JPlex Software Demonstration. AMS Short Course on Computational Topology New Orleans Jan 4, 2011 Henry Adams Stanford University
|
|
|
- Rosalyn Tate
- 5 years ago
- Views:
Transcription
1 JPlex Software Demonstration AMS Short Course on Computational Topology New Orleans Jan 4, 2011 Henry Adams Stanford University
2 What does JPlex do? Input: a filtered simplicial complex or finite metric space Output: a Betti barcode describing the persistent homology over Z p
3 What does JPlex do? Input: a filtered simplicial complex or finite metric space Output: a Betti barcode describing the persistent homology over Z p Java software Matlab or standalone interface By Harlan Sexton and Mikael Vejdemo-Johansson. Previous version by Vin de Silva and Patrick Perry Algorithm from Computing Persistent Homology by Afra Zomorodian and Gunnar Carlsson (2005)
4 Getting started Download from
5 Download from Javadoc (follow links) Getting started
6 Getting started Download from Javadoc (follow links) Tutorials: toy examples, exercises, real data 3.3. Subclass ExplicitStream and persistent homology. Let s build a stream with nontrivial filtration times. We build a house, with the square appearing at time 0, the top vertex at time 1, the roof edges at times 2 and 3, and the roof 2-simplex at time 7. >> house=explicitstream; >> house.add([1;2;3;4;5], [0;0;0;0;1]) >> house.add([1,2;2,3;3,4;4,1;3,5;4,5], [0;0;0;0;2;3]) >> house.add([3,4,5], 7) We compute the Betti intervals. >> house.close >> intervals=plex.persistence.computeintervals(house); There are four intervals.
7 There exist other options besides JPlex: CHomP CGAL Dionysus
8 1. Toy filtration Four JPlex examples % % % % &'(') &'('! &'('" &'(' &'('*
9 1. Toy filtration Four JPlex examples % % % % &'(') &'('! &'('" &'(' &'('* house = ExplicitStream; house.add([1;2;3;4;5], [0;0;0;0;1]) house.add([1,2; 2,3; 3,4; 4,1; 3,5; 4,5], [0;0;0;0;2;3]) house.add([3,4,5], 7) house.close intervals = Plex.Persistence.computeIntervals(house); Plex.plot(intervals, 'Barcode plot', 8)
10 1. Toy filtration Four JPlex examples % % % % &'(') &'('! &'('" &'(' &'('*
11 Four JPlex examples 2. Vietoris-Rips filtration on torus
12 Four JPlex examples 2. Vietoris-Rips filtration on torus points = pointstorus(20); size(points) % 400 by 4 pdata = EuclideanArrayData(points); rips = Plex.RipsStream(0.001, 3, 0.9, pdata); intervals = Plex.Persistence.computeIntervals(rips); Plex.plot(intervals, 'Barcode plot', 0.9)
13 Four JPlex examples 2. Vietoris-Rips filtration on torus
14 Four JPlex examples 2. Vietoris-Rips filtration on torus
15 Four JPlex examples 2. Vietoris-Rips filtration on torus
16 3. Witness filtration on torus Four JPlex examples
17 3. Witness filtration on torus Four JPlex examples points = pointstorus(100); pdata = EuclideanArrayData(points); L = maxminlandmarks(points, 50, 'e'); witness = Plex.LazyWitnessStream(0.001, 3, 0.4, 1, L, pdata); intervals = Plex.Persistence.computeIntervals(witness); Plex.plot(intervals, 'Barcode plot', 0.4)
18 3. Witness filtration on torus Four JPlex examples
19 3. Witness filtration on torus Four JPlex examples rips.size % 83,175 simplices witness.size % 3,047 simplices The witness complex has many fewer simplices than the Vietoris- Rips complex (not surprisingly so, as it has only 50 0-simplices).
