Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Towards Integrative Machine Learning and Knowledge Extraction Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Persistent Topology for Natural Data Analysis — A Survey

verfasst von : Massimo Ferri

Erschienen in: Towards Integrative Machine Learning and Knowledge Extraction

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, liver and skin lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Probabilistic Logic Programming in Action
Nächstes Kapitel Predictive Models for Differentiation Between Normal and Abnormal EEG Through Cross-Correlation and Machine Learning Techniques
Literatur
1.
Adcock, A., Rubin, D., Carlsson, G.: Classification of hepatic lesions using the matching metric. Comput. Vis. Image Underst. 121, 36–42 (2014)CrossRef
2.
Banerjee, S.: Size functions in the study of the evolution of cyclones. Int. J. Meteorol. 36(358), 39 (2011)
3.
Banerjee, S.: Size functions in galaxy morphology classification. Int. J. Comput. Appl. 100(3), 1–4 (2014)
4.
Bazaikin, Y.V., Baikov, V.A., Taimanov, I.A., Yakovlev, A.A.: Chislennyi analiz topologicheskih harakteristik trehmernyh geologicheskih modelei neftegazovyh mestorozhdenii. Matematicheskoe Modelirovanie 25(10), 19–31 (2013)MathSciNet
5.
Belchí, F., Murillo, A.: A\(_\infty \)-persistence. Appl. Algebra Eng. Commun. Comput. 26(1–2), 121–139 (2015)CrossRefMATH
6.
Bergomi, M.G., Baratè, A., Di Fabio, B.: Towards a topological fingerprint of music. In: Bac, A., Mari, J.I. (eds.) CTIC 2016. LNCS, vol. 9667, pp. 88–100. Springer, Cham (2016). doi:10.​1007/​978-3-319-39441-1_​9
7.
8.
Biasotti, S., Cerri, A., Frosini, P., Giorgi, D., Landi, C.: Multidimensional size functions for shape comparison. J. Math. Imag. Vis. 32(2), 161–179 (2008)CrossRefMathSciNet
9.
Bigo, L., Andreatta, M., Giavitto, J.-L., Michel, O., Spicher, A.: Computation and visualization of musical structures in chord-based simplicial complexes. In: Yust, J., Wild, J., Burgoyne, J.A. (eds.) MCM 2013. LNCS (LNAI), vol. 7937, pp. 38–51. Springer, Heidelberg (2013). doi:10.​1007/​978-3-642-39357-0_​3 CrossRef
10.
11.
12.
Carlsson, G., Zomorodian, A., Collins, A., Guibas, L.J.: Persistence barcodes for shapes. IJSM 11(2), 149–187 (2005)MATH
13.
Cerri, A., Di Fabio, B., Ferri, M., Frosini, P., Landi, C.: Betti numbers in multidimensional persistent homology are stable functions. Math. Methods Appl. Sci. 36(12), 1543–1557 (2013)CrossRefMATHMathSciNet
14.
Cerri, A., Ethier, M., Frosini, P.: A study of monodromy in the computation of multidimensional persistence. In: Gonzalez-Diaz, R., Jimenez, M.-J., Medrano, B. (eds.) DGCI 2013. LNCS, vol. 7749, pp. 192–202. Springer, Heidelberg (2013). doi:10.​1007/​978-3-642-37067-0_​17 CrossRef
15.
Cerri, A., Frosini, P.: Necessary conditions for discontinuities of multidimensional persistent betti numbers. Math. Methods Appl. Sci. 38(4), 617–629 (2015)CrossRefMATHMathSciNet
16.
Chung, M.K., Bubenik, P., Kim, P.T.: Persistence diagrams of cortical surface data. In: Prince, J.L., Pham, D.L., Myers, K.J. (eds.) IPMI 2009. LNCS, vol. 5636, pp. 386–397. Springer, Heidelberg (2009). doi:10.​1007/​978-3-642-02498-6_​32 CrossRef
17.
d’Amico, M., Ferri, M., Stanganelli, I.: Qualitative asymmetry measure for melanoma detection. In: IEEE International Symposium on Biomedical Imaging: Nano to Macro, pp. 1155–1158. IEEE (2004)
18.
