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.

How is Bhattacharyya distance calculated?

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.

What does Mahalanobis distance do?

Mahalanobis distance is an effective multivariate distance metric that measures the distance between a point and a distribution. It is an extremely useful metric having, excellent applications in multivariate anomaly detection, classification on highly imbalanced datasets and one-class classification.

What is histogram distance?

A distance measure between two histograms has applications in feature selection, image indexing and retrieval, pattern classification and clustering, etc. We propose a distance between sets of measurement values as a measure of dissimilarity of two histograms.

What is Bhattacharyya?

Bhattacharyanoun. A noble title or upādhi used as a surname in India. Etymology: From the Sanskrit titles bhaṭṭa (“Vedic expert”) and ācārya (“teacher, preceptor”).

What is Bhattacharya bound?

SUMMARY Bhattacharyya bounds are considered for the unbiased estimation of a parametric func- tion when the sampling distribution is a member of an exponential family of distributions. It is shown that the Bhattacharyya bounds converge to the variance of the best unbiased estimator.

What is the difference between Mahalanobis distance and Euclidean distance?

The Mahalanobis distance (MD) is the distance between two points in multivariate space. In a regular Euclidean space, variables (e.g. x, y, z) are represented by axes drawn at right angles to each other; The distance between any two points can be measured with a ruler.

How is Mahalanobis distance different from Euclidean distance?

Unlike the Euclidean distance though, the Mahalanobis distance accounts for how correlated the variables are to one another. For example, you might have noticed that gas mileage and displacement are highly correlated. Because of this, there is a lot of redundant information in that Euclidean distance calculation.

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 Mukherjee a Brahmin?

Mukherjee, Mukerjee, Mookerjee, Mukerji, Mukherji, Mukhujje or Mookherjee is a Kulin Brahmin surname of the Hindu Religion, common among residents of the Indian state of West Bengal.

What is Bhattacharyya distance used for?

The Bhattacharyya distance is successfully used in engineering and statistical sciences. In the context of control theory and in the study of the problem of signal selection [a7], $ B ( 1, 2 ) $ is found superior to the Kullback–Leibler distance (cf. also Kullback–Leibler-type distance measures ).

Is Bhattacharyya distance a measure of divergence?

The Bhattacharyya distance is a measure of divergence. It can be defined formally as follows. Let $ ( \\Omega, B, u ) $ be a measure space, and let $ P $ be the set of all probability measures (cf. Probability measure) on $ B $ that are absolutely continuous with respect to $ u $.

How do you calculate Bhattacharyya distance between two classes?

In its simplest formulation, the Bhattacharyya distance between two classes under the normal distribution can be calculated by extracting the mean and variances of two separate distributions or classes: are two different distributions.

How do you calculate Bhattacharyya distance from normal distribution?

In its simplest formulation, the Bhattacharyya distance between two classes under the normal distribution can be calculated by extracting the mean and variances of two separate distributions or classes: