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Classification and Data Analysis in Vector Spaces

  • Chapter
Pattern Recognition

Abstract

Here, as in Chapters 3 and 5, we shall primarily be concerned with methods for making decisions. We shall assume that the primary pattern has already been coded to yield a vector containing numeric descriptors. Such a pattern description is natural in a wide variety of applications, as the following examples show:

  1. 1.

    An autoanalyzer* may be used to define a multielement vector which describes the hormone, protein, salt, and sugar concentrations in human blood.

  2. 2.

    A time-varying signal, such as an EEG or ECG, may be applied to a set of parallel band-pass filters whose outputs are rectified and then integrated. The outputs from the integrators represent the elements of the measurement vector.

  3. 3.

    The color of vegetation, as seen from a satellite, may be used to identify certain crops. A “color” vector might contain three measurements on components from the visible spectrum, as well as ultraviolet or infrared measurements.

A multichannel instrument for performing chemical titrations on a routine basis.

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References

  • Anderson, G. D., 1969, Comparison of Methods of Estimating a Probability Density Function, Ph.D Thesis, University of Washington, Seattle, Wash.

    Google Scholar 

  • Batchelor, B. G., 1968, Learning Machines for Pattern Recognition, Ph.D Thesis, University of Southampton, Southampton, England.

    Google Scholar 

  • Batchelor, B. G., 1971, Improved distance measure for pattern recognition,Electron. Lett., 7: 521.

    Article  Google Scholar 

  • Batchelor, B. G., 1973a, Growing and Pruning a Pattern Classifier, Inform. Sci. 6: 97.

    Article  Google Scholar 

  • Batchelor, B. G., 1973b, Instability of the decision surfaces of the nearest-neighbour and potential function classifiers, Inform. Sci. 5: 179.

    Article  Google Scholar 

  • Batchelor, B. G., 1974a, Practical Approach to Pattern Classification, Plenum Press, London and New York.

    Google Scholar 

  • Batchelor, B. G., 1974b, Design for a high-speed euclidean distance calculator and its use in pattern recognition, Proc. Conf. Computer Systems Technol., IEE Conf. Publ. 121: 213.

    Google Scholar 

  • Batchelor, B. G., and Hand, D. J., 1975, On the graphical analysis of PDF estimators for pattern recognition, Kybernetes 4: 239.

    Article  Google Scholar 

  • Batchelor, B. G., and Wilkins, B. R., 1968, Adaptive discriminant functions. In: Pattern Recognition, IEE Conf. Publ. 42: 168.

    Google Scholar 

  • Batchelor, B. G., and Wilkins, B. R., 1969, Method for location of clusters of patterns to initialise a learning machine, Electron. Lett. 5: 481.

    Article  Google Scholar 

  • Cover, T. M., and Hart, P. E., 1967, Nearest neighbor pattern classification, Trans. IEEE IT-13: 21.

    Google Scholar 

  • Everitt, B., 1974, Cluster Analysis, Heinemann, London.

    Google Scholar 

  • Ford, N. L., 1974, Pattern Classification and the Analysis of Training Sets, Ph.D. Thesis, University of Southampton, Southampton, England.

    Google Scholar 

  • Ford, N. L., Batchelor, B. G., and Wilkins, B. R., 1970, Learning scheme for the nearest neighbour classifier, Inform. Sci. 2: 139.

    Article  Google Scholar 

  • Fukunaga, K., 1972, An Introduction to Statistical Pattern Recognition, Academic Press, New York.

    Google Scholar 

  • Hand, D. J., and Batchelor, B. G., 1974, A preliminary note on pattern classification using incomplete vectors, Proc. 2nd Int. Joint Conf. Pattern Recognition, p. 15.

    Google Scholar 

  • Hand, D. J., and Batchelor, B. G., 1975, Classification of incomplete pattern vectors using orthogonal function methods, Proc. 3rd Int. Conf. on Cybernetics and Systems, Bucharest, Rumania.

    Google Scholar 

  • Hart, P. E., 1968, Condensed nearest neighbour rule, Trans. IEEE IT-14: 515.