Dehmer, M., Emmert-Streib, F., Pickl, S., Holzinger, A.: Big Data of Complex Networks. CRC Press, Boca Raton (2016)MATH
19.
Donatini, P., Frosini, P.: Lower bounds for natural pseudodistances via size functions. Arch. Inequal. Appl. 1(2), 1–12 (2004)MATHMathSciNet
20.
21.
Donatini, P., Frosini, P.: Natural pseudodistances between closed surfaces. J. Eur. Math. Soc. 9(2), 231–253 (2007)MATHMathSciNet
22.
Edelsbrunner, H., Harer, J.: Persistent homology–a survey. In: Surveys on Discrete and Computational Geometry, vol. 453, pp. 257–282, Providence, RI (2008). Contemp. Math. Amer. Math. Soc
23.
Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction. American Mathematical Society, Providence (2009)CrossRefMATH
24.
Ferri, M., Frosini, P., Lovato, A., Zambelli, C.: Point selection: a new comparison scheme for size functions (with an application to monogram recognition). In: Chin, R., Pong, T.-C. (eds.) ACCV 1998. LNCS, vol. 1351, pp. 329–337. Springer, Heidelberg (1997). doi:10.​1007/​3-540-63930-6_​138
25.
Ferri, M., Gallina, S., Porcellini, E., Serena, M.: On-line character and writer recognition by size functions and fuzzy logic. In: Proceedings of ACCV 1995, pp. 5–8 (1995)
26.
Ferri, M., Lombardini, S., Pallotti, C.: Leukocyte classifications by size functions. In: Proceedings of the Second IEEE Workshop on Applications of Computer Vision, pp. 223–229. IEEE (1994)
27.
Ferri, M., Stanganelli, I.: Size functions for the morphological analysis of melanocytic lesions. J. Biomed. Imaging 2010, 5 (2010)
28.
Ferri, M., Tomba, I., Visotti, A., Stanganelli, I.: A feasibility study for a persistent homology-based k-nearest neighbor search algorithm in melanoma detection. J. Math. Imaging Vis. 57, 1–16 (2016)MATHMathSciNet
29.
Frosini, P., Jabłoński, G.: Combining persistent homology and invariance groups for shape comparison. Discrete Comput. Geom. 55(2), 373–409 (2016)CrossRefMATHMathSciNet
30.
Giorgi, D., Frosini, P., Spagnuolo, M., Falcidieno, B.: 3D relevance feedback via multilevel relevance judgements. Vis. Comput. 26(10), 1321–1338 (2010)CrossRef
31.
Giusti, C., Pastalkova, E., Curto, C., Itskov, V.: Clique topology reveals intrinsic geometric structure in neural correlations. Proc. Natl. Acad. Sci. 112(44), 13455–13460 (2015)CrossRefMATHMathSciNet
32.
Handouyahia, M., Ziou, D., Wang, S.: Sign language recognition using moment-based size functions. In: Proceedings of International Conference on Vision, Interface, pp. 210–216 (1999)
33.
Hatcher, A.: Algebraic Topology. Cambridge University Press, New York (2001)MATH
34.
Holzinger, A.: On knowledge discovery and interactive intelligent visualization of biomedical data. In: Proceedings of the International Conference on Data Technologies and Applications DATA 2012, Rome, Italy, pp. 5–16 (2012)
35.
Holzinger, A.: On topological data mining. In: Holzinger, A., Jurisica, I. (eds.) Interactive Knowledge Discovery and Data Mining in Biomedical Informatics. LNCS, vol. 8401, pp. 331–356. Springer, Heidelberg (2014). doi:10.​1007/​978-3-662-43968-5_​19 CrossRef
36.
Kelly, D., McDonald, J., Lysaght, T., Markham, C.: Analysis of sign language gestures using size functions and principal component analysis. In: Machine Vision and Image Processing Conference, IMVIP 2008. International, pp. 31–36. IEEE (2008)
37.
Lamar-León, J., García-Reyes, E.B., Gonzalez-Diaz, R.: Human gait identification using persistent homology. In: Alvarez, L., Mejail, M., Gomez, L., Jacobo, J. (eds.) CIARP 2012. LNCS, vol. 7441, pp. 244–251. Springer, Heidelberg (2012). doi:10.​1007/​978-3-642-33275-3_​30 CrossRef
