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Volumn 9, Issue , 2015, Pages 1173-1204

Probabilistic Fréchet means for time varying persistence diagrams

Author keywords

Fr chet mean; Time varying data; Topological data analysis

Indexed keywords


EID: 84937862578     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/15-EJS1030     Document Type: Article
Times cited : (61)

References (30)
  • 2
    • 2442519215 scopus 로고    scopus 로고
    • Interface surfaces for protein-protein complexes. In Proceedings of the Eighth Annual International Conference on Resaerch in Computational Molecular Biology
    • ACM, New York, NY, USA
    • Ban, Y.-E. A., Edelsbrunner, H. and Rudolph, J. (2004). Interface surfaces for protein-protein complexes. In Proceedings of the Eighth Annual International Conference on Resaerch in Computational Molecular Biology. RECOMB'04 205-212. ACM, New York, NY, USA. DOI:10. 1145/974614. 974642.
    • (2004) RECOMB'04 , pp. 205-212
    • Ban, Y.-E.A.1    Edelsbrunner, H.2    Rudolph, J.3
  • 3
    • 84937925234 scopus 로고    scopus 로고
    • Persistent homology for metric measure spaces, and robust statistics for hypothesis testing and confidence intervals
    • Blumberg, A. J., Gal, I., Mandell, M. A. and Pancia, M. (2012). Persistent homology for metric measure spaces, and robust statistics for hypothesis testing and confidence intervals. arXiv:1206. 4581.
    • (2012) arXiv:1206. 4581
    • Blumberg, A.J.1    Gal, I.2    Mandell, M.A.3    Pancia, M.4
  • 4
  • 7
    • 70849097151 scopus 로고    scopus 로고
    • Proximity of persistence modules and their diagrams. In Proceedings of the 25th Annual Symposium on Computational Geometry
    • ACM, New York, NY, USA
    • Chazal, F., Cohen-Steiner, D., Glisse, M., Guibas, L. J. and Oudot, S. Y. (2009). Proximity of persistence modules and their diagrams. In Proceedings of the 25th Annual Symposium on Computational Geometry. SCG'09 237-246. ACM, New York, NY, USA. DOI:10. 1145/1542362. 1542407.
    • (2009) SCG'09 , pp. 237-246
    • Chazal, F.1    Cohen-Steiner, D.2    Glisse, M.3    Guibas, L.J.4    Oudot, S.Y.5
  • 8
    • 84937848530 scopus 로고    scopus 로고
    • Optimal rates of convergence for persistence diagrams in topological data analysis
    • Chazal, F., Glisse, M., Labruere, C. and Michel, B. (2013). Optimal rates of convergence for persistence diagrams in topological data analysis. arXiv:1305. 6239.
    • (2013) arXiv:1305. 6239
    • Chazal, F.1    Glisse, M.2    Labruere, C.3    Michel, B.4
  • 9
    • 33846839317 scopus 로고    scopus 로고
    • Stability of persistence diagrams
    • MR2279866
    • Cohen-Steiner, D., Edelsbrunner, H. and Harer, J. (2007). Stability of persistence diagrams. Discrete Comput. Geom. 37 103-120. DOI:10. 1007/s00454-006-1276-5. MR2279866
    • (2007) Discrete Comput. Geom , vol.37 , pp. 103-120
    • Cohen-Steiner, D.1    Edelsbrunner, H.2    Harer, J.3
  • 11
    • 84866088345 scopus 로고    scopus 로고
    • A topological paradigm for hippocampal spatial map formation using persistent homology
    • Dabaghian, Y., Mémoli, F., Frank, L. and Carlsson., G. (2012). A topological paradigm for hippocampal spatial map formation using persistent homology. PLoS Comput. Biol. 8 e1002581. DOI:10. 1371/journal. pcbi. 1002581.
    • (2012) PLoS Comput. Biol , vol.8
    • Dabaghian, Y.1    Mémoli, F.2    Frank, L.3    Carlsson, G.4
  • 12
    • 84937851564 scopus 로고    scopus 로고
    • SW1PerS: SlidingWindows and 1-Persistence Scoring: Discovering Periodicity in Gene Expression Time Series Data
    • Deckard, A., Perea, J. A., Harer, J. and Haase, S. (2013). SW1PerS: SlidingWindows and 1-Persistence Scoring: Discovering Periodicity in Gene Expression Time Series Data. Preprint.
