Application of spatial auto-beta models in statistical classification

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.

Discriminant analysis of the equicorrelated Gaussian observations

In this paper the problem of classification of an observation into one of two Gaussian populations with different means and common variance is considered in the case when equicorrelated training sample is given. Unknown means and common variance are estimated from training sample and these estimators are pluged in the Bayes discriminant function. The maximum likelihood estimators are used. The approximation of the expected error rate associated with Bayes plug-in discriminant function is derived. Numerical analysis of the accuracy of that approximation for various values of correlation is presented.

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

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.

Linear discriminant analysis of spatial Gaussian data with estimated anisotropy ratio

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.

Comparison of linear discriminant functions in image classification

In statistical image classification it is usually assumed that feature observations given labels are independently distributed. We have retracted this assumption by proposing stationary Gaussian random field (GRF) model for features observations. Conditional distribution of label of observation to be classified is assumed to be dependent on its spatial adjacency with training sample spatial framework. Perfomance of the Bayes discriminant function (BDF) and performance of plug-in BDFare tested and are compared with ones ignoring spatial correlation among feature observations.For illustration image of figure corrupted by additive GRF is analyzed. Advantage of proposed BDF against competing ones is shown visually and numerically.