From Covariance Matrices to Covariance Operators: Data Representation from Finite to Infinite-Dimensional Settings

2016 ◽  
pp. 115-143 ◽  
Author(s):  
Hà Quang Minh ◽  
Vittorio Murino
Keyword(s):  
Data Representation ◽  
Covariance Matrices ◽  
Infinite Dimensional ◽  
Covariance Operators

Infinite Dimensional Analysis

1994 ◽  
Author(s):  
Charalambos D. Aliprantis ◽  
Kim C. Border
Keyword(s):  
Dimensional Analysis ◽  
Infinite Dimensional ◽  
Infinite Dimensional Analysis

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

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