FNN (version 1.1.3)

KL.divergence: 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.

Value

Return the Kullback-Leibler divergence from X to Y.

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.

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.

See Also

KL.dist

Examples

# NOT RUN {
    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
# }