Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Spatio-Temporal Scale Selection in Video Data Read chapter Read first chapter

2017 | OriginalPaper | Chapter

A Fast MBO Scheme for Multiclass Data Classification

Author : Matt Jacobs

Published in: Scale Space and Variational Methods in Computer Vision

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We describe a new variant of the MBO scheme for solving the semi-supervised data classification problem on a weighted graph. The scheme is based on the minimization of the graph heat content energy. The resulting algorithms guarantee dissipation of the graph heat content energy for an extremely wide class of weight matrices. As a result, our method is both flexible and unconditionally stable. Experimental results on benchmark machine learning datasets show that our approach matches or exceeds the performance of current state-of-the-art variational methods while being considerably faster.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now
previous chapter Graphical Model Parameter Learning by Inverse Linear Programming
next chapter Convex Non-Convex Segmentation over Surfaces
Literature
1.
Alberti, G., Bellettini, G.: A non-local anisotropic model for phase transitions: asymptotic behavior of rescaled energies. Eur. J. Appl. Math. 9, 261–284 (1998)CrossRefMATH
2.
Bresson, X., Chan, T., Tai, X., Szlam, A.: Multi-class trans- ductive learning based on l1 relaxations of cheeger cut and mumford-shah-potts model. J. Math. Imaging Vis. 49(1), 191–201 (2013)CrossRefMATH
3.
Cheeger, J.: A lower bound for the smallest eigenvalue of the Laplacian. In: Problems in Analysis, pp. 195–199 (1970)
4.
Coifman, R.R., Lafon, S., Lee, A.B., Maggioni, M., Nadler, B., Warner, F., Zucker, S.W.: Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. PNAS 102, 7426–7431 (2005)CrossRef
5.
Elsey, M., Esedo\(\bar{\text{g}}\)lu, S.: Threshold dynamics for anisotropic surface energies. Technical report, UM (2016). Under review
6.
Esedo\(\bar{\text{ g }}\)lu, S., Otto, F.: Threshold dynamics for networks with arbitrary surface tensions. Commun. Pure Appl. Math. 68(5), 808–864 (2015)
7.
Esedo\(\bar{\text{ g }}\)lu, S., Tsai, Y.-H.: Threshold dynamics for the piecewise constant Mumford-Shah functional. J. Comput. Phys. 211(1), 367–384 (2006)
8.
Esedo\(\bar{\text{ g }}\)lu, S., Jacobs, M.: Convolution kernels, and stability of threshold dynamics methods. Technical report, University of Michigan (2016)
9.
Garcia-Cardona, C., Merkurjev, E., Bertozzi, A.L., Flenner, A., Percus, A.G.: Multiclass data segmentation using diffuse interface methods on graphs. IEEE Trans. Pattern Anal. Mach. Intell. 36(8), 1600–1613 (2014)CrossRefMATH
10.
Hein, M., Setzer, S.: Beyond spectral clustering - tight relaxations of balanced graph cuts. In: Advances in Neural Information Processing Systems 24 (NIPS) (2011)
11.
Kaynak, C.: Methods of combining multiple classifiers and their applications to handwritten digit recognition. Master’s thesis, Institute of Graduate Studies in Science and Engineering, Bogazici University (1995)
12.
Malik, J., Shi, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)CrossRef
13.
Merkurjev, E., Bertozzi, A., Chung, F.: A semi-supervised heat kernel pagerank MBO algorithm for data classification (2016, submitted)
14.
Merriman, B., Bence, J.K., Osher, S.J.: Diffusion generated motion by mean curvature. In: Taylor, J. (ed.) Proceedings of the Computational Crystal Growers Workshop, pp. 73–83. AMS (1992)
15.
Miranda, M., Pallara, D., Paronetto, F., Preunkert, M.: Short-time heat flow and functions of bounded variation in \({\mathbb{R}}^N\). Ann. Fac. Sci. Toulouse Math. 16(1), 125–145 (2007)MathSciNetCrossRefMATH
16.
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42, 577–685 (1989)MathSciNetCrossRefMATH
17.
Nene, S.A., Nayar, S.K., Murase, H.: Columbia object image library (coil-100). Technical report, Columbia University (1996)
18.
Zien, A., Chapelle, O., Scholkopf, B.: Semi-Supervised Learning. The MIT Press, Cambridge (2006)
19.
Scherzer, O. (ed.): Handbook of Mathematical Methods in Imaging. Springer, Heidelberg (2011)MATH
20.
Yin, K., Tai, X.-Y., Osher, S.J.: An effective region force for some variational models for learning and clustering. Technical report, UCLA (2016)
21.
Yu, S.X., Shi, J.: Multiclass spectral clustering. In: Ninth IEEE International Coference on Computer Vision, vol. 1, pp. 313–319, October 2003
22.
Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: Advances in Neural Information Processing Systems (2004)
Metadata
Title
A Fast MBO Scheme for Multiclass Data Classification
Author
Matt Jacobs
Copyright Year
2017
Book
Scale Space and Variational Methods in Computer Vision

Print ISBN: 978-3-319-58770-7

Electronic ISBN: 978-3-319-58771-4

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-58771-4_27

Premium Partner

    Image Credits