R: Approximate and Sample Entropy

approx_entropy {pracma} | R Documentation

## 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`.

### 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.

### Value

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

### Note

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

### 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)                      # -0.0004610253
    sample_entropy(ts, edim = 2)                      #  0

    set.seed(8237)
    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")
    grid()
    ## End(Not run)

[Package pracma version 2.0.4 Index]