Abstract
We present an approach for supervised pattern recognition based on combinatorial analysis of optimum paths from key samples (prototypes), which creates a discrete optimal partition of the feature space such that any unknown sample can be classified according to this partition. A training set is interpreted as a complete graph with at least one prototype in each class. They compete among themselves and each prototype defines an optimum-path tree, whose nodes are the samples more strongly connected to it than to any other. The result is an optimum-path forest in the training set. A test sample is assigned to the class of the prototype which offers it the optimum path in the forest. The classifier is designed to achieve zero classification errors in the training set, without over-fitting, and to learn from its errors. A comparison with several datasets shows the advantages of the method in accuracy and efficiency with respect to support vector machines.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allène, C., Audibert, J.Y., Couprie, M., Cousty, J., Keriven, R.: Some links between min-cuts, optimal spanning forests and watersheds. In: Mathematical Morphology and its Applications to Image and Signal Processing (ISMM’07), MCT/INPE, pp. 253–264 (2007)
Asuncion, A., Newman, D.: UCI machine learning repository (2007)
Beucher, S., Meyer, F.: The morphological approach to segmentation: The watershed. Mathematical Morphology in Image Processing, 433–481 (1993)
Boser, B., Guyon, I., Vapnik, V.: A training algorithm for optimal margin classifiers. In: Proc. 5th Workshop on Comp. Learning Theory, pp. 144–152 (1992)
Chang, C.C., Lin, C.J.: LIBSVM: A library for support vector machines (2001), http://www.csie.ntu.edu.tw/~cjlin/libsvm .
Cohen, J.: A coefficient of agreement for nominal scales. Educational and Psychological Measurement 20, 37–46 (1960)
Collins, D., Zijdenbos, A., Kollokian, V., Sled, J., Kabani, N., Holmes, C., Evans, A.: Design and construction of a realistic digital brain phantom. IEEE Trans. on Medical Imaging 17(3), 463–468 (1998)
Collobert, R., Bengio, S.: Links between perceptrons, mlps and svms. In: Proceedings of the 21th Int. Conf. on Machine learning, p. 23 (2004)
Corel: Corel stock photo images, http://www.corel.com
Cover, T., Hart, P.: Nearest neighbor pattern classification. IEEE Transactions on Information Theory 13(1), 21–27 (1967)
Duan, K., Keerthi, S.S.: Which is the best multiclass svm method? an empirical study. Multiple Classifier Systems, 278–285 (2005)
Falcão, A., Stolfi, J., Lotufon, R.: The image foresting transform: Theory, algorithms, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 19–29 (2004)
Haykin, S.: Neural networks: A comprehensive foundation. Prentice Hall, Englewood Cliffs (1994)
Jain, A.K., Dubes, R.C.: Algorithms for clustering data. Prentice-Hall, Inc., Upper Saddle River, NJ, USA (1988)
Kuncheva, L.: Fuzzy classifier design. Physica-Verlag and Springer (2000)
Kuncheva, L.I.: Combining Pattern Classifiers: Methods and Algorithms. Wiley-Interscience, Chichester (2004)
Lotufo, R.A., Falcão, A.X., Zampirolli, F.A.: Fast euclidean distance transform using a graph-search algorithm. In: Proc. of the 13th Braz. Symposium on Computer Graphics and Image Processing, pp. 269–275 (2000)
Montoya-Zegarra, J., Papa, J., Leite, N., Torres, R., Falcão, A.: Rotation-invariant texture recognition. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Paragios, N., Tanveer, S.-M., Ju, T., Liu, Z., Coquillart, S., Cruz-Neira, C., Müller, T., Malzbender, T. (eds.) ISVC 2007, Part II. LNCS, vol. 4842, pp. 193–204. Springer, Heidelberg (2007)
MPEG-7: Mpeg-7: The generic multimedia content description standard, part 1. IEEE MultiMedia 09(2), 78–87 (2002)
Panda, N., Chang, E.Y., Wu, G.: Concept boundary detection for speeding up svms. In: Proc. of the 23rd Int. Conf. on Machine learning, pp. 681–688 (2006)
Papa, J.P., Falcão, A.X., Miranda, P.A.V., Suzuki, C.T.N., Mascarenhas, N.D.A.: Design of robust pattern classifiers based on optimum-path forests. In: Mathematical Morphology and its Applications to Image and Signal Processing (ISMM 2007), MCT/INPE, pp. 337–348 (2007)
Persoon, E., Fu, K.: Shape Discrimination Using Fourier Descriptors. IEEE Transanctions on Systems, Man, and Cybernetics 7(3), 170–178 (1977)
Reyzin, L., Schapire, R.E.: How boosting the margin can also boost classifier complexity. In: Proc. of the 23rd Int. Conf. on Machine learning, pp. 753–760 (2006)
Rocha, L.M., Falcão, A.X., Meloni, L.G.P.: A robust extension of the mean shift algorithm using optimum path forest. In: 8th International Workshop on Combinatorial Image Analysis (accepted, 2008)
Saha, P.K., Udupa, J.K.: Relative fuzzy connectedness among multiple objects: theory, algorithms, and applications in image segmentation. Comput. Vis. Image Underst. 82(1), 42–56 (2001)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence 22(8), 888–905 (2000)
Swain, M., Ballard, D.: Color Indexing. International Journal of Computer Vision 7(1), 11–32 (1991)
Tang, B., Mazzoni, D.: Multiclass reduced-set support vector machines. In: Proc. of the 23rd Int. Conf. on Machine learning, pp. 921–928 (2006)
Torres, R., Falcão, A.X., Costa, L.: A graph-based approach for multiscale shape analysis. Pattern Recognition 37(6), 1163–1174 (2004)
Vincent, L., Soille, P.: Watersheds in digital spaces: An efficient algorithm based on immersion simulations. IEEE TPAMI 13(6), 583–598 (1991)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Papa, J.P., Falcão, A.X., Suzuki, C.T.N., Mascarenhas, N.D.A. (2008). A Discrete Approach for Supervised Pattern Recognition. In: Brimkov, V.E., Barneva, R.P., Hauptman, H.A. (eds) Combinatorial Image Analysis. IWCIA 2008. Lecture Notes in Computer Science, vol 4958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78275-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-78275-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78274-2
Online ISBN: 978-3-540-78275-9
eBook Packages: Computer ScienceComputer Science (R0)