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Singular Value Decomposition (SVD) Entropy

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

Computes the SVD entropy of a one-dimensional signal (Roberts et al., 1999) – a measure of the signal's dimensionality / the number of eigenvectors needed to explain it. The signal is time-delay embedded into an order-dimensional matrix; the normalized singular values of that matrix are treated as a probability distribution, and their Shannon entropy is the SVD entropy. Low SVD entropy indicates a low-dimensional (structured, e.g. oscillatory) signal; high SVD entropy indicates a high-dimensional (complex or noise-like) signal.

Usage

svdEntropy(x, order = 3L, delay = 1L, normalize = FALSE)

Arguments

x

A numeric vector (the time series).

order

Embedding dimension (default 3); the number of singular values.

delay

Embedding delay / lag in samples (default 1).

normalize

If TRUE, divide by log2(order) to bound the result in \([0, 1]\); otherwise return the entropy in bits (default FALSE).

Value

A single numeric value, the SVD entropy (in bits, or normalized).

References

Roberts, S. J., Penny, W., & Rezek, I. (1999). "Temporal and spatial complexity measures for electroencephalogram based brain-computer interfacing." Medical & Biological Engineering & Computing, 37(1), 93–98. doi:10.1007/BF02513272

See also

eegComplexity for the multi-measure complexity wrapper (permutation entropy, Lempel-Ziv, Hjorth, DFA, ...).

Examples

set.seed(1)
svdEntropy(sin(seq(0, 20 * pi, length.out = 500)))  # low (structured)
#> [1] 0.44732
svdEntropy(rnorm(500))                               # high (noise-like)
#> [1] 1.584797