Towards topological analysis of high-dimensional feature spaces

Computer Vision and Image Understanding

Volumn 121, Issue , 2014, Pages 21-26

  Wagner, Hubert ^a   Dłotko, Paweł ^a,b  

^a JAGIELLONIAN UNIVERSITY   (Poland)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Computational topology; Feature space; Persistent homology; Rips complex; Text mining

Indexed keywords

DATA MINING;

COMPUTATIONAL TOPOLOGY; FEATURE SPACE; PERSISTENT HOMOLOGY; RIPS COMPLEX; TEXT MINING;

TOPOLOGY;

EID: 84896955405     PISSN: 10773142     EISSN: 1090235X     Source Type: Journal    
DOI: 10.1016/j.cviu.2014.01.005     Document Type: Article

References (23)

1. U. Bauer, M. Kerber, J. Reininghaus, Clear and compress: computing persistent homology in chunks, in: TopoInVis, 2013.
2. S. Biasotti, A. Cerri, D. Giorgi, and M. Spagnuolo PHOG: photometric and geometric functions for textured shape retrieval Comput. Graph. Forum 32 5 2013 13 22
3. G. Carlson Topology and data Bullet. AMS 46 2 2009 255 308
4. A. Cerri, B. Di Fabio, M. Ferri, P. Frosini, and C. Landi Betti numbers in multidimensional persistent homology are stable functions Math. Meth. Appl. Sci. 36 2 2013 1099 1476
5. C. Chen, M. Kerber, Persistent homology computation with a twist, in: 27th European Workshop on Computational Geometry (EuroCG 2011), 2011.
6. F. Chazal, V. de Silva, S. Oudot, Persistence Stability for Geometric Complexes, 2012, arXiv:1207.3885v1.
7. D. Cohen-Steiner, H. Edelsbrunner, and J. Harer Stability of persistence diagrams Discrete Comput. Geom. 37 1 2007 103 120
8. H. Edelsbrunner, and J. Harer Computational Topology. An Introduction 2010 Amer. Math. Soc. Providence, Rhode Island
9. D. Eppstein, D. Strash, Listing All Maximal Cliques in Large Sparse Real-World Graphs, in: SEA 2011, 2011, arXiv:1103.0318.
10. A-X. Feng, C-H. Fu, X-L. Xu, A-F. Liu, H. Chang, D-R. He, G-L. Feng, An empirical investigation on important subgraphs in cooperation-competition networks, Science, 2011, arXiv:1105.1421.
11. R. Forman A user's guide to discrete morse theory Sminaire Lotharingien de Combinatoire B48c 2002 1 35
12. P. Jaccard The distribution of the flora in the alpine zone New Phytol. 11 1912 37 50
13. T. Lewiner, Geometric Discrete Morse Complexes, Ph.D. Thesis, 2005.
14. T. Lewiner, H. Lopes, and G. Tavares Toward optimality in discrete morse theory Experiment. Math. Volume 12 3 2003 271 286
15. X. Polanco, E.S. Juan, Text data network analysis using graph approach, in: Proceedings of InSciT, 2006, pp. 586-592.
16. V. Robins, P.J. Wood, A.P. Sheppard, Theory and algorithms for constructing discrete morse complexes from grayscale digital images, in: TPAMI 33, 2011, pp. 1646-1658.
17. G. Salton, A. Wong, and C.S. Yang A vector space model for automatic indexing Commun. ACM 18 11 1975 613 620
18. B. Scholkopf et al. Input space versus feature space in kernel-based methods IEEE Trans. Neural Network. 10 5 1999
19. V. de Silva, D. Morozov, and M. Vejdemo-Johansson Dualities in persistent (co)homology Inverse Prob. 27 2011 124003
20. A. Zomorodian Fast construction of the Vietoris-Rips complex Comput. Graph. 34 3 2010 263 271
21. H. Wagner, P. Dłotko, M. Mrozek, A computatinal topology in text mining, in: CTIC 2012, LNCS, vol. 7309, 2012, pp. 68-78.
22. English Wikipedia Corpus < http://dumps.wikimedia.org/enwiki/ >.
23. Gensim Library < http://radimrehurek.com/gensim/ >.