20 Four JPlex examples 4. Three circle model from natural images
21 Four JPlex examples 4. Three circle model from natural images load pointsnatural plot(pointsnatural(:,1), pointsnatural(:,2), '.'), axis equal
22 Four JPlex examples 4. Three circle model from natural images load pointsnatural plot(pointsnatural(:,1), pointsnatural(:,2), '.'), axis equal !0.2!0.4!0.6!0.8!1!
23 Four JPlex examples 4. Three circle model from natural images pdata = EuclideanArrayData(pointsNatural); L = maxminlandmarks(pointsnatural, 50, 'e'); witness = Plex.LazyWitnessStream(0.001, 3, 0.15, 1, L, pdata); intervals = Plex.Persistence.computeIntervals(witness); Plex.plot(intervals, 'Barcode plot', 0.15)
24 Four JPlex examples 4. Three circle model from natural images pdata = EuclideanArrayData(pointsNatural); L = maxminlandmarks(pointsnatural, 50, 'e'); witness = Plex.LazyWitnessStream(0.001, 3, 0.15, 1, L, pdata); intervals = Plex.Persistence.computeIntervals(witness); Plex.plot(intervals, 'Barcode plot', 0.15)
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
JPlex with BeanShell Tutorial
JPlex with BeanShell Tutorial Henry Adams henry.adams@colostate.edu December 26, 2011 NOTE: As of 2011, JPlex is being phased out in favor of the software package Javaplex, which is also written in Java
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
S 1 S 3 S 5 S 7. Homotopy type of VR(S 1,r) as scale r increases
Research Statement, 2016 Henry Adams (adams@math.colostate.edu) I am interested in computational topology and geometry, combinatorial topology, and topology applied to data analysis and to sensor networks.
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
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
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
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
On the Nonlinear Statistics of Range Image Patches
SIAM J. IMAGING SCIENCES Vol. 2, No. 1, pp. 11 117 c 29 Society for Industrial and Applied Mathematics On the Nonlinear Statistics of Range Image Patches Henry Adams and Gunnar Carlsson Abstract. In [A.
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
An Analysis of Spaces of Range Image Small Patches
Send Orders for Reprints to reprints@benthamscience.ae The Open Cybernetics & Systemics Journal, 2015, 9, 275-279 275 An Analysis of Spaces of Range Image Small Patches Open Access Qingli Yin 1,* and Wen
Topology and the Analysis of High-Dimensional Data
Topology and the Analysis of High-Dimensional Data Workshop on Algorithms for Modern Massive Data Sets June 23, 2006 Stanford Gunnar Carlsson Department of Mathematics Stanford University Stanford, California
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
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
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
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
Finding Holes in Data
Finding Holes in Data Leonid Pekelis Stat 208 June 18th, 2009 Abstract Attempts are made to employ persistent homology to infer topological properties of point cloud data. Two potential approaches are
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
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
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
On the Topology of Finite Metric Spaces
On the Topology of Finite Metric Spaces Meeting in Honor of Tom Goodwillie Dubrovnik Gunnar Carlsson, Stanford University June 27, 2014 Data has shape The shape matters Shape of Data Regression Shape of
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
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,
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
What will be new in GUDHI library version 2.0.0
What will be new in GUDHI library version 2.0.0 Jean-Daniel Boissonnat, Paweł Dłotko, Marc Glisse, François Godi, Clément Jamin, Siargey Kachanovich, Clément Maria, Vincent Rouvreau and David Salinas DataShape,
Applied Topology. Instructor: Sara Kališnik Verovšek. Office Hours: Room 304, Tu/Th 4-5 pm or by appointment.
