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Paul L Bendich, Assistant Research Professor

I work in computational topology, which for me means adapting and using tools from algebraic topology in order to study noisy and high-dimensional datasets arising from a variety of scientific applications. My thesis research involved the analysis of datasets for which the number of degrees of freedom varies across the parameter space. The main tools are local homology and intersection homology, suitably redefined in this fuzzy multi-scale context. I am also working on building connections between computational topology and various statistical data analysis algorithms, such as clustering or manifold learning, as well as building connections between computational topology and diffusion geometry.

Contact Info:
Office Location:  121
Office Phone:  (919) 660-2811
Email Address: send me a message
Web Page:  http://www.paulbendich.com

Teaching (Fall 2016):

  • MATH 465.01, INTRO HIGH DIM DATA ANALYSIS Synopsis
    Gross Hall 304B, TuTh 08:30 AM-09:45 AM
    (also cross-listed as COMPSCI 445.01)
Office Hours:

Monday, 11 AM - Noon, Math 210

Friday, 11:45 - 1 PM Gross Hall 327
Education:

Ph.D.Duke University2008
Specialties:

Topology
Applied Math
Research Interests:

I work in computational topology, which for me means adapting and using tools from algebraic topology in order to study noisy and high-dimensional datasets arising from a variety of scientific applications. My thesis research involved the analysis of datasets for which the number of degrees of freedom varies across the parameter space. The main tools are local homology and intersection homology, suitably redefined in this fuzzy multi-scale context. I am also working on building connections between computational topology and various statistical data analysis algorithms, such as clustering or manifold learning, as well as building connections between computational topology and diffusion geometry.

Undergraduate Research Supervised

  • Marshall Ratliff (2014/08-present)
    Data RTG Topology for Music and Brains Program, and Research Independent Study (Cover Trees for Jazz Data) 
  • Derrick Nowak (2014/08-present)
    Data RTG Topology for Music and Brains Program 
  • Carmen Cox (2014/08-present)
    Data RTG Topology for Music and Brains Program 
  • Alex Pieloch (2014/08-present)
    Data RTG Topology for Music and Brains Program 
  • Aaron Park (2014/08-present)
    co-mentored with Ezra Miller 
  • Bingxi Lin (May, 2013 - July, 2013)
    Data RTG REU program on Multi-Scale Topology for Signals and Images 
  • Michael Ogez (May, 2013 - July, 2013)
    Data RTG REU program on Multi-Scale Topology for Signals and Images 
  • Ben Dreyzen (May, 2013 - July, 2013)
    Data RTG REU program on Multi-Scale Topology for Signals and Images 
  • Bryan Jacobson (2012 - 2014)  
Recent Publications   (More Publications)

  1. P Bendich, JS Marron, E Miller, A Pieloch and S Skwerer, Persistent homology analysis of brain artery trees, The Annals of Applied Statistics, vol. 10 no. 1 (March, Accepted, 2016), pp. 198-218, ISSN 1932-6157 (to appear.) [repository], [doi]  [abs]
  2. Paul Bendich, Ellen Gasparovic, John Harer, and Christopher J. Tralie, Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology (Submitted, 2016) [1602.06245]
  3. P Bendich, E Gasparovic, J Harer, R Izmailov and L Ness, Multi-scale local shape analysis and feature selection in machine learning applications, Proceedings of the International Joint Conference on Neural Networks, vol. 2015-September (September, 2015), pp. 1-8 [arXiv:1410.3169], [repository], [doi]  [abs]
  4. Paul Bendich and Peter Bubenik, Stabilizing the output of persistent homology computations, Proc. 2016 Symposium on Computational Geometry (Submitted, 2015) [1512.01700]
  5. Paul Bendich, Sang Chin ,Jesse Clarke, Jonathan DeSena, John Harer, Liz Munch , Andrew Newman , David Porter, David Rouse, Nate Strawn, and Adam Watkins., Topological and Statistical Behavior Classifiers for Tracking Applications, IEEE Transactions on Aerospace and Electronic Systems (Accepted, 2015)
Recent Grant Support

  • BIGDATA: F: DKA: CSD: Topological Data Analysis and Machine-Learning with Community-Accepted Features, National Science Foundation, IIS-1447491, 2014/09-2018/08.      
  • Collaborative Research: Statistical inference for stratified spaces and persistent homology, National Science Foundation, DMS-1361208, 2014/07-2017/06.      
Conferences Organized

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320