KL.divergence {FNN} R Documentation

## Kullback-Leibler Divergence

### Description

Compute Kullback-Leibler divergence.

### Usage

  KL.divergence(X, Y, k = 10, algorithm=c("kd_tree", "cover_tree", "brute"))
KLx.divergence(X, Y, k = 10, algorithm="kd_tree")


### Arguments

 X An input data matrix. Y An input data matrix. k The maximum number of nearest neighbors to search. The default value is set to 10. algorithm nearest neighbor search algorithm.

### Details

If p(x) and q(x) are two continuous probability density functions, then the Kullback-Leibler divergence of q from p is defined as E_p[\log \frac{p(x)}{q(x)}].

KL.* versions return divergences from C code to R but KLx.* do not.

### Value

Return the Kullback-Leibler divergence from X to Y.

### Author(s)

Shengqiao Li. To report any bugs or suggestions please email: lishengqiao@yahoo.com

### References

S. Boltz, E. Debreuve and M. Barlaud (2007). “kNN-based high-dimensional Kullback-Leibler distance for tracking”. Image Analysis for Multimedia Interactive Services, 2007. WIAMIS '07. Eighth International Workshop on.

S. Boltz, E. Debreuve and M. Barlaud (2009). “High-dimensional statistical measure for region-of-interest tracking”. Trans. Img. Proc., 18:6, 1266–1283.

KL.dist

### Examples

    set.seed(1000)
X<- rexp(10000, rate=0.2)
Y<- rexp(10000, rate=0.4)

KL.divergence(X, Y, k=5)
#theoretical divergence = log(0.2/0.4)+(0.4-0.2)-1 = 1-log(2) = 0.307


[Package FNN version 1.1.3.2 Index]