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Petrosian Fractal Dimension

Source: R/eeg-complexity.R
petrosianFD.Rd

Computes the Petrosian fractal dimension of a one-dimensional signal (Petrosian, 1995) – a fast waveform-complexity measure based on the number of sign changes in the signal's derivative (i.e. the density of local extrema). A smooth, oscillatory signal has few derivative sign changes and a Petrosian FD near 1; a complex or noise-like signal has many and a higher FD. \(P = \log_{10} N / (\log_{10} N + \log_{10}(N / (N + 0.4\,N_\delta)))\), where \(N\) is the signal length and \(N_\delta\) the number of sign changes in the first difference.

Usage

petrosianFD(x)

Arguments

x

A numeric vector (the time series).

Value

A single numeric value, the Petrosian fractal dimension (typically in \([1, \sim1.1]\) for physiological signals).

References

Petrosian, A. (1995). "Kolmogorov complexity of finite sequences and recognition of different preictal EEG patterns." In Proceedings of the Eighth IEEE Symposium on Computer-Based Medical Systems, 212–217. doi:10.1109/CBMS.1995.465426

See also

svdEntropy for the singular-value complexity view, eegComplexity for the multi-measure wrapper.

Examples

petrosianFD(sin(seq(0, 20 * pi, length.out = 500)))  # low (smooth oscillation)
#> [1] 1.002561
set.seed(1); petrosianFD(rnorm(500))                 # higher (noise-like)
#> [1] 1.039285