scholarly journals Application of spatial auto-beta models in statistical classification

2021 ◽  
Vol 62 ◽  
pp. 36-43
Author(s):  
Eglė Zikarienė ◽  
Kęstutis Dučinskas
Keyword(s):  
Discriminant Function ◽  
Spatial Data ◽  
Supervised Classification ◽  
Classification Problem ◽  
Error Rates ◽  
Classification Rules ◽  
Linear Discriminant ◽  
Actual Error ◽  
Two Populations ◽  
Bayes Discriminant Function

In this paper, spatial data specified by auto-beta models is analysed by considering a supervised classification problem of classifying feature observation into one of two populations. Two classification rules based on conditional Bayes discriminant function (BDF) and linear discriminant function (LDF) are proposed. These classification rules are critically compared by the values of the actual error rates through the simulation study.

scholarly journals Effect of anisotropy coeficient on error rates of linear discriminant functions

2021 ◽  
Vol 47 ◽  
Author(s):  
Kęstutis Dučinskas ◽  
Lina Dreižienė
Keyword(s):  
Spatial Data ◽  
Supervised Classification ◽  
Statistical Approach ◽  
Gaussian Random Field ◽  
Error Rates ◽  
Discriminant Functions ◽  
Linear Discriminant ◽  
Recognition Error ◽  
Two Populations

Paper deals with statistical classification of spatial data as a part of widely applicable statistical approach to pattern recognition. Error rates in supervised classification of Gaussian random field observation into one of two populations specified by different constant means and common stationary geometric anisotropic covariance are considered. Formula for the exact Bayesian error rate is derived. The influence of the ratio of anisotropy to the error rates is evaluated numerically for the case of complete parametric certainty.

scholarly journals Linear discriminant analysis of spatial Gaussian data with estimated anisotropy ratio

2011 ◽  
Vol 52 ◽  
Author(s):  
Lina Dreižienė
Keyword(s):  
Spatial Data ◽  
Asymptotic Approximation ◽  
Covariance Function ◽  
Anisotropy Ratio ◽  
Linear Discriminant ◽  
Gaussian Data ◽  
Unknown Covariance ◽  
Two Populations ◽  
Bayes Discriminant Function

The paper deals with a problem of classification of Gaussian spatial data into one of two populations specified by different parametric mean models and common geometric anisotropic covariance function. In the case of an unknown mean and covariance parameters the Plug-in Bayes discriminant function based on ML estimators is used. The asymptotic approximation of expected error rate (AER) is derived in the case of unknown mean parameters and single unknown covariance parameter i.e., anisotropy ratio.  

The Performance of the Linear Discriminant Function in Nonoptimal Situations and the Estimation of Classification Error Rates: A Review of Recent Findings

1979 ◽  
Vol 16 (3) ◽  
pp. 370-381 ◽  
Author(s):  
William R. Dillon
Keyword(s):  
Discriminant Function ◽  
Error Rates ◽  
Linear Discriminant Function ◽  
Alternative Methods ◽  
Misclassification Error ◽  
Practical Significance ◽  
Classification Error ◽  
Continuous Variables ◽  
Discrete Variables ◽  
Linear Discriminant

This article is a review of the results, as are available, on the performance of the linear discriminant function in situations where the assumptions of multivariate normality and equal group dispersion structures are violated. Some new results are discussed for the case of classification using discrete variables, and in the case of both binary and continuous variables. In addition, alternative methods which have been proposed, and evaluated, for estimating misclassification error rates are thoroughly reviewed. In all cases, the material is reviewed in terms of practical significance, with particular emphasis on the conditions unfavorable to the performance of each procedure.

scholarly journals Performance of Robust Linear Classifier with Multivariate Binary Variables

2015 ◽  
Vol 7 (4) ◽  
pp. 104
Author(s):  
I. Egbo ◽  
M. Egbo ◽  
S. I. Onyeagu
Keyword(s):  
Maximum Likelihood ◽  
Discriminant Function ◽  
Likelihood Function ◽  
Error Rates ◽  
Linear Discriminant Function ◽  
Data Set ◽  
Binary Variables ◽  
Linear Discriminant ◽  
Linear Classifiers ◽  
Fisher’S Linear Discriminant

<p>This paper focuses on the robust classification procedures in two group discriminant analysis with multivariate binary variables. A normal distribution based data set is generated using the R-software statistical analysis system 2.15.3 using Barlett’s approximation to chi-square, the data set was found to be homogenous and was subjected to five linear classifiers namely: maximum likelihood discriminant function, fisher’s linear discriminant function, likelihood ratio function, full multinomial function and nearest neighbour function rule. To judge the performance of these procedures, the apparent error rates for each procedure are obtained for different sample sizes. The results obtained ranked the procedures as follows: fisher’s linear discriminant function, maximum likelihood, full multinomial, likelihood function and nearest neigbour function.</p>

scholarly journals Inventory model for deteriorating items with negative exponential demand, probabilistic deterioration and fuzzy lead time under partial back logging

2020 ◽  
Vol 30 (2) ◽  
Author(s):  
Nabendu Sen ◽  
Sumit Saha
Keyword(s):  
Binary Classification ◽  
Classification Problem ◽  
Solution Technique ◽  
Phase Method ◽  
Bound Constraints ◽  
Two Phase ◽  
Linear Discriminant ◽  
Binary Classification Problem ◽  
Negative Exponential ◽  
Two Populations

This paper is centred on a binary classification problem in which it is desired to assign a new object with multivariate features to one of two distinct populations as based on historical sets of samples from two populations. A linear discriminant analysis framework has been proposed, called the minimised sum of deviations by proportion (MSDP) to model the binary classification problem. In the MSDP formulation, the sum of the proportion of exterior deviations is minimised subject to the group separation constraints, the normalisation constraint, the upper bound constraints on proportions of exterior deviations and the sign unrestriction vis-à-vis the non-negativity constraints. The two-phase method in linear programming is adopted as a solution technique to generate the discriminant function. The decision rule on group-membership prediction is constructed using the apparent error rate. The performance of the MSDP has been compared with some existing linear discriminant models using a previously published dataset on road casualties. The MSDP model was more promising and well suited for the imbalanced dataset on road casualties.

scholarly journals The influence of training sampling size on the expected error rate in spatial classification

2012 ◽  
Vol 53 ◽  
Author(s):  
Lina Dreižienė ◽  
Marta Karaliutė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Asymptotic Approximation ◽  
Covariance Function ◽  
Spatial Sampling ◽  
Anisotropy Ratio ◽  
Gaussian Data ◽  
Two Populations ◽  
Bayes Discriminant Function

In this paper we use the pluged-in Bayes discriminant function (PBDF) for classification of spatial Gaussian data into one of two populations specified by different parametric mean models and common geometric anisotropic covariance function. The pluged-in Bayes discriminant function is constructed by using ML estimators of unknown mean and anisotropy ratio parameters. We focus on the asymptotic approximation of expected error rate (AER) and our aim is to investigate the effects of two different spatial sampling designs (based on increasing and fixed domain asymptotics) on AER.

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