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Random Vectors and Their Properties
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algorithm approximation assume autocorrelation matrix Bayes classifier becomes Bhattacharyya distance boundary calculate central limit theorem Chapter characteristic function Chernoff bound class separability clustering coefficients components computation conditional density convergence coordinate system covariance matrix criteria criterion density function diagonal discussed distance function eigenvalues and eigenvectors equal covariance Equation estimate Example expected value expected vector feature selection follows Fukunaga given hyperplane independent intersample distances intrinsic dimensionality iterative likelihood ratio linear classifier linear discriminant function linear transformation maximize mean-square error minimize mixture normalization multiclass problems neighbor decision rule node nonlinear mapping normal distributions number of samples observation vectors obtain orthonormal orthonormal transformation parameters pattern recognition probability of error procedure random variables random vector region sample covariance matrix sample mean sample mean vector satisfy sequence shown in Fig shows Standard Data stochastic approximation term theorem threshold value tion upper bound zero