skbio.diversity.alpha.renyi#
- skbio.diversity.alpha.renyi(counts, order=2, base=None)[source]#
Calculate Renyi entropy.
Renyi entropy (\(^qH\)) is a generalization of Shannon index, with an exponent (order) \(q\) instead of 1. It is defined as:
\[^qH = \frac{1}{1-q}\log_b{(\sum_{i=1}^S p_i^q)}\]where \(S\) is the number of taxa and \(p_i\) is the proportion of the sample represented by taxon \(i\).
- Parameters:
- counts1-D array_like, int
Vector of counts.
- orderint or float, optional
Order (\(q\)). Ranges between 0 and infinity. Default is 2.
- baseint or float, optional
Logarithm base to use in the calculation. Default is
e.
- Returns:
- float
Renyi entropy.
See also
Notes
Renyi entropy was originally defined in [1]. It is a generalization of multiple entropy notions, as determined by the order (\(q\)). Special cases of Renyi entropy include:
\(q=0\): Max-entropy (\(\log{S}\)).
\(q \to 1\): Shannon entropy (index).
\(q=2\): Collision entropy, a.k.a, Renyi’s quadratic entropy, or “Renyi entropy”. Equivalent to the logarithm of inverse Simpson index.
\(q \to \infty\): Min-entropy (\(-\log{\max{p}}\)).
Renyi entropy is equivalent to the logarithm of Hill number.
References
[1]Rényi, A. (1961, January). On measures of entropy and information. In Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, volume 1: contributions to the theory of statistics (Vol. 4, pp. 547-562). University of California Press.