How to calculate Bhattacharyya distance?

The Bhattacharyya distance is defined as DB(p,q)=−ln(BC(p,q)), where BC(p,q)=∑x∈X√p(x)q(x) for discrete variables and similarly for continuous random variables.

How do you measure similar two distributions?

The simplest way to compare two distributions is via the Z-test. The error in the mean is calculated by dividing the dispersion by the square root of the number of data points. In the above diagram, there is some population mean that is the true intrinsic mean value for that population.

Why is Hellinger a distance?

Hellinger distance can be used to measure the degree of sim- ilarity between two probability distributions; when the distance is 0 the two distributions are identical and when it is 1 they are the furthest apart.

How do you compare two standard deviations?

Since P was not less than 0.05, you can conclude that there is no significant difference between the two standard deviations. If you want to compare two known variances, first calculate the standard deviations, by taking the square root, and next you can compare the two standard deviations.

What caste is Bhattacharya?

Origin. The Bhattacharyas are Kanyakubja Brahmins and originally belonged to the Kanyakubja region of northern India.

What is Hellinger transformation?

Ad b) Hellinger transformation converts species abundances from absolute to relative values (i.e. standardizes the abundances to sample totals) and then square roots them. This could be useful if we are not interested in changes of absolute species abundances, but relative abundances.

How is the Bhattacharyya coefficient used in statistics?

Bhattacharyya coefficient. The Bhattacharyya coefficient is an approximate measurement of the amount of overlap between two statistical samples. The coefficient can be used to determine the relative closeness of the two samples being considered.

What kind of research is done with Bhattacharyya distance?

The Bhattacharyya distance is widely used in research of feature extraction and selection, image processing, speaker recognition, phone clustering.

Which is the second term of the Bhattacharyya distance?

As seen in ( 3.152 ), the Bhattacharyya distance consists of two terms. The first or second term disappears when M1 = M2 or Σ 1 = Σ 2, respectively.

When to use the Bhattacharyya coefficient for polar codes?

The Bhattacharyya coefficient will be 0 if there is no overlap at all due to the multiplication by zero in every partition. This means the distance between fully separated samples will not be exposed by this coefficient alone. The Bhattacharyya coefficient is used in the construction of polar codes.