R package implementing the multiscale multivariate sample entropy measure described by Ahmed and Mandic (2011). The implementation is more or less a direct translation of the author's Matlab code, though some changes have been made for speed and efficiency:
- The embedding function has been rewritten in C++, for a substantial speedup.
- The authors estimate Bm(r) by computing the full distance matrix for the embedded delay vectors, which can easily exhaust system RAM for even moderately sized datasets. Instead, I simply tally the number of vectors lying within the distance threshold r, sidestepping the distance matrix calculation entirely.
The package additionally implements the distribution entropy (DistEn) measure described by Karmakar, Udhayakumar, and Palaniswami (2015), which I call differential entropy or "DiffEn" because I made a typo and have no motivation to change it. Unlike SampEn, this requires the full distance matrix to be stored in memory at once. To avoid this, I randomly sample elements of the distance matrix 1000 at a time, and compute the average of the resulting entropy estimates.
The package can easily be installed with the
devtools package using
Entropy is then computed using the
MSMVSampEn() function. For example,
to compute the entropy of a 3-variate time series containing white noise,
we create a
data <- matrix(rnorm(3000), nrow = 3)
and then do
MSMVSampEn(mat = data, M, tau, r, eps, scaleMat = T)
M is the embedding dimension,
tau is the time lag parameter,
r is the
eps is the time scale, and
scaleMat = T specifies that the data are scaled.
MSMVSampEn is capable of computing sample entropy for univariate or multivariate signals at arbitrary time scales. Currently, it only implements the coarsegraining procedure described by Ahmed and Mandic, although, as Humeau-Heurtier (2015) points out, this method has serious shortcomings. In the future, I hope to implement more sophistic methods of extracting informations at larger timescales.
The package allows for the specification of an arbitrary summary statistic to be used during coarsegraining by passing a function argument to MSMVSampEn(). This function is applied to each bin during coarsegraining. When this function in the mean (default), this gives the usual sample entropy, though, as Humeau-Heurtier mentions, other statistics (such as higher moments), are occasionally interesting.
Ahmed, M. U., & Mandic, D. P. (2011). Multivariate multiscale entropy: A tool for complexity analysis of multichannel data. Physical Review E, 84(6), 061918.
Humeau-Heurtier, A. (2015). The multiscale entropy algorithm and its variants: A review. Entropy, 17(5), 3110-3123.