kl.dist {seewave}

Kullback-Leibler distance

Description

Compare two distributions (e.g. two frequency spectra) by computing the Kullback-Leibler distance

Usage

kl.dist(spec1, spec2, base = 2)

Arguments

spec1

any distribution, especially a spectrum obtained with spec or meanspec (not in dB). This can be either a two-column matrix (col1 = frequency, col2 = amplitude) or a vector (amplitude).

spec2

any distribution, especially a spectrum obtained with spec or meanspec (not in dB). This can be either a two-column matrix (col1 = frequency, col2 = amplitude) or a vector (amplitude).

base

the logarithm base used to compute the distance. See log.

Details

The Kullback-Leibler distance or relative entropy is a non-symmetric measure of the difference between two probability distributions. It is here adapted for frequency spectra. The distance is asymmetric, ie computing the K-L distance between spec1 and spec2 is not the same as computing it between spec2 and spec1. A symmetry can be obtained by calculating the mean between the two directions.
The distance is obtained following:

D_{K-L}(spec1 \Vert spec2) = \sum{spec1 \times log(\frac{spec1}{spec2})}

Value

The function returns a list of three items:

D1

The K-L distance of 'spec2' with respect to 'spec1' (i.e. D(spec1 || spec2))

D2

The K-L distance of 'spec1' with respect to 'spec2' (i.e. D(spec2 || spec1))

D

The symmetric K-L distance (i.e. D = 0.5*(D1+D2))

Note

The base of the logarithm can be changed using the argument base. When sets to base 2, the information is measured in units of bits. When sets to base e, the information is measured in nats.
The function works for both Hz and (htk-)mel scales.

Author(s)

Jerome Sueur, improved by Laurent Lellouch

References

Kullback, S., Leibler, R.A. (1951). On information and sufficiency. Annals of Mathematical Statistics, 22: 79-86

See Also

ks.dist, logspec.dist, simspec, diffspec

Examples

# Comparison of two spectra
data(tico)
tico1 <- spec(tico, at=0.65, plot=FALSE)
tico2 <- spec(tico, at=1.1, plot=FALSE)
kl.dist(tico1, tico2)    # log2 (binary logarithm)
kl.dist(tico1, tico2, base=exp(1))  # ln (natural logarithm)