# dbhatta: Bhattacharyya Distance In ICGE: Estimation of Number of Clusters and Identification of Atypical Units

 dbhatta R Documentation

## Bhattacharyya Distance

### Description

`dbhatta` computes and returns the Bhattacharyya distance matrix between the rows of a data matrix. This distance is defined between two units i=(p_{i1},...,p_{im}) and j=(p_{j1},...,p_{jm}) being p_{kl} frequencies with p_{kl}>=0 and p_{k1}+...+p_{km}=1.

### Usage

```dbhatta(x)
```

### Arguments

 `x` a matrix containing, in its rows, the frequencies for each unit. Note: check that each row adds up to 1

### Value

A `dist` object with distance information.

### Author(s)

Itziar Irigoien itziar.irigoien@ehu.eus; Konputazio Zientziak eta Adimen Artifiziala, Euskal Herriko Unibertsitatea (UPV-EHU), Donostia, Spain.

Conchita Arenas carenas@ub.edu; Departament d'Estadistica, Universitat de Barcelona, Barcelona, Spain.

### References

Bhattacharyya, A. (1946). On a measure of divergence of two multinomial populations. Sankhya: The Indian Journal of Statistics, Series A. 14, 177-136.

`dist`, `dmahal`, `dgower`, `dcor`, `dproc2`

### Examples

```#5 individuals represented by their relative frequencies of 4 characteristics (M1-M4):
f <- matrix(c(0.36, 0.21, 0.23, 0.20,
0.66, 0.18, 0.11, 0.05,
0.01, 0.24, 0.62, 0.13,
0.43, 0.38, 0.08, 0.11,
0.16, 0.07, 0.09, 0.68),
byrow=TRUE, nrow=5, dimnames=list(1:5, paste("M", 1:4, sep="")))

# Bhattacharyya distances between pairs
d <- dbhatta(f)
```

ICGE documentation built on Oct. 17, 2022, 5:10 p.m.