R: Symbol analysis of a numeric (time) series

symba {seewave}

R Documentation

Symbol analysis of a numeric (time) series

Description

This function analyses one or two sequences of symbols from numeric (time) series.

Usage

symba(x, y = NULL, symb = 5, collapse = TRUE, entropy = "abs",
plot = FALSE, type = "l", lty1 = 1, lty2 = 2, col1 = 2, col2 = 4,
cex1 = 0.75, cex2= 0.75, xlab = "index", ylab = "Amplitude", legend=TRUE, ...)

Arguments

`x`	a first R object.
`y`	a second R object
`symb`	the number of symbols used for the discretisation, can be set to 3 or 5 only.
`collapse`	logical, if `TRUE`, the symbols are pasted in a character string of length 1.
`entropy`	either "abs" for an absolute value or "rel" for a relative value, i. e. between 0 and 1.
`plot`	logical, if `TRUE` plots the series `x` (and `y`) and the respective symbols.
`type`	if `plot` is `TRUE`, type of plot that should be drawn. See `plot` for details (by default "l" for lines).
`lty1`	line type of the object `x` if `type`="l".
`lty2`	line type of the object `y` if `type`="l".
`col1`	colour of the object `x`.
`col2`	colour of the object `y`.
`cex1`	character size of `x` symbols.
`cex2`	character size of `y` symbols.
`xlab`	title of the x axis.
`ylab`	title of the y axis.
`legend`	logical, if `TRUE` and if `y` is not `NULL` adds a legend to the plot.
`...`	other `plot` graphical parameters.

Details

The analysis consists in transforming the series into a sequence of symbols (see the function discrets) and in computing the absolute frequency of each symbol within the sequence.
The entropy (H) is then calculated using the symbol frequencies. Using the argument entropy, the entropy can be expressed along an absolute scale or as a relative value varying between 0 and 1.
If two numeric (time) series are provided (x and y) the absolute symbol frequencies and entropy of each series is returned. Besides the mutual information (I) is estimated according to:

I = Hx + Hy - Hxy

with Hx the entropy of x symbol series, Hy the entropy of y symbol series, and Hxy$ the joint entropy of x and y symbol series.

Value

If y is NULL a list of three items is returned (s1, freq1, h1).
If y is not NULL, a list of 6 items is returned (s1, freq1, h1, s2, freq2, h2, I):

`s1`	the sequence of symbols of `x`,
`freq1`	the relative frequency of each `x` symbol,
`h1`	the entropy of `x` symbol sequence,
`s2`	the sequence of symbols of `y`,
`freq2`	the relative frequency of each `y` symbol,
`h2`	the entropy of `y` symbol sequence,
`I`	the mutual information between `x` and `y`.

Note

It might be useful to round the values of the input series (see examples).
The mutual information (I) should increase with the similarity between the series to compare (x and y).

Author(s)

Jerome Sueur sueur@mnhn.fr

References

Cazelles, B. 2004 Symbolic dynamics for identifying similarity between rhythms of ecological time series. Ecology Letters, 7: 755-763.

Examples

# analysis of a frequency spectrum
data(tico)
spec1<-spec(tico,f=22050,at=0.2,plot=FALSE)
symba(spec1[,2],plot=TRUE)
# it might be better to round the values
symba(round(spec1[,2],2),plot=TRUE)
# in that case the symbol entropy is close to the spectral entropy
symba(round(spec1[,2],2),entrop="rel")$h1
sh(spec1)
# to compare two frequency spectra
spec2<-spec(tico,f=22050,wl=512,at=1.1,plot=FALSE)
symba(round(spec1[,2],2),round(spec2[,2],2),plot=TRUE)

[Package seewave version 2.1.6 Index]