entropy: Approximate and Sample Entropy

approx_entropyR Documentation

Approximate and Sample Entropy


Calculates the approximate or sample entropy of a time series.


approx_entropy(ts, edim = 2, r = 0.2*sd(ts), elag = 1)

sample_entropy(ts, edim = 2, r = 0.2*sd(ts), tau = 1)



a time series.


the embedding dimension, as for chaotic time series; a preferred value is 2.


filter factor; work on heart rate variability has suggested setting r to be 0.2 times the standard deviation of the data.


embedding lag; defaults to 1, more appropriately it should be set to the smallest lag at which the autocorrelation function of the time series is close to zero. (At the moment it cannot be changed by the user.)


delay time for subsampling, similar to elag.


Approximate entropy was introduced to quantify the the amount of regularity and the unpredictability of fluctuations in a time series. A low value of the entropy indicates that the time series is deterministic; a high value indicates randomness.

Sample entropy is conceptually similar with the following differences: It does not count self-matching, and it does not depend that much on the length of the time series.


The approximate, or sample, entropy, a scalar value.


This code here derives from Matlab versions at Mathwork's File Exchange, “Fast Approximate Entropy” and “Sample Entropy” by Kijoon Lee under BSD license.


Pincus, S.M. (1991). Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA, Vol. 88, pp. 2297–2301.

Kaplan, D., M. I. Furman, S. M. Pincus, S. M. Ryan, L. A. Lipsitz, and A. L. Goldberger (1991). Aging and the complexity of cardiovascular dynamics, Biophysics Journal, Vol. 59, pp. 945–949.

Yentes, J.M., N. Hunt, K.K. Schmid, J.P. Kaipust, D. McGrath, N. Stergiou (2012). The Appropriate use of approximate entropy and sample entropy with short data sets. Ann. Biomed. Eng.

See Also



ts <- rep(61:65, 10)
approx_entropy(ts, edim = 2)                      # -0.0004610253
sample_entropy(ts, edim = 2)                      #  0

approx_entropy(rnorm(500), edim = 2)              # 1.351439  high, random
approx_entropy(sin(seq(1,100,by=0.2)), edim = 2)  # 0.171806  low,  deterministic
sample_entropy(sin(seq(1,100,by=0.2)), edim = 2)  # 0.2359326

## Not run: (Careful: This will take several minutes.)
# generate simulated data
N <- 1000; t <- 0.001*(1:N)
sint   <- sin(2*pi*10*t);    sd1 <- sd(sint)    # sine curve
whitet <- rnorm(N);          sd2 <- sd(whitet)  # white noise
chirpt <- sint + 0.1*whitet; sd3 <- sd(chirpt)  # chirp signal

# calculate approximate entropy
rnum <- 30; result <- zeros(3, rnum)
for (i in 1:rnum) {
    r <- 0.02 * i
    result[1, i] <- approx_entropy(sint,   2, r*sd1)
    result[2, i] <- approx_entropy(chirpt, 2, r*sd2)
    result[3, i] <- approx_entropy(whitet, 2, r*sd3)

# plot curves
r <- 0.02 * (1:rnum)
plot(c(0, 0.6), c(0, 2), type="n",
     xlab = "", ylab = "", main = "Approximate Entropy")
points(r, result[1, ], col="red");    lines(r, result[1, ], col="red")
points(r, result[2, ], col="green");  lines(r, result[2, ], col="green")
points(r, result[3, ], col="blue");   lines(r, result[3, ], col="blue")
## End(Not run)

pracma documentation built on Sept. 22, 2022, 5:05 p.m.