Pincus, S. () Approximate Entropy (ApEn) as a Complexity Measure. Chaos, 5, APPROXIMATE ENTROPY: A COMPLEXITY MEASURE FOR. BIOLOGICAL family of statistics, ApEn, that can classify complex systems, given at least I In statistics, an approximate entropy (ApEn) is a technique used to quantify the amount of Regularity was originally measured by exact regularity statistics, which has mainly “Approximate entropy as a measure of system complexity”.

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This description originally appeared in slightly modified form, and without the example, in Ho, Moody, Peng, et al. Intuitively, one may reason that the presence of repetitive patterns of fluctuation in a time series renders it more predictable than a time series in which such patterns are absent.

## Approximate Entropy (ApEn)

A time series containing many repetitive patterns has a relatively small ; a less predictable i. The algorithm for computing has been published elsewhere []. Here, we provide a brief summary of the calculations, as applied to a time series of heart rate measurements. Given a sequenceconsisting of instantaneous heart rate measurements, we must choose values for two input parameters, andto compute the approximate entropy,of the sequence.

The second of these parameters,specifies the pattern length, and the third,defines the criterion of similarity. Approximste denote a subsequence or pattern of heart rate measurements, beginning at measurement withinby the vector. Two patterns, andare similar if the difference between any pair of corresponding measurements in the patterns is less thani. Now consider the set of all patterns of length [i.

We may now define. The quantity is the fraction of patterns of length that resemble the pattern of the same length that begins at interval.

We can calculate for each pattern inand we define as the mean of these values. The quantity expresses the prevalence of repetitive patterns of length in. Finally, we define the approximate entropy offor patterns of length and similarity criterionas. Thus, if we find similar patterns in aa heart rate time series, estimates the logarithmic likelihood that the next intervals after each of the patterns will differ i.

Smaller values of imply a greater likelihood that similar patterns of measurements will be followed by additional similar measurements. If the time series is highly irregular, the occurrence of similar patterns will not be predictive for the following measurements, and will be relatively large. It should be noted that has significant weaknesses, notably its strong dependence on sequence length and its poor self-consistency i.

For an excellent review of the shortcomings of and the strengths of alternative statistics, see reference [5]. An apprlximate may help to clarify the process of calculating. Suppose thatand that the sequence consists of 50 samples of the function illustrated above: Let’s choose this choice simplifies the calculations for this example, but similar results would be obtained for other nearby values of and again, the value of can be varied somewhat without affecting the result.

The first question to be answered is: Since we have chosen as the similarity criterion, this means that each of the 5 components of must be within units of the corresponding component of. Thus, for example, is not similar tosince their last components 61 and 65 differ by more than 2 units.

The conditions for similarity to will be satisfied only appproximate,aapen, Since the total number of is. We can now repeat the above steps to determine how many of the are similar to, etc. By the same reasoning, is similar to,Hence is either ordepending onand the mean value of all 46 of the is: In order to obtainwe need to repeat all of the calculations above for.

Doing so, we obtain: Finally, we calculate that.

### Approximate entropy (ApEn) as a complexity measure. – Semantic Scholar

This is a very small value of ApEn, which suggests that the original time series is highly predictable as indeed it is. This description is provided here so that researchers who wish to use ApEn can write their own code for doing so. Approximate entropy as a measure of system complexity. What does regularity quantify? Gender and age-related differences in heart rate dynamics: Are women more complex than men?

J Am Coll Cardiol ; Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics.

Circulation August ; 96 3: Physiological time-series analysis using approximate entropy and sample entropy. If you would like help understanding, using, or approdimate content, please see our Frequently Asked Questions.

## Approximate entropy (ApEn) as a complexity measure.

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