Applied Topology Instructor: Sara Kališnik Verovšek Office Hours: Room 304, Tu/Th 4-5 pm or by appointment. Textbooks We will not follow a single textbook for the entire course. For point-set topology,
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,
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
Computational Topology in Neuroscience
Computational Topology in Neuroscience Bernadette Stolz Lincoln College University of Oxford A dissertation submitted for the degree of Master of Science in Mathematical Modelling & Scientific Computing
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]
Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data
Libraries Conference on Applied Statistics in Agriculture 2015-27th Annual Conference Proceedings Statistical Methods in Topological Data Analysis for Complex, High-Dimensional Data Patrick S. Medina Purdue
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
Open Problems Column Edited by William Gasarch
Open Problems Column Edited by William Gasarch 1 This Issues Column! This issue s Open Problem Column is by Brittany Terese Fasy and Bei Wang and is on Open Problems in Computational Topology; however,
Computing the Betti Numbers of Arrangements. Saugata Basu School of Mathematics & College of Computing Georgia Institute of Technology.
1 Computing the Betti Numbers of Arrangements Saugata Basu School of Mathematics & College of Computing Georgia Institute of Technology. 2 Arrangements in Computational Geometry An arrangement in R k is
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
arxiv: v1 [cs.ir] 27 Sep 2018
![arxiv: v1 [cs.ir] 27 Sep 2018](/thumbs/87/96043794.jpg "arxiv: v1 [cs.ir] 27 Sep 2018")
A SHORT SURVEY OF TOPOLOGICAL DATA ANALYSIS IN TIME SERIES AND SYSTEMS ANALYSIS A PREPRINT arxiv:1809.10745v1 [cs.ir] 27 Sep 2018 Shafie Gholizadeh Department of Computer Science University of North Carolina
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
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
PSB Workshop Big Island of Hawaii Jan.4-8, 2015
PSB Workshop Big Island of Hawaii Jan.4-8, 2015 Part I Persistent homology & applications Part II TDA & applications Motivating problem from microbiology Algebraic Topology 2 Examples of applications
On the Local Behavior of Spaces of Natural Images
Int J Comput Vis (2008) 76: 1 12 DOI 10.1007/s11263-007-0056-x POSITION PAPER On the Local Behavior of Spaces of Natural Images Gunnar Carlsson Tigran Ishkhanov Vin de Silva Afra Zomorodian Received: 19
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
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
arxiv: v1 [cs.it] 10 May 2016
![arxiv: v1 [cs.it] 10 May 2016](/thumbs/93/112959514.jpg "arxiv: v1 [cs.it] 10 May 2016")
Separating Topological Noise from Features using Persistent Entropy Nieves Atienza 1, Rocio Gonzalez-Diaz 1, and Matteo Rucco 2 arxiv:1605.02885v1 [cs.it] 10 May 2016 1 Applied Math Department, School
COMPUTATIONAL TOPOLOGY TO MONITOR HUMAN OCCUPANCY. Institute of Information Science and Technologies - CNR, Via G. Moruzzi 1, Pisa, ITALY
COMPUTATIONAL TOPOLOGY TO MONITOR HUMAN OCCUPANCY Paolo Barsocchi, Pietro Cassará, Daniela Giorgi, Davide Moroni, Maria Antonietta Pascali Institute of Information Science and Technologies - CNR, Via G.
