scholarly journals Comparison of linear discriminant functions in image classification

2010 ◽  
Vol 51 ◽  
Author(s):  
Lijana Stabingienė ◽  
Giedrius Stabingis ◽  
Kęstutis Dučinskas
Keyword(s):  
Random Field ◽  
Image Classification ◽  
Spatial Correlation ◽  
Conditional Distribution ◽  
Gaussian Random Field ◽  
Training Sample ◽  
Discriminant Functions ◽  
Linear Discriminant ◽  
And Performance ◽  
Bayes Discriminant Function

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.

scholarly journals Using Linear Discriminant Analysis to Classify Snowfall Situations into Avalanching and Non-Avalanching Ones

1977 ◽  
Vol 19 (81) ◽  
pp. 679-680
Author(s):  
N.F. Drozdovskaya
Keyword(s):  
Discriminant Analysis ◽  
Statistical Methods ◽  
Training Sample ◽  
Dispersion Analysis ◽  
Snow Accumulation ◽  
Discriminant Functions ◽  
Prognostic Information ◽  
Individual Parameter ◽  
Linear Discriminant ◽  
Avalanche Forecasting

Abstract The existing methods of predicting avalanche danger often do not meet users’ demands because of the empiric character of the insufficient volume of information used. In such forecasts the contribution of each individual parameter into the prognostic information is unknown, and this is very important when studying such an event as avalanche formation, which is conditioned by a complex interaction of numerous factors, including snow accumulation, the state of snow thickness, and the conditions of its development. It is obvious that such problems can be successfully solved by statistical methods, and that explains the growing interest in numerical methods of avalanche forecasting. Problems of multi-dimensional observations arises in many scientific fields. The method suited for this problem is discriminant analysis, the purpose of which is to divide a multi-dimensional observation vector into predetermined classes. This study considers the prognostic (diagnostic) problems of fresh-snow avalanches released during snowfall or in the two days after it has ceased. The theoretical basis is a complex of statistical methods: correlation and dispersion analysis, “sifting" for the choice of predictors’ informative groups, construction of linear parametric discriminant functions, predictions based on training sample, and verification of discriminant functions based on independent material. The archive used in the study consisted of 500 avalanching cases and 1 300 non-avalanching ones. All situations were grouped according to geomorphological characteristics. Each situation is described by eight meteorological characteristics. The results of classification of snowfall situations into avalanching and non-avalanching ones are as follows: reliability of ρ is from 75% to 91%, H from 0.15 to 0.51; based on independent material the reliability of ρ is from 63% to 85%, H from 0.10 to 0.56. This paper has been accepted in revised form for publication in a later issue of the Journal of Glaciology.

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 Using Linear Discriminant Analysis to Classify Snowfall Situations into Avalanching and Non-Avalanching Ones

1979 ◽  
Vol 22 (86) ◽  
pp. 127-133
Author(s):  
N.F. Drozdovskaya
Keyword(s):  
Discriminant Analysis ◽  
Statistical Methods ◽  
Training Sample ◽  
Dispersion Analysis ◽  
Snow Accumulation ◽  
Discriminant Functions ◽  
Prognostic Information ◽  
Individual Parameter ◽  
Linear Discriminant ◽  
Avalanche Forecasting

AbstractThe existing methods of predicting avalanche danger often do not meet users’ demands because of the empiric character of the insufficient volume of information used. In such forecasts the contribution of each individual parameter into the prognostic information is unknown, and this is very important when studying such an event as avalanche formation, which is conditioned by a complex interaction of numerous factors, including snow accumulation, snow thickness, and the conditions of its development. It is obvious that such problems can be successfully solved by statistical methods, and that explains the growing interest in numerical methods of avalanche forecasting. Problems of multi-dimensional observations arises in many scientific fields. The method suited for this problem is discriminant analysis, the purpose of which is to divide a multi-dimensional observation vector into predetermined classes.This study considers the prognostic (diagnostic) problems of fresh-snow avalanches released during snowfall or in the two days after it has ceased. The theoretical basis is a complex of statistical methods: correlation and dispersion analysis, “sifting” for the choice of predictors’ informative groups, construction of linear parametric discriminant functions, predictions based on training sample, and verification of discriminant functions based on independent material.The archive used in the study consisted of 500 avalanching cases and 1 300 non-avalanching ones. All situations were grouped according to geomorphological characteristics. Each situation is described by eight meteorological characteristics. The results of classification of snowfall situations into avalanching and non-avalanching ones are as follows: reliability of p is from 75% to 91%, H from 0.15 to 0.51; based on independent material the reliability of p is from 63% to 85%, H from 0. 10 to 0.56.

