In neural network literature, the matrix
in equation
3 is often called a correlation matrix. This can be a bit
confusing, since
does not contain the correlations between
the variables in a statistical sense, but rather the expected values
of the products between them. The correlation between x_{i} and x_{j}is defined as
The diagonal terms of are the second order origin moments, E[x_{i}^{2}], of x_{i}. The diagonal terms in a covariance matrix are the variances or the second order central moments, , of x_{i}.
The maximum likelihood estimator of is obtained by replacing the expectation operator in equation 18 by a sum over the samples. This estimator is sometimes called the Pearson correlation coefficient after K. Pearson[16].