# KL.divergence: Kullback-Leibler Divergence In FNN: Fast Nearest Neighbor Search Algorithms and Applications

## Description

Compute Kullback-Leibler divergence.

## Usage

 ```1 2``` ``` 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 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: [email protected]

## 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`
 ```1 2 3 4 5 6``` ``` 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 ```