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)
a boolean value specifying whether input vectors shall be tested for NA values.
a character string specifying the logarithm unit that shall be used to compute distances that depend on log computations.
method to estimate probabilities from input count vectors such as non-probability vectors. Default:
a distance value or matrix based on JSD computations.
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.
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.
# 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 #> 0.03792749# Jensen-Shannon Divergence between P and Q using different log bases JSD(x, unit = "log2") # Default#>#> jensen-shannon #> 0.03792749JSD(x, unit = "log")#>#> jensen-shannon #> 0.02628933JSD(x, unit = "log10")#>#> jensen-shannon #> 0.01141731# 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")#>#> jensen-shannon #> 0.03792749# 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)