Abstract
In Section 1.1 we defined a classifier as any function D:ℜp ↦ Npc. The value y = D(z) is the label vector for z in ℜP. D is a crisp classifier if D [ℜp] = Nhc; otherwise, the classifier is fuzzy, possibilistic or probabilistic, which for convenience we lump together as soft classifiers. This chapter describes some of the most basic (and often most useful) classifier designs, along with some fuzzy generalizations and relatives.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Comments and bibliography
Hughes, G. F. (1968). On the mean accuracy of statistical pattern recognizers, IEEE Trans. Inf. Theory, 14, 55–63.
Haykin, S. (1994). Neural Networks: A Comprehensive Foundation, MacMillan, NY.
Chiang, J. and Gader, P. (1997). Hybrid fuzzy-neural systems in handwritten word recognition. IEEE Trans. Fuzzy Syst., 5 (4), 497–510.
Gader, P., Keller, J. M., Krishnapuram, R., Chiang, J., and Mohamed, M. (1997b). Neural and fuzzy methods in handwriting recognition, IEEE Computer, 30 (2) 79–86.
Rosenfeld, A. (1979). Fuzzy digital topology, Inf. and Control, 40, 7687.
Rosenfeld, A. (1984). The fuzzy geometry of image subsets, Patt. Recog. Lett., 2, 311–317.
Rosenfeld, A. (1992). Fuzzy geometry: An overview, Proc. IEEE Int. Conf on Fuzzy Syst., 113–118.
Rosenfeld, A. and Haber, S. (1985). The perimeter of a fuzzy set, Patt. Recog., 18, 125–130.
Pal, S. K. and Rosenfeld, A. (1988). Image enhancement and thresholding by optimization of fuzzy compactness, Patt. Recog. Lett., 7, 77–86.
Pal, S. K. and Ghosh, A. (1990). Index of area coverage of fuzzy subsets and object extraction, Patt. Recog. Lett., 11, 831–841.
Pal, S. K. (1992a). Fuzzy set theoretic measure for automatic feature evaluation–II, Inform. Sci., 64, 165–179.
Dubois, D. and Jaulent, M. C. (1987). A general approach to parameter evaluation in fuzzy digital pictures, Patt. Recog. Lett., 6, 251–259.
Krishnapuram, R. and Chen, L. (1993). Implementation of parallel thinning algorithms using recurrent neural networks, IEEE Trans. Neural Networks, 4, 142–147.
Krishnapuram, R. and Medasani, S. (1995). Recovery of geometric properties of binary objects from blurred images, Proc. IEEE Int. Conf. on Fuzzy Syst., IEEE Press Piscataway, NJ, 1793–1798.
Medasani, S., Krishnapuram, R. and Keller, J. M. (1999). Are fuzzy definitions of image properties really useful?, IEEE Trans. Syst., Man and Cyberns., in press.
Keller, J. M. and Chen, Z. (1992a). Learning in fuzzy neural networks utilizing additive hybrid operators, Proc. Int. Conf. on Fuzzy Logic and Neural Networks, Iizuka, Japan, 85–87.
Keller, J. M. and Wang, X. (1996). Learning spatial relationships in computer vision, Proc. IEEE Int. Conf on Fuzzy Syst., IEEE Press, Piscataway, NJ, 118–124.
Miyajima, K. and Ralescu, A. L. (1994). Spatial organization in 2D segmented images: representation and recognition of primitive spatial relations, Fuzzy Sets and Syst., 65, 225–236.
Wang, X. and Keller, J. M. (1999a). Human-based spatial relationship generalization through neural/fuzzy approaches, Fuzzy Sets and Syst., 101 (1), 5–20.
Bezdek, J. C. and Castelaz, P. F. (1977). Prototype classification and feature selection with fuzzy sets, IEEE Trans. Syst., Man and Cyberns., 7, 87–92.
Gesu, V. and Maccarone, M.C. (1986). Feature selection and possibility theory, Patt. Recog., 19, 63–72.
