Multidimensional Interleavings and Applications to Topological Inference

Released on by Michael Phillip Lesnick
preview-18

  • Multidimensional Interleavings and Applications to Topological Inference Book Detail

  • Author : Michael Phillip Lesnick
  • Release Date : 2012
  • Publisher :
  • Genre :
  • Pages :
  • ISBN 13 :
  • File Size : 34,34 MB
DOWNLOAD BOOK

Multidimensional Interleavings and Applications to Topological Inference by Michael Phillip Lesnick PDF Summary

Book Description: This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at the (topological) level of filtrations rather than only at the (algebraic) level of persistent homology modules. Our main mathematical objects of study are interleavings. These are tools for quantifying the similarity between two multidimensional filtrations or persistence modules. They were introduced for 1-D filtrations and persistence modules by Chazal, Cohen-Steiner, Glisse, Guibas, and Oudot. We introduce generalizations of the definitions of interleavings given by Chazal et al. and use these to define pseudometrics, called interleaving distances, on multidimensional filtrations and multidimensional persistence modules. We present an in-depth study of interleavings and interleaving distances. We then use them to formulate and prove several multidimensional analogues of a topological inference theorem of Chazal, Guibas, Oudot, and Skraba. These results hold directly at the level of filtrations; they yield as corollaries corresponding results at the module level.

Disclaimer: www.yourbookbest.com does not own Multidimensional Interleavings and Applications to Topological Inference books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.

Topological Inference from Measures

Topological Inference from Measures

File Size : 11,11 MB
Total View : 8845 Views
DOWNLOAD

Massive amounts of data are now available for study. Asking questions that are both relevant and possible to answer is a difficult task. One can look for someth