Back
 OJS  Vol.5 No.7 , December 2015
Statistical Classification Using the Maximum Function
T. Pham-Gia1, Nguyen D. Nhat2, Nguyen V. Phong3
Show more
Abstract: The maximum of k numerical functions defined on , , by ,   is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theoretical results on this function, and then its application in classification using a computer program we have developed. This approach leads to clear decisions, even in cases where the extension to several classes of Fisher’s linear discriminant function fails to be effective.
Keywords: Maximum, Discriminant Function, Pattern Classification, Normal Distribution, Bayes Error, L1-Norm, Linear, Quadratic, Space Curves
Cite this paper: Pham-Gia, T. , Nhat, N. and Phong, N. (2015) Statistical Classification Using the Maximum Function. Open Journal of Statistics, 5, 665-679. doi: 10.4236/ojs.2015.57068.
References

[1]   Pham-Gia, T., Turkkan, N. and Vovan, T. (2008) Statistical Discrimination Analysis Using the Maximum Function, Communic. in Stat., Computation and Simulation, 37, 320-336.
http://dx.doi.org/10.1080/03610910701790475

[2]   Vovan, T. and Pham-Gia, T. (2010) Clustering Probability Densities. Journal of Applied Statistics, 37, 1891-1910.

[3]   Duda, R.O., Hart, P.E. and Stork, D.G. (2001) Pattern Classification. John Wiley and Sons, New York.

[4]   Johnson and Wichern (1998) Applied Multivariate Statistical Analysis. 4th Edition, Prentice-Hall, New York.
http://dx.doi.org/10.2307/2533879

[5]   Gonzalez, R.C., Woods, R.E. and Eddins, S.L. (2004) Digital Image Processing with Matllab. Prentice-Hall, New York.

[6]   Glick, N. (1972) Sample-Based Classification Procedures Derived from Density Estimators. Journal of the American Statistical Association, 67, 116-122.
http://dx.doi.org/10.1080/01621459.1972.10481213

[7]   Glick, N. (1973) Separation and Probability of Correct Classification among Two or More Distributions. Annals of the Institute of Statistical Mathematics, 25, 373-382.
http://dx.doi.org/10.1007/BF02479383

[8]   Fukunaga (1990) Introduction to Statistical Pattern Recognition. 2nd Edition, Academic Press, New York.

[9]   Fisher, R.A. (1936) The Statistical Utilization of Multiple Measurements. Annals of Eugenic, 7, 376-386.

[10]   Flury, B. and Riedwyl, H. (1988) Multivariate Statistics. Chapman and Hall, New York.
http://dx.doi.org/10.1007/978-94-009-1217-5

[11]   Martinez, W.L. and Martinez, A.R. (2002) Computational Statistics Handbook with Matlab. Chapman & Hall/CRC, Boca Raton.

 
 
Top