Davenport, J. W., Bezdek, J. C. and Hathaway, R. (1988). Parameter estimation for finite mixture distributions, Int. J. Comp. and Math. with Applications, 15 (10), 819–828.
Petersen, J., Stockmanns, G., Kochs, H-D. and Kochs, E. (1997). Automatic feature extraction in clinical monitoring data, Proc. Fuzzy-Neuro Systems- Computational Intelligence, eds. A. Grauel, W. Becker and F. Belli, Infix Press, St. Augustine, Germany, 411–418.
Cios, K. and Sztandera, L. M. (1992). Continuous ID3 algorithm with fuzzy entropy measures, Proc. IEEE Int. Conf. on Fuzzy Syst., IEEE Press, Piscataway, NJ 469–476.
Pal, S. K. and Chakraborty, B. (1986). Fuzzy set theoretic measure for automatic feature evaluation, IEEE Trans. Syst. Man and Cyberns., 16 (5), 754–760.
Pal, S. K. (1991). Fuzzy tools for the management of uncertainty in pattern recognition, image analysis, vision and expert system, Int. J. Syst. Sci., 22 (3), 511–549.
Pal, S. K. (1992a). Fuzzy set theoretic measure for automatic feature evaluation–II, Inform. Sci., 64, 165–179.
Thawonmas R. and Abe S. (1997). A novel approach to feature selection based on analysis of class regions, IEEE Trans. Syst., Man and Cyberns., B27 (2), 196–207.
DePalma, G.F. and Yau, S. S. (1975). Fractionally fuzzy grammars with application to pattern recognition, in Fuzzy Sets and their Applications to Cognitive and Decision Processes, eds. L. A. Zadeh, K.S. Fu, K. Tanaka and M. Shimura, Academic Press, NY, 329–351.
Devijver, P. and Kittler, J. (1982). Pattern Recognition: A Statistical Approach, Prentice-Hall, Englewood Cliffs, NJ.
Dasarathy, B.V. (1990). Nearest Neighbor (NN) Norms: NN Pattern Classification Techniques, IEEE Computer Society Press, Los Alamitos, CA.
Kuncheva, L. I. and Bezdek, J. C. (1998). Nearest prototype classification: clustering, genetic algorithms or random search?, IEEE Trans. Syst. Man and Cyberns., C28 (1), 160–164.
Velthuizen, R. P., Hall, L. O. and Clarke, L. P. (1996). Feature extraction with genetic algorithms for fuzzy clustering, Biomed. Engineering Appl., Basis and Communications, 8 (6), 496–517.
Chang, C.L. (1974). Finding prototypes for nearest neighbor classification, IEEE Trans. Computer, 23 (11), 1179–1184.
Blonda, P. N., Satalino, G., Baraldi, A. and De Blasi, R. (1998). Segmentation of multiple sclerosis lesions in MRI by fuzzy neural networks: FLVQ and FOSART, Proc. NAFIPS Conf., eds. J. C. Bezdek and L. O. Hall, 39–43.
Bobrowski, L. and Bezdek, J. C. (1991). c-Means Clustering with the e l and e Norms, IEEE Trans. Syst.,Man and Cyberns.,21(3), 545–554.
Bookstein, F. L. (1979). Fitting conic sections to scattered data, CVGIP, 9, 56–71.
Bombardier, V., Jaulent, M.-C., Bubel, A. and Bremont, J. (1997). Cooperation of two fuzzy segmentation operators for digital substract angiograms analysis. Proc. Sixth IEEE Int. Conf. on Fuzzy Syst., 2, IEEE Press, Piscataway, NJ, 1057–1062.
Boudraa, A. E. (1997). Automated detection of the left ventricle region in magnetic resonance images by the fuzzy c-means model, Int. J. of Cardiac Imaging, 13, 347–355.
Boudraa, A. E., Mallet, J. J., Besson, J. E., Bouyoucef, S. E. and Champier, J. (1993). Left ventricle automated detection method in gated isotropic ventriculography using fuzzy clustering, IEEE Trans. Med. Imaging, 12 (3), 451–465.
