Generalized statistical operators for signal processing

Generalized correlation and covariance are defined using the Minkowski distance and other functions. In the case of normally distributed random variables, the defined generalized correlation function has similar properties to the Pearson correlation coefficient and gives approximately the same numerical values. These generalized covariance or correlation functions, between random variables with different distribution functions, are different from zero for orthogonal random variables. This important property is used for decomposition into independent components of random variables. Using an independent component analysis based on these new statistical operators, sleep stages and their transitions from a 3D movie have been detected.