Persistent Homology for Defect Detection in Non-Destructive Evaluation of Materials
More Info at Open Access Database www.ndt.net/?id=18663 Persistent Homology for Defect Detection in Non-Destructive Evaluation of Materials Jose F. CUENCA 1, Armin ISKE 1 1 Department of Mathematics, University
Computing the k-coverage of a wireless network
Computing the k-coverage of a wireless network Anaïs Vergne, Laurent Decreusefond, and Philippe Martins LTCI, Télécom ParisTech, Université Paris-Saclay, 75013, Paris, France arxiv:1901.00375v1 [cs.ni]
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
Topology and Data. Gunnar Carlsson Department of Mathematics, Stanford University Stanford, California October 2, 2008
Topology and Data Gunnar Carlsson Department of Mathematics, Stanford University Stanford, California 94305 October 2, 2008 1 Introduction An important feature of modern science and engineering is that
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
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
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
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
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)
Persistent Homology of Directed Networks
Persistent Homology of Directed Networks Samir Chowdhury and Facundo Mémoli Abstract While persistent homology has been successfully used to provide topological summaries of point cloud data, the question
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
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
A Multicover Nerve for Geometric Inference
A Multicover Nerve for Geometric Inference Donald R. Sheehy Abstract We show that filtering the barycentric decomposition of a Čech complex by the cardinality of the vertices captures precisely the topology
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
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
Geometric Data. Goal: describe the structure of the geometry underlying the data, for interpretation or summary
Geometric Data - ma recherche s inscrit dans le contexte de l analyse exploratoire des donnees, dont l obj Input: point cloud equipped with a metric or (dis-)similarity measure data point image/patch,
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,
Cohomological Learning of Periodic Motion
AAECC manuscript No. (will be inserted by the editor) Cohomological Learning of Periodic Motion Mikael Vejdemo-Johansson Florian T. Pokorny Primoz Skraba Danica Kragic 3 January 2014 Abstract This work
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
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
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
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
Topology and fmri Data
Topology and fmri Data Adam Jaeger Statistical and Applied Mathematical Sciences Institute & Duke University May 5, 2016 fmri and Classical Methodology Most statistical analyses examine data with a variable
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
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
On Topological Data Mining
On Topological Data Mining Andreas Holzinger 1,2 1 Research Unit Human-Computer Interaction, Institute for Medical Informatics, Statistics & Documentation, Medical University Graz, Austria a.holzinger@hci4all.at
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
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,
QUANTIFYING HOMOLOGY CLASSES
QUANTIFYING HOMOLOGY CLASSES CHAO CHEN 1 AND DANIEL FREEDMAN 1 1 Rensselaer Polytechnic Institute, 110 8th street, Troy, NY 12180, U.S.A. E-mail address, {C. Chen, D. Freedman}: {chenc3,freedman}@cs.rpi.edu
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
THE BASIC THEORY OF PERSISTENT HOMOLOGY
THE BASIC THEORY OF PERSISTENT HOMOLOGY KAIRUI GLEN WANG Abstract Persistent homology has widespread applications in computer vision and image analysis This paper first motivates the use of persistent
Topological Data Analysis (Spring 2018) Persistence Landscapes
Topological Data Analysis (Spring 2018) Persistence Landscapes Instructor: Mehmet Aktas March 27, 2018 1 / 27 Instructor: Mehmet Aktas Persistence Landscapes Reference This presentation is inspired by
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
arxiv: v2 [math.at] 28 Oct 2017
![arxiv: v2 [math.at] 28 Oct 2017](/thumbs/71/65798657.jpg "arxiv: v2 [math.at] 28 Oct 2017")
Noname manuscript No. (will be inserted by the editor) Weighted Persistent Homology Shiquan Ren Chengyuan Wu Jie Wu arxiv:1708.06722v2 [math.at] 28 Oct 2017 Received: date / Accepted: date Abstract In
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
DNS Tunneling Detection
DNS Tunneling Detection Yakov Bubnov 1 1 Department of Electronic Computing Machines, Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus Abstract This paper surveys the problems,
Persistent Homology for Characterizing Stimuli Response in the Primary Visual Cortex
Persistent Homology for Characterizing Stimuli Response in the Primary Visual Cortex Avani Wildani Tatyana O. Sharpee (PI) ICML Topology 6/25/2014 The big questions - How do we turn sensory stimuli into
Multivariate Data Analysis Using Persistence-Based Filtering and Topological Signatures
Multivariate Data Analysis Using Persistence-Based Filtering and Topological Signatures Bastian Rieck, Student Member, IEEE, Hubert Mara, and Heike Leitte, Member, IEEE Fig. 1. Analysis of a cuneiform
TOPOLOGY AND DATA GUNNAR CARLSSON. Received by the editors August 1, Research supported in part by DARPA HR and NSF DMS
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 46, Number 2, April 2009, Pages 255 308 S0273-0979(09)01249-X Article electronically published on January 29, 2009 TOPOLOGY AND DATA GUNNAR
6.2 Classification of Closed Surfaces
Table 6.1: A polygon diagram 6.1.2 Second Proof: Compactifying Teichmuller Space 6.2 Classification of Closed Surfaces We saw that each surface has a triangulation. Compact surfaces have finite triangulations.
