
Tutorial 3 Comparing Biological Shapes Patrice Koehl and Joel Hass University of California, Davis, USA http://www.cs.ucdavis.edu/~koehl/ims2017/ What is a shape? A shape is a 2-manifold with a Riemannian
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
PyDEC: Software and Algorithms for Discretization of Exterior Calculus Nathan Bell 1 and Anil N. Hirani 2 1 NVIDIA Corporation, nbell@nvidia.com 2 Department of Computer Science, University of Illinois
Computational Topology in Reconstruction, Mesh Generation, and Data Analysis
Computational Topology in Reconstruction, Mesh Generation, and Data Analysis Tamal K. Dey Department of Computer Science and Engineering The Ohio State University Dey (2014) Computational Topology CCCG
Diffusion Maps and Topological Data Analysis
Diffusion Maps and Topological Data Analysis Melissa R. McGuirl McGuirl (Brown University) Diffusion Maps and Topological Data Analysis 1 / 19 Introduction OVERVIEW Topological Data Analysis The use of
Discrete Surfaces. David Gu. Tsinghua University. Tsinghua University. 1 Mathematics Science Center
Discrete Surfaces 1 1 Mathematics Science Center Tsinghua University Tsinghua University Discrete Surface Discrete Surfaces Acquired using 3D scanner. Discrete Surfaces Our group has developed high speed
Towards topological analysis of high-dimensional feature spaces.
Towards topological analysis of high-dimensional feature spaces. Hubert Wagner and Pawe l D lotko January 7, 2014 Abstract In this paper we present ideas from computational topology, applicable in analysis
Elements of Combinatorial Topology
Elements of Combinatorial Topology Companion slides for Distributed Computing Through Maurice Herlihy & Dmitry Kozlov & Sergio Rajsbaum 1 Road Map Simplicial Complexes Standard Constructions Carrier Maps
Lecture 7: Jan 31, Some definitions related to Simplical Complex. 7.2 Topological Equivalence and Homeomorphism
CS 6170 Computational Topology: Topological Data Analysis University of Utah Spring 2017 School of Computing Lecture 7: Jan 31, 2017 Lecturer: Prof. Bei Wang Scribe: Avani Sharma,
Computational Homology of cubical and permutahedral complexes
Computational Homology of cubical and permutahedral complexes by Fintan Hegarty School of Mathematics, Statistics, and Applied Mathematics Supervised by Prof. Graham Ellis SUBMITTED IN PARTIAL FULFILLMENT
Homology of Simplicial Complexes
Homology of Simplicial Complexes Math, David Perkinson Introduction. This is an introduction to the homology of simplicial complexes suitable for a first course in linear algebra. It uses little more than
Surface Reconstruction. Gianpaolo Palma
Surface Reconstruction Gianpaolo Palma Surface reconstruction Input Point cloud With or without normals Examples: multi-view stereo, union of range scan vertices Range scans Each scan is a triangular mesh
Building a coverage hole-free communication tree
Building a coverage hole-free communication tree Anaïs Vergne, Laurent Decreusefond, and Philippe Martins LTCI, Télécom ParisTech, Université Paris-Saclay, 75013, Paris, France arxiv:1802.08442v1 [cs.ni]
Exact discrete Morse functions on surfaces. To the memory of Professor Mircea-Eugen Craioveanu ( )
Stud. Univ. Babeş-Bolyai Math. 58(2013), No. 4, 469 476 Exact discrete Morse functions on surfaces Vasile Revnic To the memory of Professor Mircea-Eugen Craioveanu (1942-2012) Abstract. In this paper,
SimBa: An Efficient Tool for Approximating Rips-filtration Persistence via Simplicial Batch-collapse
SimBa: An Efficient Tool for Approximating Rips-filtration Persistence via Simplicial Batch-collapse Tamal K. Dey 1, Dayu Shi 2, and Yusu Wang 3 1 Dept. of Computer Science and Engineering, and Dept. of
25 HIGH-DIMENSIONAL TOPOLOGICAL DATA ANALYSIS
25 HIGH-DIMENSIONAL TOPOLOGICAL DATA ANALYSIS Frédéric Chazal INTRODUCTION Modern data often come as point clouds embedded in high-dimensional Euclidean spaces, or possibly more general metric spaces.
