Graph Based Multi-class Semi-supervised Learning Using Gaussian Process

  • Yangqiu Song
  • Changshui Zhang
  • Jianguo Lee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4109)


This paper proposes a multi-class semi-supervised learning algorithm of the graph based method. We make use of the Bayesian framework of Gaussian process to solve this problem. We propose the prior based on the normalized graph Laplacian, and introduce a new likelihood based on softmax function model. Both the transductive and inductive problems are regarded as MAP (Maximum A Posterior) problems. Experimental results show that our method is competitive with the existing semi-supervised transductive and inductive methods.


Gaussian Process Unlabeled Data Unseen Data Prediction Phase Graph Base Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Belkin, M., Niyogi, P.: Using manifold structure for partially labeled classification. NIPS 15, 929–936 (2003)Google Scholar
  2. 2.
    Belkin, M., Niyogi, P., Sindhwani, V.: On Manifold Regularization. AI and Statistics, 17–24 (2005)Google Scholar
  3. 3.
    Blake, C.L., Merz, C.J.: UCI Repository of Machine Learning Databases,
  4. 4.
    Chang, C., Lin, C.: LIBSVM: A Library for Support Vector Machines (2001)Google Scholar
  5. 5.
    Chung, F.: Spectral Graph Theory. Tegional Conference Series in Mathematics, vol. 92. American Mathematical Society (1997)Google Scholar
  6. 6.
    Georghiades, A., Belhumeur, P., Kriegman, D.: From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose. IEEE Trans. on PAMI 23(6), 643–660 (2001)Google Scholar
  7. 7.
    Graham, D., Allinson, N.: Characterizing Virtual Eigensignatures for General Purpose Face Recognition. Face Recognition: From Theory to Applications 163, 446–456 (1998)Google Scholar
  8. 8.
    Delalleau, O., Bengio, Y., Roux, N.L.: Efficient Non-Parametric Function Induction in Semi-Supervised Learning. AI and Statistics, 96–103 (2005)Google Scholar
  9. 9.
    Hull, J.: A database for handwritten text recognition research. IEEE Trans. on PAMI 16(5), 550–554 (1994)Google Scholar
  10. 10.
    Lawrence, N.D., Jordan, M.I.: Semi-supervised learning via Gaussian processes. NIPS 17, 753–760 (2005)Google Scholar
  11. 11.
    Mackay, D.: Introduction to Gaussian processes. Technical Report (1997)Google Scholar
  12. 12.
    Nene, S.A., Nayar, S.K., Murase, H.: Columbia Object Image Library (COIL-20), Technical Report (1996)Google Scholar
  13. 13.
  14. 14.
    Seeger, M.: Relationships between Gaussian processes, Support Vector machines and Smoothing Splines. Technical Report (1999)Google Scholar
  15. 15.
    Seeger, M.: Learning with Labeled and Unlabeled Data. Technical Report (2000)Google Scholar
  16. 16.
    Williams, C.K.I., Barber, D.: Bayesian Classification with Gaussian Processes. IEEE Trans. on PAMI 20(12), 1342–1351 (1998)Google Scholar
  17. 17.
    Williams, C., Seeger, M.: Using the Nyström Method to Speed Up Kernel Machines. NIPS 13, 682–688 (2001)Google Scholar
  18. 18.
    Zhou, D., Bousquet, O., Lal, T.N., Weston, J., Schölkopf, B.: Learning with Local and Global Consistency. NIPS 16, 321–328 (2003)Google Scholar
  19. 19.
    Zhu, X., Ghahramani, Z., LaKerty, J.: Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions. ICML 20, 912–919 (2003)Google Scholar
  20. 20.
    Zhu, X., Ghahramani, Z.: Semi-Supervised Learning: From Gaussian Fields to Gaussian Processes. Technical Report (2003)Google Scholar
  21. 21.
    Zhu, X.: Semi-Supervised Learning Literature Survey. Technical Report (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yangqiu Song
    • 1
  • Changshui Zhang
    • 1
  • Jianguo Lee
    • 1
  1. 1.State Key Laboratory of Intelligent Technology and Systems, Department of AutomationTsinghua UniversityBeijingChina

Personalised recommendations