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2 - The Shape of Data

Published online by Cambridge University Press:  05 December 2012

G. Carlsson
Affiliation:
Stanford University
Felipe Cucker
Affiliation:
City University of Hong Kong
Teresa Krick
Affiliation:
Universidad de Buenos Aires, Argentina
Allan Pinkus
Affiliation:
Technion - Israel Institute of Technology, Haifa
Agnes Szanto
Affiliation:
North Carolina State University
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Publisher: Cambridge University Press
Print publication year: 2012

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References

[1] H., Adams and G., Carlsson, On the non-linear statistics of range image patches. SIAM Journal on Imaging Sciences 2, 110–117, 2009.Google Scholar
[2] G. R., Bowman, X., Huang, Y., Yao, J., Sun, G., Carlsson, L. J., Guibas and V.S., Pande, Structural insight into RNA hairpin folding intermediates. J. Amer. Chemical Soc. Comm., 130, 9676–9678, 2008.Google Scholar
[3] G., Carlsson, Topology and data. Bull. Amer. Math. Soc., 46, 255–308, 2009.Google Scholar
[4] G., Carlsson, T., Ishkanov, V., de Silva and A., Zomorodian, On the local behavior of spaces of natural images. International Journal of Computer Vision, 76, 1–12, 2008.Google Scholar
[5] G., Carlsson and A., Zomorodian, The theory of multidimensional persistence. Discrete & Computational Geometry, 42, 71–93, 2009.Google Scholar
[6] G., Carlsson, G., Singh and A., Zomorodian, Computing multidimensional persistence. in Algorithms and Computation, Lecture Notes in Computer Science, 5878, 730–739, 2009.
[7] F., Chazal, D., Cohen-Steiner, L., Guibas, F., Mémoli and S., Oudot, Gromov-Hausdorff stable signatures for shapes using persistence. Computer Graphics Forum, 28, 1393–1403, (2009).Google Scholar
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[10] H., Edelsbrunner, D., Letscher, and A., Zomorodian, Topological persistence and simplification. Discrete and Computational Geometry, 28, 511–533, 2002.Google Scholar
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[13] M., Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces. Progress in Mathematics, vol. 152. Birkhäuser Boston Inc., Boston, MA, 1999.
[14] J., Hartigan, Clustering Algorithms. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York-London-Sydney, 1975.
[15] A., Hatcher, Algebraic Topology. Cambridge University Press, Cambridge, 2002.
[16] R., MacPherson and B., Schweinhart, Measuring shape with topology. arXiv:1011.2258v2, 2010.
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[20] M., Nicolau, A., Levine and G., Carlsson, Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival. Proc. National Acad. Sciences, 108, 7265–7270, 2011.Google Scholar
[21] G., Singh, F., Memoli and G., Carlsson, Topological methods for the analysis of high dimensional data sets and 3D object recognition. Point Based Graphics 2007, Prague, September 2007.
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[23] M., van de Vijver et al. A gene-expression signature as a predictor of survival in breast cancer. New Engl. J. Med., 347, 1999–2009, 2002.Google Scholar
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  • The Shape of Data
  • Edited by Felipe Cucker, City University of Hong Kong, Teresa Krick, Universidad de Buenos Aires, Argentina, Allan Pinkus, Technion - Israel Institute of Technology, Haifa, Agnes Szanto, North Carolina State University
  • Book: Foundations of Computational Mathematics, Budapest 2011
  • Online publication: 05 December 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139095402.003
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  • The Shape of Data
  • Edited by Felipe Cucker, City University of Hong Kong, Teresa Krick, Universidad de Buenos Aires, Argentina, Allan Pinkus, Technion - Israel Institute of Technology, Haifa, Agnes Szanto, North Carolina State University
  • Book: Foundations of Computational Mathematics, Budapest 2011
  • Online publication: 05 December 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139095402.003
Available formats
×

Save book to Google Drive

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  • The Shape of Data
  • Edited by Felipe Cucker, City University of Hong Kong, Teresa Krick, Universidad de Buenos Aires, Argentina, Allan Pinkus, Technion - Israel Institute of Technology, Haifa, Agnes Szanto, North Carolina State University
  • Book: Foundations of Computational Mathematics, Budapest 2011
  • Online publication: 05 December 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139095402.003
Available formats
×