JSD | R Documentation |
This function computes a distance matrix or distance value based on the Jensen-Shannon Divergence with equal weights.
JSD(x, test.na = TRUE, unit = "log2", est.prob = NULL)
x |
a numeric |
test.na |
a boolean value specifying whether input vectors shall be tested for NA values. |
unit |
a character string specifying the logarithm unit that shall be used to compute distances that depend on log computations. |
est.prob |
method to estimate probabilities from input count vectors such as non-probability vectors. Default:
|
Function to compute the Jensen-Shannon Divergence JSD(P || Q) between two
probability distributions P and Q with equal weights \pi_1
=
\pi_2
= 1/2
.
The Jensen-Shannon Divergence JSD(P || Q) between two probability distributions P and Q is defined as:
JSD(P || Q) = 0.5 * (KL(P || R) + KL(Q || R))
where R = 0.5 * (P + Q)
denotes the mid-point of the probability
vectors P and Q, and KL(P || R), KL(Q || R) denote the Kullback-Leibler
Divergence of P and R, as well as Q and R.
General properties of the Jensen-Shannon Divergence:
1)
JSD is non-negative.
2)
JSD is a symmetric measure JSD(P || Q) = JSD(Q || P).
3)
JSD = 0, if and only if P = Q.
a distance value or matrix based on JSD computations.
Hajk-Georg Drost
Lin J. 1991. "Divergence Measures Based on the Shannon Entropy". IEEE Transactions on Information Theory. (33) 1: 145-151.
Endres M. and Schindelin J. E. 2003. "A new metric for probability distributions". IEEE Trans. on Info. Thy. (49) 3: 1858-1860.
KL
, H
, CE
, gJSD
, distance
# Jensen-Shannon Divergence between P and Q
P <- 1:10/sum(1:10)
Q <- 20:29/sum(20:29)
x <- rbind(P,Q)
JSD(x)
# Jensen-Shannon Divergence between P and Q using different log bases
JSD(x, unit = "log2") # Default
JSD(x, unit = "log")
JSD(x, unit = "log10")
# Jensen-Shannon Divergence Divergence between count vectors P.count and Q.count
P.count <- 1:10
Q.count <- 20:29
x.count <- rbind(P.count,Q.count)
JSD(x.count, est.prob = "empirical")
# Example: Distance Matrix using JSD-Distance
Prob <- rbind(1:10/sum(1:10), 20:29/sum(20:29), 30:39/sum(30:39))
# compute the KL matrix of a given probability matrix
JSDMatrix <- JSD(Prob)
# plot a heatmap of the corresponding JSD matrix
heatmap(JSDMatrix)
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