Sample Covariance

Covariance for a data sequence.

c(x,t)=1n∑k=1n(xk−M(x))(tk−M(t))c(\boldsymbol{x}, \boldsymbol{t})=\frac{1}{n} \sum_{k=1}^n\left(x_k-M(\boldsymbol{x})\right)\left(t_k-M(\boldsymbol{t})\right)

where MM is the Arithmetic Mean.

Other Definitions (mainly from EMD and KDD)

sxy=1N−1∑i=1N(xi−xˉ)(yi−yˉ)\begin{equation} s_{x y}=\frac{1}{N-1} \sum_{i=1}^{N}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right) \end{equation} Cov⁡(A,B)=∑i=1n(ai−μA)(bi−μB)n=∑i=1naibin−μAμB\operatorname{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}