symba: Symbol analysis of a numeric (time) series

In seewave: Sound Analysis and Synthesis

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 = H_{x} + H_{y} - H{xy}

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 [e-mail]

References

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

See Also

discrets, SAX

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)

seewave documentation built on Oct. 19, 2023, 5:07 p.m.