separability

Source: R/separability.R

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.

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.

Author

Jeffrey S. Evans jeffrey_evans@tnc.org

Examples

   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) 

#>            B         JM M mdif         D         TD
#> 1 0.03854306 0.07561946 0    0 0.3333837 0.08163315
           
   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) 

#>           B       JM         M  mdif        D       TD
#> 1 0.9940818 1.259874 0.2910931 829.5 104.1721 1.999996