Entropy Reduction Strategies on Tree Structured Retrieval Spaces

  • Alain Trouvé
  • Yong Yu
Conference paper
Part of the Trends in Mathematics book series (TM)


In this paper, we study the performance of exact retrieval strategies in the case of tree structured retrieval spaces. We assume that the database B is indexed by the leaves of a hierarchical partitioning tree T. We study retrieval processes based on interaction with the user through simple questions attached to the nodes of T as follows: for each node b, the system can display a summary of the subset attached to b (e.g. some typical images) and get the user answer according to the target. We consider retrieval strategies based on step-wise entropy reduction, built on a user model where the answers are independent given the target. We prove an upper bound for the expected number of questions which appears to be nearly optimal in an interesting case. Moreover, we show that at each step, the next question can be found among an adaptive subset of nodes of size log(|ß|). Finally, the overall complexity of the algorithm (for the computer) per retrieval is O(log(∣ß∣)3) whereas the average number of questions (for the user) is O(log(∣ß∣)).


Mutual Information Image Retrieval User Model Retrieval Strategy Uncertainty Reduction 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Y. Amit, D. Geman, and B. Jedynak. Efficient focusing and face detection. In H. Wechsler and J. Phillips, editors Face Recognition: From Theory to Applications NATO ASI Series G. Springer Verlag, 1998.Google Scholar
  2. [2]
    J. Buhmann Data clustering and learning. In The Hand-book of Brain Theory and Neural Networks pages 278–281. MIT Press, 1995.Google Scholar
  3. [3]
    I. Cox, M. Miller, T. Minka, T. Papathomas, and P. Yianilos. The bayesian image retrieval system, pichunter: Theory, implementation and psychophysical experiments. IEEE Trans. Image Processing 9:20–37, 2000.CrossRefGoogle Scholar
  4. [4]
    I. Cox, M. Miller, T. Minka, and P. Yianilos. An optimized interaction strategy for bayesian relevance feedback. In IEEE Conf. on Comp. Vis. and Pattern Recognition pages 553–558, 1998.Google Scholar
  5. [5]
    F. Fleuret and D. Geman. Coarse-to-fine visual selection. International Journal of Computer Vision 2001. To appear.Google Scholar
  6. [6]
    D. Geman and B. Jedynak. Model-based classification trees. To appear in IEEE Information Theory, 2000.Google Scholar
  7. [7]
    D. Geman and R. Moquet. Q & A models for interactive search. Preprint, December, 2000.Google Scholar
  8. [8]
    M. S. Pinsker. Information and Information Stability of Random Variables and Processes. San-Fransisco: Holden Day, 1964.zbMATHGoogle Scholar
  9. [9]
    A. Smeulders, M. Worring, S. Santini, A. Gupta, and R. Jain. Content-based image retrieval at the end of the early years. IEEE Trans. PAMI 22:13481375, 2000.Google Scholar
  10. [10]
    A. Trouvé and Y. Yu. A lower bound on performance of exact retrieval strategies on simple retrieval spaces. Technical Report 2002–07, Université Paris 13, 2002.Google Scholar
  11. [11]
    A. Trouvé and Y. Yu. Metric similarities learning through examples: An application to shape retieval. In Proceeding of the Third International Workshop EMMCVPR’01 Sophia Antipolis September 3–5 2001 Lecture Notes in Computer Science. Springer Verlag, 2001.Google Scholar
  12. [12]
    A. Trouvé and Y. Yu. Unsupervised clustering trees by non-linear principal component analysis. Pattern Recognition and Image Analysis II:108–112, 2001.Google Scholar

Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Alain Trouvé
    • 1
  • Yong Yu
    • 2
  1. 1.Université Paris 13, LAGA et L2TIVilletaneuseFrance
  2. 2.ENST, Départment TSIParisFrance

Personalised recommendations