38.
Liu, J.-Y., Jeng, S.-K., Yang, Y.-H.: Applying topological persistence in convolutional neural network for music audio signals. arXiv preprint arXiv:​1608.​07373 (2016)
39.
Lord, L.-D., Expert, P., Fernandes, H.M., Petri, G., Van Hartevelt, T.J., Vaccarino, F., Deco, G., Turkheimer, F., Kringelbach, M.L.: Insights into brain architectures from the homological scaffolds of functional connectivity networks. Front. Syst. Neurosci. 10, 85 (2016)CrossRef
40.
Micheletti, A.: The theory of size functions applied to problems of statistical shape analysis. In: S4G-International Conference in Stereology, Spatial Statistics and Stochastic Geometry, pp. 177–183. Union of Czech Mathematicians and Physicists (2006)
41.
Micheletti, A., Landini, G.: Size functions applied to the statistical shape analysis and classification of tumor cells. In: Bonilla, L.L., Moscoso, M., Platero, G., Vega, J.M. (eds.) ECMI 2006. Mathematics in Industry, vol. 12, pp. 538–542. Springer, Heidelberg (2008)CrossRef
42.
Petri, G., Expert, P., Turkheimer, F., Carhart-Harris, R., Nutt, D., Hellyer, P.J., Vaccarino, F.: Homological scaffolds of brain functional networks. J. Roy. Soc. Interface 11(101), 20140873 (2014)CrossRef
43.
Platt, D.E., Basu, S., Zalloua, P.A., Parida, L.: Characterizing redescriptions using persistent homology to isolate genetic pathways contributing to pathogenesis. BMC Syst. Biol. 10(1), S10 (2016)CrossRef
44.
Port, A., Gheorghita, I., Guth, D., Clark, J.M., Liang, C., Dasu, S., Marcolli, M.: Persistent topology of syntax. arXiv preprint arXiv:​1507.​05134 (2015)
45.
Ringermacher, H.I., Mead, L.R.: A new formula describing the scaffold structure of spiral galaxies. Mon. Not. R. Astron. Soc. 397(1), 164–171 (2009)CrossRef
46.
Sizemore, A., Giusti, C., Betzel, R.F., Bassett, D.S.: Closures and cavities in the human connectome. arXiv preprint arXiv:​1608.​03520 (2016)
47.
Stanganelli, I., Brucale, A., Calori, L., Gori, R., Lovato, A., Magi, S., Kopf, B., Bacchilega, R., Rapisarda, V., Testori, A., Ascierto, P.A., Simeone, E., Ferri, M.: Computer-aided diagnosis of melanocytic lesions. Anticancer Res. 25(6C), 4577–4582 (2005)
48.
Turner, K., Mukherjee, S., Boyer, D.M.: Persistent homology transform for modeling shapes and surfaces. Inf. Inference J. IMA 3(4), 310–344 (2014)CrossRefMathSciNet
49.
Uras, C., Verri, A.: On the recognition of the alphabet of the sign language through size functions. In: Proceedings of the 12th IAPR International Conference on Pattern Recognition, Vol. 2-Conference B: Computer Vision & Image Processing, vol. 2, pp. 334–338. IEEE (1994)
50.
Verri, A., Uras, C., Frosini, P., Ferri, M.: On the use of size functions for shape analysis. Biol. Cybern. 70, 99–107 (1993)CrossRefMATH
51.
Ziefle, M., Himmel, S., Holzinger, A.: How usage context shapes evaluation and adoption criteria in different technologies. In: AHFE 2012, Proceeding of International Conference on Applied Human Factors and Ergonomics, San Francisco, pp. 2812–2821 (2012)
Metadaten
Titel
Persistent Topology for Natural Data Analysis — A Survey
verfasst von
Massimo Ferri
Copyright-Jahr
2017
Buch
Towards Integrative Machine Learning and Knowledge Extraction

Print ISBN: 978-3-319-69774-1

Electronic ISBN: 978-3-319-69775-8

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-69775-8_6