Statistical Classification Using the Maximum Function
Affiliation(s)
1 Université de Moncton, Moncton, Canada. 2 University of Economics and Law, Hochiminh City, Vietnam. 3 University of Finance and Marketing, Hochiminh City, VietNam.
1 Université de Moncton, Moncton, Canada. 2 University of Economics and Law, Hochiminh City, Vietnam. 3 University of Finance and Marketing, Hochiminh City, VietNam.
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.
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
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.
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.
[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.