A Purity Measure Based Transductive Learning Algorithm

  • João Roberto Bertini Junior
  • Liang Zhao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7952)


The increasing on the human ability to gather data has led to an increasing effort on labeling them to be used in specific applications such as classification and regression. Therefore, automatic labeling methods such as semi-supervised transdutive learning algorithms are of a major concern on the machine learning and data mining community nowadays. This paper proposes a graph-based algorithm which uses the purity measure to help spreading the labels throughout the graph. The purity measure determines how intertwined are different subspaces of data regarding its classes. As high values of purity indicate low mixture among patterns of different classes, its maximization helps finding well-separated connected subgraphs; which facilitates the label spreading process. Results on benchmark data sets comparing to state-of-the-art methods show the potential of the proposed algorithm.


Graph-based Transduction Purity Measure KNN Mutual Graph Semi-supervised Learning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bertini Jr., J.R., Zhao, L., Motta, R., Lopes, A.A.: A Nonparametric Classification Method based on K-associated Graphs. Inform. Sciences 181, 5435–5456 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bertini Jr., J.R., Lopes, A.A., Zhao, L.: Partially Labeled Data Stream Classification with the Semi-supervised K-associated Graph. J. Brazil. Comp. Soc. 18, 299–310 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Blum, A., Mitchell, T.: Combining Labeled and Unlabeled Data with Co-training. In: Proc. 11th Annual Conf. on Computational Learning Theory, pp. 92–100 (1998)Google Scholar
  4. 4.
    Chapelle, O., Zien, A., Schölkopf, B. (eds.): Semi-supervised Learning. MIT Press (2006)Google Scholar
  5. 5.
    Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms. MIT Press (2009)Google Scholar
  6. 6.
    Culp, M., Michailidis, G.: Graph-based Semisupervised Learning. IEEE T. Pattern Anal. 30, 174–179 (2008)CrossRefGoogle Scholar
  7. 7.
    Delalleau, O., Bengio, Y., Roux, N.: Efficient Non-parametric Function Induction in Semi-supervised Learning. In: Proc. 10th Int. Workshop on Artificial Intelligence and Statistics, Society for Artificial Intelligence and Statistics, pp. 96–103 (2005)Google Scholar
  8. 8.
    Joachims, T.: Transductive Learning via Spectral Graph Partitioning. In: Proc. 20th Int. Conf. on Machine Learning, pp. 290–297 (2003)Google Scholar
  9. 9.
    Lopes, A.A., Bertini Jr., J.R., Motta, R., Zhao, L.: Classification based on the Optimal K-associated Network. In: Zhou, J. (ed.) Complex 2009. LNICST, vol. 4, pp. 1167–1177. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Nigam, K., Mccallum, A.K., Thrun, S., Mitchell, T.: Text Classification from Labeled and Unlabeled Documents using EM. Machine Learning 39, 103–134 (2000)zbMATHCrossRefGoogle Scholar
  11. 11.
    Silva, T.C., Zhao, L.: Network-based Stochastic Semisupervised Learning. IEEE T. Neural Networ. 23, 451–466 (2012)Google Scholar
  12. 12.
    Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (2008)Google Scholar
  13. 13.
    Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised Learning using Gaussian fields and Harmonic Functions. In: Proc. 20th Int. Conf. on Machine Learning, pp. 912–919 (2003)Google Scholar
  14. 14.
    Zhu, X.: Semi-Supervised Learning Literature Survey. Technical Report 1530, Computer-Science, University of Wisconsin-Madison (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • João Roberto Bertini Junior
    • 1
  • Liang Zhao
    • 1
  1. 1.Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrasil

Personalised recommendations