Using Linear Discriminant Analysis to Classify Snowfall Situations into Avalanching and Non-Avalanching Ones

1979 ◽  
Vol 22 (86) ◽  
pp. 127-133
Author(s):  
N.F. Drozdovskaya
Keyword(s):  
Discriminant Analysis ◽  
Statistical Methods ◽  
Training Sample ◽  
Dispersion Analysis ◽  
Snow Accumulation ◽  
Discriminant Functions ◽  
Prognostic Information ◽  
Individual Parameter ◽  
Linear Discriminant ◽  
Avalanche Forecasting

AbstractThe existing methods of predicting avalanche danger often do not meet users’ demands because of the empiric character of the insufficient volume of information used. In such forecasts the contribution of each individual parameter into the prognostic information is unknown, and this is very important when studying such an event as avalanche formation, which is conditioned by a complex interaction of numerous factors, including snow accumulation, snow thickness, and the conditions of its development. It is obvious that such problems can be successfully solved by statistical methods, and that explains the growing interest in numerical methods of avalanche forecasting. Problems of multi-dimensional observations arises in many scientific fields. The method suited for this problem is discriminant analysis, the purpose of which is to divide a multi-dimensional observation vector into predetermined classes.This study considers the prognostic (diagnostic) problems of fresh-snow avalanches released during snowfall or in the two days after it has ceased. The theoretical basis is a complex of statistical methods: correlation and dispersion analysis, “sifting” for the choice of predictors’ informative groups, construction of linear parametric discriminant functions, predictions based on training sample, and verification of discriminant functions based on independent material.The archive used in the study consisted of 500 avalanching cases and 1 300 non-avalanching ones. All situations were grouped according to geomorphological characteristics. Each situation is described by eight meteorological characteristics. The results of classification of snowfall situations into avalanching and non-avalanching ones are as follows: reliability ofpis from 75% to 91%,Hfrom 0.15 to 0.51; based on independent material the reliability ofpis from 63% to 85%,Hfrom 0. 10 to 0.56.

scholarly journals Using Linear Discriminant Analysis to Classify Snowfall Situations into Avalanching and Non-Avalanching Ones

1977 ◽  
Vol 19 (81) ◽  
pp. 679-680
Author(s):  
N.F. Drozdovskaya
Keyword(s):  
Discriminant Analysis ◽  
Statistical Methods ◽  
Training Sample ◽  
Dispersion Analysis ◽  
Snow Accumulation ◽  
Discriminant Functions ◽  
Prognostic Information ◽  
Individual Parameter ◽  
Linear Discriminant ◽  
Avalanche Forecasting

AbstractThe existing methods of predicting avalanche danger often do not meet users’ demands because of the empiric character of the insufficient volume of information used. In such forecasts the contribution of each individual parameter into the prognostic information is unknown, and this is very important when studying such an event as avalanche formation, which is conditioned by a complex interaction of numerous factors, including snow accumulation, the state of snow thickness, and the conditions of its development.It is obvious that such problems can be successfully solved by statistical methods, and that explains the growing interest in numerical methods of avalanche forecasting. Problems of multi-dimensional observations arises in many scientific fields. The method suited for this problem is discriminant analysis, the purpose of which is to divide a multi-dimensional observation vector into predetermined classes.This study considers the prognostic (diagnostic) problems of fresh-snow avalanches released during snowfall or in the two days after it has ceased. The theoretical basis is a complex of statistical methods: correlation and dispersion analysis, “sifting" for the choice of predictors’ informative groups, construction of linear parametric discriminant functions, predictions based on training sample, and verification of discriminant functions based on independent material.The archive used in the study consisted of 500 avalanching cases and 1 300 non-avalanching ones. All situations were grouped according to geomorphological characteristics. Each situation is described by eight meteorological characteristics. The results of classification of snowfall situations into avalanching and non-avalanching ones are as follows: reliability of ρ is from 75% to 91%, H from 0.15 to 0.51; based on independent material the reliability of ρ is from 63% to 85%, H from 0.10 to 0.56.This paper has been accepted in revised form for publication in a later issue of the Journal of Glaciology.

RETRACTED: Application of Bayes linear discriminant functions in image classification

2012 ◽  
Vol 33 (3) ◽  
pp. 278-282 ◽  
Author(s):  
Kęstutis Dučinskas ◽  
Lijana Stabingienė ◽  
Giedrius Stabingis
Keyword(s):  
Image Classification ◽  
Discriminant Functions ◽  
Linear Discriminant
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