    Google Scholar 

  • Hellerman, H., 1967, Digital Computer System Principles, McGraw-Hill, New York.

    Google Scholar 

  • Iverson, K., 1962, A Programming Language, Wiley, New York.

    Google Scholar 

  • Jardine, N., and Sibson, R., 1971, Mathematical Taxonomy, Wiley, New York.

    Google Scholar 

  • Katzan, H., 1970, APL Programming and Computer Techniques, Van Nostrand-Reinhold, New York.

    Google Scholar 

  • Lewin, D. W., 1972, Theory and Design of Digital Computers, Nelson, London.

    Google Scholar 

  • Lill, B., and Redstone, L., 1968, A study of learning and recognition algorithms, IEE Conf. Publ. 42.

    Google Scholar 

  • Martin, J., 1973, Design of Man-Computer Dialogues, Prentice-Hall, Englewood-Cliffs, N.J.

    Google Scholar 

  • Mattson, A. L., and Damman, J. E., 1965, A technique for determining and coding subclasses in pattern recognition problems, IBM J. 9: 4.

    Article  Google Scholar 

  • Miller, G. A., 1967, Psychology of Communication, Penguin, Harmondsworth, U.K.

    Google Scholar 

  • Mucciardi, A. N., and Gose, E. E., 1971, Comparison of seven techniques for choosing subsets of pattern recognition properties, Trans. IEEE C-20: 1023.

    Google Scholar 

  • Mucciardi, A. N., and Gose, E. E., 1972, An automatic clustering algorithm and its properties in high dimensional spaces, Trans. IEEE SMC-2: 247.

    Google Scholar 

  • Nilsson, N. J., 1965, Learning Machines, McGraw-Hill, New York.

    Google Scholar 

  • Patrick, E. A., 1972, Fundamentals of Pattern Recognition, Prentice-Hall, Englewood-Cliffs, N.J.

    Google Scholar 

  • Rosenfeld, A., and Pfaltz, J. L., 1968, Distance functions on digital pictures, Pattern Recognition 1: 33.

    Article  Google Scholar 

  • Sammon, J. W., 1969, Non-linear mapping for data structure analysis, Trans. IEEE C-18: 401.

    Google Scholar 

  • Sebestyen, G. S., 1962, Decision-Making Processes in Pattern Recognition, Macmillan, New York.

    Google Scholar 

  • Sebestyen, G. S., and Edie, J., 1966, An algorithm for non-parametric pattern recognition, Trans. IEEE EC-15: 908.

    Google Scholar 

  • Sokal, R. R., and Sneath, P. H. A., 1963, Principles of Numerical Taxonomy, Freeman, San Francisco.

    Google Scholar 

  • Wilkins, B. R., and Batchelor, B. G., 1970, Evolution of a descriptor set for pattern recognition, Proc. Conf. Technical Biol. Probl. Control, Instrument Society of America, p. 794.

    Google Scholar 

  • Wilkins, B. R., and Ford, N. L., 1972, Analysis of training sets for adaptive pattern recognition. In Machine Perception of Patterns and Pictures, Inst. Physics, Conf. Ser. 13: 267.

    Google Scholar 

  • Wolfe, J. H., 1967, Normix: Computational Methods for Estimating the Parameters of a Multivariate Normal Mixture of Distributions. (Research Memo SRM 68-2), U.S. Naval Personnel Research Activity, San Diego, Calif. (Defense Documentation Center Ad 656 588).

    Google Scholar 

  • Wolfe, J. H., 1970, Pattern clustering by multivariate mixture analysis, Multivariate Behav. Res., 5: 329.

    Article  Google Scholar 

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© 1978 Plenum Press, New York

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Batchelor, B.G. (1978). Classification and Data Analysis in Vector Spaces. In: Batchelor, B.G. (eds) Pattern Recognition. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-4154-3_4

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  • DOI: https://doi.org/10.1007/978-1-4613-4154-3_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4156-7

  • Online ISBN: 978-1-4613-4154-3

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