    • (2013) Preprint
    • Deckard, A.1    Perea, J.A.2    Harer, J.3    Haase, S.4
  • 14
    • 70349220130 scopus 로고    scopus 로고
    • Surveys on discrete and computational geometry: Twenty years later. American Mathematical Society, Providence, RI. MR2405684
    • Edelsbrunner, H. and Harer, J. (2008). Persistent Homology-A Survey. Surveys on discrete and computational geometry: Twenty years later, 257-282. American Mathematical Society, Providence, RI. MR2405684
    • (2008) Persistent Homology-A Survey , pp. 257-282
    • Edelsbrunner, H.1    Harer, J.2
  • 15
    • 0038376464 scopus 로고    scopus 로고
    • Morse-smale complexes for piecewise linear 3-manifolds. In Proceedings of the Nineteenth Annual Symposium on Computational Geometry
    • ACM, New York, NY, USA
    • Edelsbrunner, H., Harer, J., Natarajan, V. and Pascucci, V. (2003). Morse-smale complexes for piecewise linear 3-manifolds. In Proceedings of the Nineteenth Annual Symposium on Computational Geometry. SCG'03 361-370. ACM, New York, NY, USA. DOI:10. 1145/777792. 777846.
    • (2003) SCG'03 , pp. 361-370
    • Edelsbrunner, H.1    Harer, J.2    Natarajan, V.3    Pascucci, V.4
  • 19
    • 77955050585 scopus 로고    scopus 로고
    • Exploring uses of persistent homology for statistical analysis of landmark-based shape data
    • MR2671209
    • Gamble, J. and Heo, G. (2010). Exploring uses of persistent homology for statistical analysis of landmark-based shape data. Journal of Multivariate Analysis 101 2184-2199. DOI:10. 1016/j. jmva. 2010. 04. 016. MR2671209
    • (2010) Journal of Multivariate Analysis , vol.101 , pp. 2184-2199
    • Gamble, J.1    Heo, G.2
  • 23
    • 82255172087 scopus 로고    scopus 로고
    • Probability measures on the space of persistence diagrams
    • MR2854323
    • Mileyko, Y., Mukherjee, S. and Harer, J. (2011). Probability measures on the space of persistence diagrams. Inverse Problems 27 124007. MR2854323
    • (2011) Inverse Problems , vol.27
    • Mileyko, Y.1    Mukherjee, S.2    Harer, J.3
  • 27
    • 84929951586 scopus 로고    scopus 로고
    • Sliding windows and persistence: An application of topological methods to signal analysis
    • Perea, J. A. and Harer, J. (2014). Sliding windows and persistence: An application of topological methods to signal analysis. Foundations of Computational Mathematics 1-40. DOI:10. 1007/s10208-014-9206-z.
    • (2014) Foundations of Computational Mathematics , pp. 1-40
    • Perea, J.A.1    Harer, J.2
  • 28
    • 33747856809 scopus 로고
    • Reexamination of the perfectness concept for equilibrium points in extensive games
    • MR0395896
    • Selten, R. (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4 25-55. MR0395896
    • (1975) International Journal of Game Theory , vol.4 , pp. 25-55
    • Selten, R.1
  • 29
    • 84937909007 scopus 로고    scopus 로고
    • Medians and means for sets of persistence diagrams
    • MR3124945
    • Turner, K. (2013). Medians and means for sets of persistence diagrams. arXiv:1307. 8300. MR3124945
    • (2013) arXiv:1307. 8300
    • Turner, K.1
  • 30
    • 84904427571 scopus 로고    scopus 로고
    • Fréchet means for distributions of persistence diagrams
    • MR3231030
    • Turner, K., Mileyko, Y., Mukherjee, S. and Harer, J. (2014). Fréchet means for distributions of persistence diagrams. Discrete & Computational Geometry 52 44-70. DOI:10. 1007/s00454-014-9604-7. MR3231030
    • (2014) Discrete & Computational Geometry , vol.52 , pp. 44-70
    • Turner, K.1    Mileyko, Y.2    Mukherjee, S.3    Harer, J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.