# separability

##### separability

Calculates variety of two-class sample separability metrics

Available statistics:

M-Statistic (Kaufman & Remer 1994) - This is a measure of the difference of the distributional peaks. A large M-statistic indicates good separation between the two classes as within-class variance is minimized and between-class variance maximized (M <1 poor, M >1 good).

Bhattacharyya distance (Bhattacharyya 1943; Harold 2003) - Measures the similarity of two discrete or continuous probability distributions.

Jeffries-Matusita distance (Bruzzone et al., 2005; Swain et al., 1971) - The J-M distance is a function of separability that directly relates to the probability of how good a resultant classification will be. The J-M distance is asymptotic to v2, where values of v2 suggest complete separability

Divergence and transformed Divergence (Du et al., 2004) - Maximum likelihood approach. Transformed divergence gives an exponentially decreasing weight to increasing distances between the classes.

##### Usage

```
separability(
x,
y,
plot = FALSE,
cols = c("red", "blue"),
clabs = c("Class1", "Class2"),
...
)
```

##### Arguments

- x
X vector

- y
Y vector

- plot
plot separability (TRUE/FALSE)

- cols
colors for plot (must be equal to number of classes)

- clabs
labels for two classes

- ...
additional arguments passes to plot

##### Value

A data.frame with the following separability metrics:

B - Bhattacharryya distance statistic

JM - Jeffries-Matusita distance statistic

M - M-Statistic

D - Divergence index

TD - Transformed Divergence index

##### References

Anderson, M. J., & Clements, A. (2000) Resolving environmental disputes: a statistical method for choosing among competing cluster models. Ecological Applications 10(5):1341-1355

Bhattacharyya, A. (1943) On a measure of divergence between two statistical populations defined by their probability distributions'. Bulletin of the Calcutta Mathematical Society 35:99-109

Bruzzone, L., F. Roli, S.B. Serpico (1995) An extension to multiclass cases of the Jefferys-Matusita distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 33:1318-1321

Du, H., C.I. Chang, H. Ren, F.M. D'Amico, J. O. Jensen, J., (2004) New Hyperspectral Discrimination Measure for Spectral Characterization. Optical Engineering 43(8):1777-1786.

Kailath, T., (1967) The Divergence and Bhattacharyya measures in signal selection. IEEE Transactions on Communication Theory 15:52-60

Kaufman Y., and L. Remer (1994) Detection of forests using mid-IR reflectance: An application for aerosol studies. IEEE T. Geosci.Remote. 32(3):672-683.

##### Examples

```
# NOT RUN {
norm1 <- dnorm(seq(-20,20,length=5000),mean=0,sd=1)
norm2 <- dnorm(seq(-20,20,length=5000),mean=0.2,sd=2)
separability(norm1, norm2)
s1 <- c (1362,1411,1457,1735,1621,1621,1791,1863,1863,1838)
s2 <- c (1362,1411,1457,10030,1621,1621,1791,1863,1863,1838)
separability(s1, s2, plot=TRUE)
# }
```

*Documentation reproduced from package spatialEco, version 1.3-2, License: GPL-3*