Sample Entropy
Sample Entropy (Time-Series Complexity) · Also known as: SampEn, Sample Entropy (SampEn), Örneklem Entropisi, Nonlinear Complexity Measure
Sample Entropy (SampEn) is a nonlinear measure of the complexity and regularity of a time series. Introduced by Richman and Moorman in 2000 as an improvement over Approximate Entropy (ApEn), it quantifies the likelihood that similar patterns of a given length in the series remain similar when extended by one additional data point. A higher SampEn value indicates greater irregularity and complexity, while a lower value indicates more regularity or self-similarity.
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When to use it
Sample Entropy is appropriate when analyzing physiological, financial, or engineering time series where complexity and regularity are meaningful quantities. It requires a sufficiently long series (typically N > 200 to 1000 points) and continuous-valued data. Key parameters m (embedding dimension, typically 1 or 2) and r (tolerance, typically 0.1–0.25 times the standard deviation) must be set carefully as results are sensitive to these choices. It is not suitable for very short series or categorical data. Alternatives include Approximate Entropy, Permutation Entropy, or Multiscale Entropy for scale-dependent analyses.
Strengths & limitations
- Avoids self-matches in template comparison, eliminating the bias present in Approximate Entropy (ApEn)
- Produces consistent results independent of time-series length over a wider range than ApEn
- Provides a single interpretable scalar reflecting overall signal complexity or regularity
- Well-validated across physiological, financial, and engineering domains with an extensive literature base
- Requires choosing embedding dimension m and tolerance r, which substantially affect results and lack universal defaults
- Performance degrades for very short time series (typically N < 200), yielding unreliable or undefined estimates
- Computationally intensive for long series due to O(N²) pairwise template comparisons
- Provides a single aggregate complexity value and does not reveal the time-varying or scale-specific structure of the signal
Frequently asked
How do I choose m and r for Sample Entropy?
The most widely used defaults are m = 2 and r = 0.2 times the standard deviation of the series, as recommended in the original Richman and Moorman paper and subsequent validation studies. However, optimal values are domain-specific. It is good practice to report sensitivity analyses showing how SampEn varies across a plausible range of m and r values for your dataset.
What is the difference between Sample Entropy and Approximate Entropy?
ApEn counts self-matches — a template is compared with itself — which introduces a positive bias and makes results dependent on series length. SampEn explicitly excludes self-matches, yielding unbiased estimates that are more consistent across different series lengths. SampEn is generally preferred when statistical rigor is required, though ApEn remains common in earlier literature.
Can Sample Entropy be applied to short time series?
SampEn becomes unreliable for very short series because the probability estimates rely on finding a sufficient number of template matches. For series with fewer than approximately 200 data points, many researchers prefer Permutation Entropy or other measures designed for short signals. When N is small, SampEn can return undefined values if no matches are found at length m+1.
Sources
- Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. American Journal of Physiology, 278(6), H2039–H2049. DOI: 10.1152/ajpheart.2000.278.6.H2039 ↗
How to cite this page
ScholarGate. (2026, June 2). Sample Entropy (Time-Series Complexity). ScholarGate. https://scholargate.app/en/complex-systems/sample-entropy
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