Learning Similarity with Fuzzy Functions of Adaptable Complexity

  • Giorgos Mountrakis
  • Peggy Agouris
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2750)


A common approach in database queries involves the multi-dimensional representation of objects by a set of features. These features are compared to the query representation and then combined together to produce a total similarity metric. In this paper we introduce a novel technique for similarity learning within features (attributes) by manipulating fuzzy membership functions (FMFs) of different complexity. Our approach is based on a gradual complexity increase adaptable to problem requirements. The underlying idea is that less adaptable functions will act as approximations for more complex ones. We begin by interpolating a set of planes in the training dataset and due to linearity we get a fast first impression of the underlying complexity. We proceed to interpolate two asymmetrical sigmoidal functions whose initial approximations are calculated from the plane properties. If satisfactory accuracy is not achieved we provide advanced modeling capabilities by investigating FMFs parameters and convolving their output with additional functions.


Similarity Function Training Dataset Input Space Sigmoidal Function Fuzzy Membership Function 
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.


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  1. 1.
    Agrawal, R., Faloutsos, C., Swami, A.: Efficient similarity search in sequence databases. In: Proc. of the Fourth Intl. Conference on Foundations of Data Organization and Algorithms, pp. 69–84 (1993)Google Scholar
  2. 2.
    Aha, D.W., Kibler, D.F., Albert, M.K.: Instance-Based Learning Algorithms. Machine Learning. 6, 37–66 (1991)Google Scholar
  3. 3.
    Batchelor, B.G.: Pattern Recognition: Ideas in Practice, pp. 71–72. Plenum Press, New York (1978)zbMATHGoogle Scholar
  4. 4.
    Berchtold, S., Kriegel, H.-P.: S3: Similarity Search in CAD Database Systems. In: Proc. ACM SIGMOD Conf., pp. 564–567 (1997)Google Scholar
  5. 5.
    Carkacioglu, A., Fatos, Y.-V.: Learning Similarity Space. In: Proc. of Intl. Conference in Image Processing, pp. 405–408 (2002)Google Scholar
  6. 6.
    Cover, T.M., Hart, P.E.: Nearest neighbor Pattern Classification. Institute of Electrical and Electronics Engineers Trans. on Information Theory 13(1), 21–27 (1967)zbMATHGoogle Scholar
  7. 7.
    Gionis, A., Indyk, P., Motwani, R.: Similarity search in high dimensions via hashing. In: Proc. of the 25th Intl. Conf. on Very Large Data Bases (VLDB), pp. 518–529 (1999)Google Scholar
  8. 8.
    Ishii, N., Wang, Y.: Learning Feature Weights for Similarity Measures using Genetic Algorithms. In: Proc. of IEEE Intl. Joint Symp. on Intelligence and Systems, pp. 27–33 (1998)Google Scholar
  9. 9.
    Lim, J.-H., Wu, J.-K., Singh, S., Narasimhalu, A.D.: Learning Similarity Matching in Multimedia Content-Based Retrieval. IEEE Transactions on Knowledge and Data Engineering. 13(5), 846–850 (2001)CrossRefGoogle Scholar
  10. 10.
    Mandl, T.: Tolerant Information Retrieval with Backpropagation Networks. Neural Computing & Applications 9(4), 280–289 (2000)CrossRefGoogle Scholar
  11. 11.
    Mitaim, S., Kosko, B.: Neural Fuzzy Agents that Learn a User’s Preference Map. In: Proc. of 4th International Forum on Research and Technology Advances in Digital Libraries, pp. 25–35 (1997)Google Scholar
  12. 12.
    Nadler, M., Smith, E.P.: Pattern Recognition Engineering. Wiley, New York (1993)zbMATHGoogle Scholar
  13. 13.
    Papadias, D., Karacapilidis, N., Arkoumanis, N.: Processing Fuzzy Spatial Queries: A Configuration Similarity Approach. International Journal of Geographic Information Science (IJGIS) 13(2), 93–128 (1999)CrossRefGoogle Scholar
  14. 14.
    Pappis, C.P., Karacapilidis, N.I.: A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems 56(21), 171–174 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Rafiei, D., Mendelzon, O.: Similarity-Based Queries for Time Series Data. In: Proc. ACM SIGMOD Conf., pp. 13–25 (1997)Google Scholar
  16. 16.
    Santini, S., Jain, R.: Similarity Measures. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(9), 871–883 (1999)CrossRefGoogle Scholar
  17. 17.
    Vlachos, M., Gunopulos, D., Kollios, G.: Robust Similarity Measures for Mobile Object Trajectories. In: Proc. of DEXA Workshops, pp. 721–728 (2002)Google Scholar
  18. 18.
    Wilson, D.R., Martinez, T.R.: An Integrated Instance-Based Learning Algorithm. Computational Intelligence. 16(1), 1–28 (2000)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Yi, B.-K., Faloutsos, C.: Fast Time Sequence Indexing for Arbitrary Lp Norms. In: Proc. of the 26th Intl. Conf. on Very Large Data Bases (VLDB), pp. 385–394 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Giorgos Mountrakis
    • 1
  • Peggy Agouris
    • 1
  1. 1.Dept. of Spatial Information Science and EngineeringNational Center for Geographic Information & Analysis, University of MaineOronoUSA

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