How is the joint entropy of a random pair defined?
The definition of entropy can be easily extended to collections of random elements. The joint entropy of a random pair ( X, Y) ∼ p is its entropy when viewed as a single random element, (2)H(X, Y) = ∑ x, yp(x, y) log 1 p ( x, y). H ( X, Y) represents the amount of randomness in both X and Y, or the number of bits required to describe both of them.
Which is an example of subadditivity in entropy?
The joint entropy of a set of variables is less than or equal to the sum of the individual entropies of the variables in the set. This is an example of subadditivity.
Which is the entropy on the left of the circle?
The circle on the left (red and violet) is the individual entropy H (X), with the red being the conditional entropy H (X|Y). The circle on the right (blue and violet) is H (Y), with the blue being H (Y|X).
The definition of entropy can be easily extended to collections of random elements. The joint entropy of a random pair ( X, Y) ∼ p is its entropy when viewed as a single random element, (2) H(X, Y) = ∑ x, yp(x, y) log 1 p ( x, y). H ( X, Y) represents the amount of randomness in both X and Y, or the number of bits required to describe both of them.
When to use conditional entropy and joint entropy?
In the domain of EMS, marginal entropy can be used to evaluate the information content of a single variable (i.e. a sensor), conditional entropy describes the dependency of two variables, while joint entropy evaluates the whole data set. Nevertheless, it is not easy to analyze time series-like data using entropies.
When to use joint entropy for image registration?
Derek L.G. Hill, David J. Hawkes, in Handbook of Medical Image Processing and Analysis (Second Edition), 2009 The minimization of joint entropy H ( A, B) has been used for image registration [ 17, 18 ], but it has been found to be unreliable.
Are the marginal entropies constant during the registration process?
It is important to remember that the marginal entropies are not constant during the registration process.