BARCODES: THE PERSISTENT TOPOLOGY OF DATA
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 45, Number 1, January 2008, Pages 61 75 S 0273-0979(07)01191-3 Article electronically published on October 26, 2007 BARCODES: THE PERSISTENT
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
Persistent Homology and Machine Learning. 1 Introduction. 2 Simplicial complexes
Informatica 42 (2018) 253 258 253 Persistent Homology and Machine Learning Primož Škraba Artificial Intelligence Laboatory, Jozef Stefan Institute E-mail: primoz.skraba@ijs.si Keywords: persistent homology,
Edge selection preserving the topological features of brain network
Edge selection preserving the topological features of brain network Presented During: 665 MT: Edge selection preserving the topological features of brain network Presented During: O-M4: Resting State Networks
Persistence Terrace for Topological Inference of Point Cloud Data
Persistence Terrace for Topological Inference of Point Cloud Data Chul Moon 1, Noah Giansiracusa 2, and Nicole A. Lazar 1 arxiv:1705.02037v2 [stat.me] 23 Dec 2017 1 University of Georgia 2 Swarthmore College
Namita Lokare, Daniel Benavides, Sahil Juneja and Edgar Lobaton
#analyticsx HIERARCHICAL ACTIVITY CLUSTERING ANALYSIS FOR ROBUST GRAPHICAL STRUCTURE RECOVERY ABSTRACT We propose a hierarchical activity clustering methodology, which incorporates the use of topological
Random Simplicial Complexes
Random Simplicial Complexes Duke University CAT-School 2015 Oxford 10/9/2015 Part III Extensions & Applications Contents Morse Theory for the Distance Function Persistent Homology and Maximal Cycles Contents
Persistent homology in TDA
Barcelona, June, 2016 Persistent homology in TDA Frédéric Chazal and Bertrand Michel Persistent homology R X topological space f : X R X persistence Persistence diagram Nested spaces A general mathematical
Branching and Circular Features in High Dimensional Data
Branching and Circular Features in High Dimensional Data Bei Wang, Brian Summa, Valerio Pascucci, Member, IEEE, and Mikael Vejdemo-Johansson Fig. 1. Given point cloud data in high-dimensional space, we
The Topological Data Analysis of Time Series Failure Data in Software Evolution
The Topological Data Analysis of Time Series Failure Data in Software Evolution Joao Pita Costa Institute Jozef Stefan joao.pitacosta@ijs.si Tihana Galinac Grbac Faculty of Engineering University of Rijeka
Topological Data Analysis and Fingerprint Classification
Topological Data Analysis and Fingerprint Classification Richard Avelar - University of Texas Jayshawn Cooper - Morgan State University Advisors: Dr. Konstantin Mischaikow Rachel Levanger Rutgers University
Topology: Basic ideas
For I will give you a mouth and wisdom, which all your adversaries shall not be able to gainsay nor resist. Topology: Basic ideas Yuri Dabaghian Baylor College of Medicine & Rice University dabaghian at
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.
2516 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 10, OCTOBER 2010
2516 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 10, OCTOBER 2010 A Distributed Topological Camera Network Representation for Tracking Applications Edgar Lobaton, Member, IEEE, Ramanarayan Vasudevan,
Persistent Homology and Nested Dissection
Persistent Homology and Nested Dissection Michael Kerber Donald R. Sheehy Primoz Skraba Abstract Nested dissection exploits the underlying topology to do matrix reductions while persistent homology exploits
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