Persistent homology: An introduction and a new text representation for natural language processing

IJCAI International Joint Conference on Artificial Intelligence

Volumn , Issue , 2013, Pages 1953-1959

  Zhu, Xiaojin ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FEATURE REPRESENTATION; MATHEMATICAL TOOLS; MULTI SCALE ANALYSIS; NATURAL LANGUAGE PROCESSING; PERSISTENT HOMOLOGY; TEXT REPRESENTATION; TOPOLOGICAL DATA ANALYSIS; TOPOLOGICAL STRUCTURE;

ALGORITHMS; NATURAL LANGUAGE PROCESSING SYSTEMS; SEMANTICS; TOPOLOGY;

ARTIFICIAL INTELLIGENCE;

EID: 84896062400     PISSN: 10450823     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (23)

1. Sivaraman Balakrishnan, Alessandro Rinaldo, Don Sheehy, Aarti Singh, and Larry A. Wasserman. Minimax rates for homology inference. In The fifteenth international conference on Artificial Intelligence and Statistics (AISTATS), pages 64-72, 2012.
2. Sivaraman Balakrishnan, Brittany Fasy, Fabrizio Lecci, Alessandro Rinaldo, Aarti Singh, and LarryWasserman. Statistical inference for persistent homology. In arXiv:1303.7117, 2013.
3. Gunnar Carlsson. Topology and data. Bulletin (New Series) of the American Mathematical Society, 46(2):255-308, 2009.
4. Moo K. Chung, Peter Bubenik, Peter T. Kim, Kim M. Dalton, and Richard J. Davidson. Persistence diagrams of cortical surface data. In Information Processing in Medical Imaging, pages 386-397, 2009.
5. Vin de Silva and Robert Ghrist. Coverage in sensor networks via persistent homology. Algebraic & Geometric Topology, 7:339-358, 2007.
6. Vin de Silva and Robert Ghrist. Homological sensor networks. Notices of the American Mathematical Society, 54, 2007.
7. H. Edelsbrunner and J. Harer. Persistent homology-a survey. In Twenty Years After, eds. J. E. Goodman, J. Pach and R. Pollack, AMS., 2007.
8. H. Edelsbrunner and J. Harer. Computational Topology: An Introduction. Applied mathematics. Amer Mathematical Society, 2010.
9. Daniel Freedman and Chao Chen. Algebraic topology for computer vision. In Sota R. Yoshida, editor, Computer Vision, chapter 5, pages 239-268. Nova Science Pub. Inc., 2011.
10. Jennifer Gamble and Giseon Heo. Exploring uses of persistent homology for statistical analysis of landmark-based shape data. J. Multivariate Analysis, 101(9):2184-2199, 2010.
11. P. Giblin. Graphs, Surfaces and Homology. Cambridge University Press, 2010.
12. Alan Gous. Spherical subfamily models. Technical report, 1999.
13. Keith Hall and Thomas Hofmann. Learning curved multinomial subfamilies for natural language processing and information retrieval. In ICML, pages 351-358, 2000.
14. Allen Hatcher. Algebraic Topology. Cambridge University Press, first edition, December 2001.
15. Peter M. Kasson, Afra Zomorodian, Sanghyun Park, Nina Singhal, Leonidas J. Guibas, and Vijay S. Pande. Persistent voids: a new structural metric for membrane fusion. Bioinformatics, 23(14):1753-1759, 2007.
16. Guy Lebanon, Yi Mao, and Joshua V. Dillon. The locally weighted bag of words framework for document representation. Journal of Machine Learning Research, 8:2405-2441, 2007.
17. Guy Lebanon. Sequential document representations and simplicial curves. In UAI. AUAI Press, 2006.
18. Günter Rote and Gert Vegter. Computational topology: an introduction. In Jean-Daniel Boissonnat and Monique Teillaud, editors, Effective Computational Geometry for Curves and Surfaces, Mathematics and Visualization, chapter 7, pages 277-312. Springer-Verlag, 2006.
19. G. Salton, editor. The SMART Retrieval System Experiments in Automatic Document Processing. Englewood Cliffs: Prentice-Hall, 1971.
20. Geoffrey R. Sampson. The structure of children's writing: moving from spoken to adult written norms. In S. Granger and S. Petch-Tyson, editors, Extending the Scope of Corpus-Based Research, pages 177-93. Rodopi, 2003. http://www.grsampson.net/RLucy.html.
21. Gurjeet Singh, Facundo Memoli, Tigran Ishkhanov, Guillermo Sapiro, Gunnar Carlsson, and Dario L. Ringach. Topological analysis of population activity in visual cortex. J. Vis., 8(8):1-18, 6 2008.
22. Andrew Tausz, Mikael Vejdemo-Johansson, and Henry Adams. Javaplex: A research software package for persistent (co)homology. Software available at http://code.google.com/javaplex, 2011.
23. A.J. Zomorodian. Computing and comprehending topology: persistence and hierarchical Morse complexes. PhD thesis, University of Illinois at Urbana-Champaign, 2001.