跳至主要内容

Correct Classification Rates in Multi-Category Discriminant Analysis of Spatial Gaussian Data

Read  full  paper  at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53437#.VMWrPizQrzE

ABSTRACT
This paper discusses the problem of classifying a multivariate Gaussian random field observation into one of the several categories specified by different parametric mean models. Investigation is conducted on the classifier based on plug-in Bayes classification rule (PBCR) formed by replacing unknown parameters in Bayes classification rule (BCR) with category parameters estimators. This is the extension of the previous one from the two category cases to the multi-category case. The novel closed-form expressions for the Bayes classification probability and actual correct classification rate associated with PBCR are derived. These correct classification rates are suggested as performance measures for the classifications procedure. An empirical study has been carried out to analyze the dependence of derived classification rates on category parameters.
 
Cite this paper
Dreižienė, L. , Dučinskas, K. and Paulionienė, L. (2015) Correct Classification Rates in Multi-Category Discriminant Analysis of Spatial Gaussian Data. Open Journal of Statistics, 5, 21-26. doi: 10.4236/ojs.2015.51003.
 
References
[1]McLachlan, G.J. (2004) Discriminant Analysis and Statistical Pattern Recognition. Wiley, New York.
 
[2]Ducinskas, K. (2009) Approximation of the Expected Error Rate in Classification of the Gaussian Random Field Observations. Statistics and Probability Letters, 79, 138-144.
http://dx.doi.org/10.1016/j.spl.2008.07.042
 
[3]Batsidis, A. and Zografos, K. (2011) Errors of Misclassification in Discrimination of Dimensional Coherent Elliptic Random Field Observations. Statistica Neerlandica, 65, 446-461.
http://dx.doi.org/10.1111/j.1467-9574.2011.00494.x
 
[4]Schervish, M.J. (1984) Linear Discrimination for Three Known Normal Populations. Journal of Statistical Planning and Inference, 10, 167-175.
http://dx.doi.org/10.1016/0378-3758(84)90068-5
 
[5]Wu, T.F., Lin, C.J. and Weng, R.C. (2004) Probability Estimates for Multi-Class Classification by Pairwise Coupling. Journal of Machine Learning Research, 5, 975-1005.
 
[6]Hirst, D. (1996) Error-Rate Estimation in Multiply-Group Linear Discriminant Analysis. Technometrics, 38, 389-399.
http://dx.doi.org/10.1080/00401706.1996.10484551
 
[7]Williams, C.K.I. and Barber, D. (1998) Bayesian Classification with Gaussian Processes. IEEE Translations on Pattern Analysis and Machine Intelligence, 20, 1342-1351.
http://dx.doi.org/10.1109/34.735807
 
[8]Xu, T. and Wang, J. (2013) An Efficient Model-Free Estimation of Multiclass Conditional Probability. Journal of Statistical Planning and Inference, 143, 2079-2088.
http://dx.doi.org/10.1016/j.jspi.2013.08.008
 
[9]Schervish, M.J. (1981) Asymptotic Expansions for the Means and Variances of Error Rates. Biometrica, 68, 295-299.
http://dx.doi.org/10.1093/biomet/68.1.295
 
[10]Anderson, T.W. (2003) An Introduction to Multivariate Statistical Analysis. Wiley, New York.
 
[11]Saltyte, J. and Ducinskas, K. (2002) Comparison of ML and OLS Estimators in Discriminant Analysis of Spatially Correlated Observations. Informatica, 13, 297-238.
 
[12]Saltyte-Benth, J. and Ducinskas, K. (2005) Linear Discriminant Analysis of Multivariate Spatial-Temporal Regressions. Scandinavian Journal of Statistics, 32, 281-294.
http://dx.doi.org/10.1111/j.1467-9469.2005.00421.x
 
[13]Ducinskas, K. (2011) Error Rates in Classification of Multivariate Gaussian Random Field Observation. Lithuanian Mathematical Journal, 51, 477-485.
http://dx.doi.org/10.1007/s10986-011-9142-4
 
[14]Ducinskas, K. and Dreiziene, L. (2011) Supervised Classification of the Scalar Gaussian Random Field Observations under a Deterministic Spatial Sampling Design. Austrian Journal of Statistics, 40, 25-36.
 
[15]Ducinskas, K., Dreiziene, L. and Zikariene, E. (2015) Multiclass Classification of the Scalar Gaussian Random Field Observation with Known Spatial Correlation Function. Statistics and Probability Letters, 98, 107-114.
http://dx.doi.org/10.1016/j.spl.2014.12.008
 
[16]Wackernagel, H. (2003) Multivariate Geostatistics: An Introduction with Applications. Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-662-05294-5                                                                eww150126lx
标签：

评论

发表评论

此博客中的热门博文

Does Immigration Promote the Investment of the Monopolistic Firm?

In the present paper, we examine the effect of increasing uncertainty of immigrants’ growth on the optimal timing of investment of a firm that has a monopolistic power over the labor market. It is revealed that when the uncertainty of immigrants’ growth is more than a threshold level, increasing uncertainty of immigrants’ growth accelerates the optimal timing of firms’ investment and enhances the economic growth, even if the uncertainty of immigrants’ growth is formulated by the geometric Brownian motion, which is in sharp contrast to the standard result that an increase in the uncertainty postpones the optimal timing. With an increase in the immigrants over the past ten years, workforces in the host countries have been growing significantly to the extent that the immigrants represent 70% of the increase in the workforce in Europe, and 47% in the United States as OECD indicates. In the present paper, we attempted to investigate the effect of increased uncertainty caused by the growi...
发表评论
阅读全文

Education Policy Implementation: A Mechanism for Enhancing Primary Education Development in Zanzibar

Education is one of the fundamental rights of individuals; therefore, the government of a country needs to develop and strengthen educational policy and quality as well as to ensure that everyone has equal access to basic education. The improvement of access and quality of education in the world is becoming as an essential factor in development, whereas the basic education (primary school), is acknowledged as a foundation of the higher educational development for every country. To fulfill this goal, governments introduce several policies and procedures; however, it requires some reforms and participation from the politician, policymakers, and other stakeholders to re-examine educational policy so that it can lead to multiplication and betterment of the reforms. Educational reforms actually focus on accountability. A positive educational development and reform is very challenging and needs more effort and strategy on how to use and utilize the resources effectively as such it can achie...
发表评论
阅读全文