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 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 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.  

scholarly journals Supervised linear classification of Gaussian spatio-temporal data

2021 ◽  
Vol 62 ◽  
pp. 9-15
Author(s):  
Marta Karaliutė ◽  
Kęstutis Dučinskas
Keyword(s):  
Time Moment ◽  
Gaussian Random Field ◽  
Covariance Structure ◽  
Simulated Data ◽  
Spatial Location ◽  
Error Rates ◽  
Prior Probabilities ◽  
Structure Factors ◽  
Spatio Temporal

In this article we focus on the problem of supervised classifying of the spatio-temporal Gaussian random field observation into one of two classes, specified by different mean parameters. The main distinctive feature of the proposed approach is allowing the class label to depend on spatial location as well as on time moment. It is assumed that the spatio-temporal covariance structure factors into a purely spatial component and a purely temporal component following AR(p) model. In numerical illustrations with simulated data, the influence of the values of spatial and temporal covariance parameters to the derived error rates for several prior probabilities models are studied.

scholarly journals Linear discriminant analysis based on gas chromatographic measurements for geographical prediction of USA medical domestic cannabis

2020 ◽  
Author(s):  
Ramia Z. Al Bakain ◽  
Yahya S. Al-Degs ◽  
James V. Cizdziel ◽  
Mahmoud A. Elsohly
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Principal Components ◽  
Supervised Classification ◽  
Geographical Origin ◽  
Active Components ◽  
Linear Discriminant ◽  
Sample Extraction ◽  
Analytical Range

AbstractFifty four domestically produced cannabis samples obtained from different USA states were quantitatively assayed by GC–FID to detect 22 active components: 15 terpenoids and 7 cannabinoids. The profiles of the selected compounds were used as inputs for samples grouping to their geographical origins and for building a geographical prediction model using Linear Discriminant Analysis. The proposed sample extraction and chromatographic separation was satisfactory to select 22 active ingredients with a wide analytical range between 5.0 and 1,000 µg/mL. Analysis of GC-profiles by Principle Component Analysis retained three significant variables for grouping job (Δ9-THC, CBN, and CBC) and the modest discrimination of samples based on their geographical origin was reported. PCA was able to separate many samples of Oregon and Vermont while a mixed classification was observed for the rest of samples. By using LDA as a supervised classification method, excellent separation of cannabis samples was attained leading to a classification of new samples not being included in the model. Using two principal components and LDA with GC–FID profiles correctly predict the geographical of 100% Washington cannabis, 86% of both Oregon and Vermont samples, and finally, 71% of Ohio samples.

scholarly journals Error rates in spatial classification of Gaussian data with random labeling

2010 ◽  
Vol 51 ◽  
Author(s):  
Lijana Stabingienė ◽  
Kęstutis Dučinskas
Keyword(s):  
Random Field ◽  
Error Rate ◽  
Field Model ◽  
Gaussian Random Field ◽  
Parametric Uncertainty ◽  
Error Rates ◽  
Spatial Classification ◽  
Random Labeling ◽  
Gaussian Data

In spatial classification it is usually assumed that features observations given labels are independently distributed. We have retracted this assumption by proposing stationary Gaussian random field model for features observations. The label are assumed to follow Disrete Random Field (DRF) model. Formula for exact error rate based on Bayes discriminant function (BDF) is derived. In the case of partial parametric uncertainty (mean parameters and variance are unknown), the approximation of the expected error rate associated with plug-in BDF is also derived. The dependence of considered error rates on the values of range and clustering parameters is investigated numerically for training locations being second-order neighbors to location of observation to be classified.

Estimation of Error Rates in Several-Population Discriminant Analysis

1982 ◽  
Vol 19 (1) ◽  
pp. 57-61 ◽  
Author(s):  
Stephen C. Hora ◽  
James B. Wilcox
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Discriminant Analysis ◽  
Classification Accuracy ◽  
Posterior Probability ◽  
Error Rates ◽  
Discriminant Functions ◽  
Linear Discriminant ◽  
Probability Estimator ◽  
Estimation Of Error

Researchers seeking to estimate the classification accuracy of linear discriminant functions in a more than two-population setting have had little guidance as to the most appropriate technique. The authors review the available techniques and present an additional alternative which combines features of the U-method and the recently developed posterior probability estimator. The new alternative is compared with other methods by Monté Carlo simulation.

scholarly journals The classification of solvents based on solvatochromic characteristics: the choice of optimal parameters for artificial neural networks

2012 ◽  
Vol 10 (4) ◽  
pp. 1318-1327
Author(s):  
Yaroslava Pushkarova ◽  
Yuriy Kholin
Keyword(s):  
Neural Networks ◽  
Hydrogen Bond ◽  
Artificial Neural Networks ◽  
Supervised Classification ◽  
Solvatochromic Parameters ◽  
Optimal Parameters ◽  
Linear Discriminant ◽  
Solvatochromic Probes ◽  
Artificial Neural

AbstractThe Taft-Kamlet-Abboud hydrogen-bond acidity, hydrogen-bond basicity and polarity-polarizability are widely used as empirical characteristics of solvent-solute interactions. These solvatochromic parameters are determined from the absorption band positions of solvatochromic probes in the standard medium and in the medium under study. The practice of solvatochromic probing is growing rapidly, and the values of solvatochromic parameters are refined from time to time. As these values are rather close for many media, the classification of media based on these values can be tedious. This increases the choice of algorithms that can be employed in order to decrease the ambiguity of classification. The classification algorithms stable to small variations of solvatochromic parameters are of special interest. The artificial neural networks (ANN) proved to be a powerful tool for the supervised classification. The paper focuses on the search of optimal parameters of probabilistic, dynamic, Elman, feed-forward, and cascade ANN for the classification of solvent on the basis of their solvatochromic characteristics. Also, the influence of data variation on the stability of classification is examined. The dynamic and probabilistic neural networks have been found to be error-free and stable; they have significantly become such a common tool for supervised classification as linear discriminant analysis.

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