pracma (version 1.7.0)

approx_entropy: Approximate and Sample Entropy

Description

Calculates the approximate or sample entropy of a time series.

Usage

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

Arguments

ts

a time series.

edim

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

r

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

elag

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.)

tau

delay time for subsampling, similar to elag.

Value

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

Details

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.

References

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

RHRV::CalculateApEn

Examples

ts <- rep(61:65, 10)
approx_entropy(ts, edim = 2)                      # -0.000936195
sample_entropy(ts, edim = 2)                      #  0

set.seed(8237)
approx_entropy(rnorm(500), edim = 2)              # 1.48944  high, random
approx_entropy(sin(seq(1,100,by=0.2)), edim = 2)  # 0.22831  low,  deterministic
sample_entropy(sin(seq(1,100,by=0.2)), edim = 2)  # 0.2359326

(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
chirpt <- sint + 0.1*whitet; sd2 <- sd(chirpt)  # chirp signal
whitet <- rnorm(N);          sd3 <- sd(whitet)  # white noise

# 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")
grid()