Sample Covariance

Covariance for a data sequence. $c(\mathbf{x},\mathbf{t})=\frac{1}{n}{\sum }_{k=1}^n\left(x_k-M(\mathbf{x})\right)\left(t_k-M(\mathbf{t})\right)$ where $M$ is the Arithmetic Mean.

Other Definitions (mainly from EMD and KDD)

$$\begin{array}{c}{s}_{xy}=\frac{1}{N-1}\sum _{i=1}^N\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)\end{array}$$

$\mathrm{Cov}(A,B)=\frac{{\sum }_{i=1}^n\left(a_i-{\mu }_A\right)\left(b_i-{\mu }_B\right)}{n}=\frac{{\sum }_{i=1}^n{a}_i{b}_i}{n}-{\mu }_A{\mu }_B$