How to calculate Bhattacharyya coefficient?

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.

When should we use Bhattacharyya distance?

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

Is Bhattacharyya distance symmetric?

Bhattacharyya distance is symmetric (DB(p,q)=DB(q,p)), whereas KL divergence is not (DKL(p∥q)≠DKL(q∥p)).

How to measure how similar two distributions are?

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.

What is chi square distance?

Chi-square distance is one of the distance measures that can be used as a measure of dissimilarity between two histograms and has been widely used in various applications such as image retrieval, texture and object classification, and shape classification [9].

Is Bhattacharya a Brahmin?

Origin. The Bhattacharyas are Kanyakubja Brahmins and originally belonged to the Kanyakubja region of northern India. They later migrated to eastern parts of the Indian subcontinent during the medieval period.

How do you compare two frequency distributions?

If you simply want to know whether the distributions are significantly different, a Kolmogorov-Smirnov test is the simplest way. A Wilcoxon rank test to compare medians can also be useful.

How do you compare two sets of data for differences?

Example: Compare Two Columns and Highlight Mismatched Data

• Select the entire data set.
• Click the Home tab.
• In the Styles group, click on the ‘Conditional Formatting’ option.
• Hover the cursor on the Highlight Cell Rules option.
• Click on Duplicate Values.
• In the Duplicate Values dialog box, make sure ‘Unique’ is selected.

Who gave chi-square test?

Pearson’s chi-squared test is used to determine whether there is a statistically significant difference between the expected frequencies and the observed frequencies in one or more categories of a contingency table.

What is chi-square distance with example?

Chi-square distance calculation is a statistical method, generally measures similarity between 2 feature matrices. Such distance is generally used in many applications like similar image retrieval, image texture, feature extractions etc.

Is Ganguly Brahmin?

Ganguly (also called Ganguli, Ganguly, Gangulee, Gangoly or Gangopadhyay) is an Indian family name of a Bengali jijhotia Brahmin caste; it is a variant of Gangele Gangopadhyay(a) Gônggopaddhae. The Savarna Roychoudhury family of Kolkata are actually Gangopadhyay.

Which is the upper bound of the Bhattacharyya bound?

The optimum s is the one which gives the maximum value for μ ( s ). Bhattacharyya bound: If we do not insist on the optimum selection of s, we may obtain a less complicated upper bound. One of the possibilities is to select s = 1/2. Then, the upper bound is

How is the Bhattacharyya distance related to the coefficient?

Bhattacharyya distance. In statistics, the Bhattacharyya distance measures the similarity of two probability distributions. It is closely related to the Bhattacharyya coefficient which is a measure of the amount of overlap between two statistical samples or populations.

How is the Bhattacharyya distance related to the Mahalanobis distance?

Note that, in this case, the first term in the Bhattacharyya distance is related to the Mahalanobis distance . 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.

Is the Bhattacharyya distance the same as the Chernoff?

Relation between μ (1/2) and ε u. Throughout this book, we use the Bhattacharyya distance rather than the Chernoff because of its simplicity. However, all discussions about the Bhattacharyya distance in this book could be extended to the Chernoff. As seen in ( 3.152 ), the Bhattacharyya distance consists of two terms.