Informatica

In current paper a problem of classification of T-distributed random field observation into one of two populations specified by common scaling function is considered. The ML and LS estimators of the mean parameters are plugged into the linear discriminant function. The closed form expressions for the Bayes error rate and the actual error rate associated with the aforementioned discriminant functions are derived. This is the extension of one for the Gaussian case. The actual error rates are used to evaluate and compare the performance of the plug-in discriminant function by means of Monte Carlo study.

In the usual statistical approach of spatial classification, it is assumed that the feature observations are independent conditionally on class labels (conditional independence). Discarding this popular assumption, we consider the problem of statistical classification by using multivariate stationary Gaussian Random Field (GRF) for modeling the conditional distribution given class labels of feature observations. The classes are specified by multivariate regression model for means and by common factorized covariance function. In the two-class case and for the class labels modeled by Random Field (RF) based on 0–1 divergence, the formula of the Expected Bayes Error Rate (EBER) is derived. The effect of training sample size on the EBER and the influence of statistical parameters to the values of EBER are numerically evaluated in the case when the spatial framework of data is the subset of the 2-dimensional rectangular lattice with unit spacing.

The problem of supervised classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and factorised covariance matrices is considered. Unknown means and the common covariance matrix of the feature vector components are estimated from spatially correlated training samples assuming spatial correlation to be known. For the estimation of unknown parameters two methods, namely, maximum likelihood and ordinary least squares are used. The performance of the plug-in discriminant functions is evaluated by the asymptotic expansion of the misclassification error. A set of numerical calculations is done for the spherical spatial correlation function.

The sample-based rule obtained from Bayes classification rule by replacing unknown parameters by ML estimates from stratified training sample is used for classification of random observations into one of two widely applicable Gamma distributions. The first order asymptotic expansions of the expected risk regret for different parametric structure cases are derived. These are used to evaluate performance of the proposed classification rule and to find the optimal training sample allocation minimizing the asymptotic expected risk regret.