Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-05T21:42:51.616Z Has data issue: false hasContentIssue false

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
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
[8] A., Dick, Emmy Noether: 1882–1935. Boston: Birkhäuser, (1981), Translated by H. I., Blocher.
[9] D., Dummit and R., Foote, Abstract Algebra. Third edition. John Wiley & Sons, Inc., Hoboken, NJ, 2004.
[10] H., Edelsbrunner, D., Letscher, and A., Zomorodian, Topological persistence and simplification. Discrete and Computational Geometry, 28, 511–533, 2002.Google Scholar
[11] S., Eilenberg, Singular homology theory. Ann. of Math. 45, 407–447, 1944.Google Scholar
[12] R., Gibbs et al, The international HapMap project. Nature, 426, 789–796, 2003.
[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.
[17] R., Miller, Discussion - projection pursuit. Ann. Statistics 13, 510–513, 1985.Google Scholar
[18] J., Munkres, Topology: A First Course. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975.
[19] M., Nicolau, R., Tibshirani, A.-L., Børresen-Dale and S., JeffreyDisease-specific genomic analysis: Identifying the signature of pathologic biology. Bioinformatics, 23, 957–965, 2007.Google Scholar
[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.
[22] G., Singh, F., Memoli, T., Ishkhanov, G., Sapiro, G., Carlsson and D., Ringach, Topological structure of population activity in primary visual cortex. Journal of Vision, 8, 1–18, 2008.Google Scholar
[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
[24] Y., Yao, J., Sun, S., Huang, G., Bowman, G., Singh, M., Lesnick, L., Guibas, V., Pande and G., Carlsson, Topological methods for exploring low-density states in biomolecular folding pathways. Journal of Chemical Physics, 130, 144115, 2009.Google Scholar
[25] A., Zomorodian and G., Carlsson, Computing persistent homology. Discrete and Computational Geometry, 33, 249–274, 2005.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • 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 Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • 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

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • 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
×