Dudani, S. A. (1976). The distance weighted k-nearest neighbor rule, IEEE Trans. Syst., Man and Cyberns., 6, 325–327.
Dunn, J. C. (1974a). A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters, J. Cyberns., 3 (3), 32–57.
Dunn, J. C. (1974b). A graph theoretic analysis of pattern classification via Tamura’s fuzzy relation, IEEE Trans. Syst., Man and Cybems., 4, 310–313.
Dunn, J. C. (1977). Indices of partition fuzziness and the detection of clusters in large data sets, in Fuzzy Automata and Decision Processes, ed. M.M. Gupta, Elsevier, NY.
Dutta, S. (1991). Approximate spatial reasoning: integrating qualitative and quantitative constraints Int. J. of Approximate Reasoning, 5, 307–331.
Fisher, P. F. and Pathirana, S. (1990). The evaluation of fuzzy membership of land cover classes in the suburban zone, Remote Sensing of the Environment, 34, 121–132.
Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems, Ann. Eugenics, 7 (2), 179–188.
Forgy, E. (1965). Cluster analysis of multivariate data: efficiency vs interpretability of classifications, Biometrics, 21 (3).
Fowlkes, E. B. and Mallows, C. L. (1983). A method of comparing two hierarchical clusterings, J. Amer. Stat. Assoc., 78, 553–569.
Freeman, J. (1975). The modeling of spatial relations, Computer Graphics and Image Processing, 4, 156–171.
Kuncheva, L. I. and Bezdek, J. C. (1999). An integrated framework for generalized nearest prototype classifier design, Int. J. Uncertainty, Fuzziness and Knowledge-Based Syst., 6 (5), 437–457.
Kuncheva, L. I., Bezdek, J. C. and Duin, R. (1999). Decision templates for multiple classifier fusion: An experimental comparison, Patt. Recog., in press.
Kuncheva, L. I., Bezdek, J. C. and Sutton, M. A. (1998). On combining multiple classifiers by fuzzy templates, Proc. NAFIPS Cont., eds. J. C. Bezdek and L.O. Hall, 193–197.
Kuncheva, L. I., Kounchev, R.K. and Zlatev, R.Z. (1995) Aggregation of multiple classification decisions by fuzzy templates, Proc. European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, 1470–1474.
Kundu, S. (1995). Defining the fuzzy spatial relationship LEFT(A,B), Proc. IFSA Congress, 1, 653–656.
Kwan, H. K. and Cai Y. (1994). A fuzzy neural network and its application to pattern recognition, IEEE Trans. Fuzzy Syst., 2 (3), 185–193.
Senay, H. (1992). Fuzzy command grammars for intelligent interface design, IEEE Trans. Syst., Man and Cyberns., 22 (5), 1124–1131.
Serrano-Gotarredona, T., Linares-Barranco, B. and Andreou, A. G. (1998). Adaptive Resonance Theory Microchips: Circuit Design Techniques, Kluwer, Boston, MA.
Sethi, I. K. (1990). Entropy nets: from decision trees to neural networks, Proc. IEEE, 78 (10), 1605–1613.
Sethi, I. K. (1995). Neural implementation of tree classifiers, IEEE Trans. Syst., Man and Cyberns., 25 (8), 1243–1249.
Sethi, I. K. and Sarvarayudu, G.P.R. (1982). Hierarchical classifier design using mutual information, IEEE Trans. Patt. Anal. and Machine Intell., 4, 441–445.
Shephard, R.N. and Arabie, P. (1979). Additive clustering: representation of similarities as combinations of discrete overlapping properties, Psychological Review, 86 (2), 87–123.
Shi, H., Gader, P. and Chen, W. (1998). Fuzzy integral filters: properties and parallel implementations, J. of Real-Time Imaging, 2 (4), 233–241.
Shih, F. Y., Moh, J. and Chang, F. (1992). A new ART-based neural architecture for pattern classification and image enhancement without prior knowledge, Patt. Recog., 25 (5), 533–542.