Persistent Homology Computation Using Combinatorial Map Simplification
Persistent Homology Computation Using Combinatorial Map Simplification Guillaume Damiand 1, Rocio Gonzalez-Diaz 2 1 CNRS, Université de Lyon, LIRIS, UMR5205, F-69622 France 2 Universidad de Sevilla, Dpto.
Brian Hamrick. October 26, 2009
Efficient Computation of Homology Groups of Simplicial Complexes Embedded in Euclidean Space TJHSST Senior Research Project Computer Systems Lab 2009-2010 Brian Hamrick October 26, 2009 1 Abstract Homology
Topological Data Analysis
Topological Data Analysis Deepak Choudhary(11234) and Samarth Bansal(11630) April 25, 2014 Contents 1 Introduction 2 2 Barcodes 2 2.1 Simplical Complexes.................................... 2 2.1.1 Representation
DISCRETE DIFFERENTIAL GEOMETRY: AN APPLIED INTRODUCTION Keenan Crane CMU /858B Fall 2017
DISCRETE DIFFERENTIAL GEOMETRY: AN APPLIED INTRODUCTION Keenan Crane CMU 15-458/858B Fall 2017 LECTURE 2: THE SIMPLICIAL COMPLEX DISCRETE DIFFERENTIAL GEOMETRY: AN APPLIED INTRODUCTION Keenan Crane CMU
Stability and Statistical properties of topological information inferred from metric data
Beijing, June 25, 2014 ICML workshop: Topological Methods for Machine Learning Stability and Statistical properties of topological information inferred from metric data Frédéric Chazal INRIA Saclay Introduction
4.2 Simplicial Homology Groups
4.2. SIMPLICIAL HOMOLOGY GROUPS 93 4.2 Simplicial Homology Groups 4.2.1 Simplicial Complexes Let p 0, p 1,... p k be k + 1 points in R n, with k n. We identify points in R n with the vectors that point
Parallel & scalable zig-zag persistent homology
Parallel & scalable zig-zag persistent homology Primoz Skraba Artificial Intelligence Laboratory Jozef Stefan Institute Ljubljana, Slovenia primoz.skraba@ijs.sl Mikael Vejdemo-Johansson School of Computer
Reflection groups 4. Mike Davis. May 19, Sao Paulo
Reflection groups 4 Mike Davis Sao Paulo May 19, 2014 https://people.math.osu.edu/davis.12/slides.html 1 2 Exotic fundamental gps Nonsmoothable aspherical manifolds 3 Let (W, S) be a Coxeter system. S
Mesh Generation. Jean-Daniel Boissonnat DataShape, INRIA
Mesh Generation Jean-Daniel Boissonnat DataShape, INRIA http://www-sop.inria.fr/datashape Algorithmic Geometry Mesh generation J-D. Boissonnat 1 / 27 Meshing surfaces and 3D domains visualization and graphics
Algebra II: Review Exercises
: Review Exercises These notes reflect material from our text, A First Course in Abstract Algebra, Seventh Edition, by John B. Fraleigh, published by Addison-Wesley, 2003. Chapter 7. Advanced Group Theory
Geometric Inference. 1 Introduction. Frédéric Chazal 1 and David Cohen-Steiner 2
Geometric Inference Frédéric Chazal 1 and David Cohen-Steiner 2 1 INRIA Futurs, 4 rue Jacques Monod - 91893 Orsay Cedex France frederic.chazal@inria.fr 2 INRIA Sophia-Antipolis, 2004 route des lucioles
arxiv: v1 [math.at] 24 Oct 2018
![arxiv: v1 [math.at] 24 Oct 2018](/thumbs/89/98880748.jpg "arxiv: v1 [math.at] 24 Oct 2018")
Tadas Temčinas 1 arxiv:1810.10136v1 [math.at] 24 Oct 2018 Abstract Topological data analysis (TDA) has been widely used to make progress on a number of problems. However, it seems that TDA application