Mean Vector and Covariance Matrix
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6.5.4.1.
Mean Vector and Covariance Matrix
The first step in analyzing multivariate data is computing the mean vector and the variance-covariance matrix.Sample data matrixConsider the following matrix:covariance matrixThe mean vector consists of the means of each variable and the variance-covariance matrix consists of the variances of the variables along the main diagonal and the covariances between each pair of variables in the other matrix positions.
The formula for computing the covariance of the variables
covariance matrix for sample data matrixThe results are:
Thus, 0.025 is the variance of the length variable, 0.0075 is the covariance between the length and the width variables, 0.00175 is the covariance between the length and the height variables, 0.007 is the variance of the width variable, 0.00135 is the covariance between the width and height variables and 0.00043 is the variance of the height variable.
Centroid, dispersion matixThe mean vector is often referred to as the centroid and the variance-covariance matrix as the dispersion or dispersion matrix. Also, the terms variance-covariance matrix and covariance matrix are used interchangeably.阅读全文
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