Simpson, P. K. (1993). Fuzzy min-max neural networks–Part 2: Clustering, IEEE Trans. Fuzzy Syst., 1(1), 32–45.
Sims, S. R. and Dasarathy, B. (1992). Automatic target recognition using a passive multisensor suite, Optical Engineering, 31 (12), 2584–2593.
Sin, S. K. and deFigueiredo, R. J. P. (1993). Fuzzy system design through fuzzy clustering and optimal predefuzzification, Proc. IEEE Int. Conf Fuzzy Syst., San Francisco, CA, 190–195.
Sinha, D., Sinha, P., Dougherty, E. R. and Batman, S. (1997). Design and analysis of fuzzy morphological algorithms for image processing, IEEE Trans. Fuzzy Syst., 5 (4), 570–584.
Sinha, D. and Dougherty, E. R. (1992). Fuzzy mathematical morphology, J. Comm. Image Representation, 3 (3), 286–302.
Solina, F. and Bajcsy, R. (1990). Recovery of parametric models from range images: the case for superquadrics, IEEE Trans. Patt. Anal. and Machine Intell., 12 (2), 131–176.
Srinivasan, R., and Kinser, J. (1998). A foveating fuzzy scoring target recognition system, Patt. Recog., 31 (8), 1149–1158.
Srinivasan, R., Kinser, J., Schamschula, J., Shamir, J. and Caulfield, H. J. (1996). Optical syntactic pattern recognition by fuzzy scoring, Optical Lett., 21 (11), 815–817.
St. Clair, D. C., Bond, W. E., Rigler, A. K. and Aylward, S. (1992). An evaluation of learning performance in backpropagation and decision-tree classifier systems, Proc. ACM/SIGAPP Symp. on Applications Computers, ACM Press, 636–642.
Stanley, R. J., Keller, J. M., Caldwell, C. W. and Gader, P. (1995). Automated chromosome classification limitations due to image processing, Proc. Rocky Mountain Bioengineering Symp., Copper Mountain, CO, 183–188.
Suh, I. H. and Kim, T. W. (1994). Fuzzy membership function based neural networks with applications to the visual servoing of robot manipulators, IEEE Trans. Fuzzy Syst., 2 (3), 203–220.
SUNY Buffalo Postal Address Image Database (1989). State U. of NY at Buffalo, CS Department, Buffalo, NY.
Tahani, H. and Keller, J. M. (1990). Information fusion in computer vision using the fuzzy integral, IEEE Trans. Syst., Man and Cyberns., 20 (3), 733–741.
Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control, IEEE Trans. Syst., Man and Cyberns., 15 (1), 116–132.
Tamura, S. and Tanaka, K. (1973). Learning of fuzzy formal language, IEEE Trans. Syst., Man and Cyberns., 3, 98–102.
Tamura, S., Higuchi, S. and Tanaka, K. (1971). Pattern classification based on fuzzy relations, IEEE Trans. Syst., Man and Cyberns., 1 (1), 61–66.
Parizeau, M. and Plamondon, R. (1995). A fuzzy-syntactic approach to allograph modeling for cursive script recognition, IEEE Trans. Patt. Anal. and Machine Intell., 17 (7), 702–712.
Parizeau, M., Plamondon, R. and Lorette, G. (1993). Fuzzy shape grammars for cursive script recognition, in Advances in Structural and Syntactic Pattern Recognition, ed. H. Bunke, World Scientific, Singapore, 320–332.
Senay, H. (1992). Fuzzy command grammars for intelligent interface design, IEEE Trans. Syst., Man and Cyberns., 22 (5), 1124–1131.
Peeva, K. (1991). Fuzzy acceptors for syntactic pattern recognition, Int. J. Approx. Reasoning, 5, 291–306.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N.R. (1999). Classifier Design. In: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. The Handbooks of Fuzzy Sets Series, vol 4. Springer, Boston, MA. https://doi.org/10.1007/0-387-24579-0_4
Download citation
DOI: https://doi.org/10.1007/0-387-24579-0_4
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24515-7
Online ISBN: 978-0-387-24579-9
eBook Packages: Springer Book Archive